Etymologie, Etimología, Étymologie, Etimologia, Etymology
US Vereinigte Staaten von Amerika, Estados Unidos de América, États-Unis d'Amérique, Stati Uniti d'America, United States of America
Mathematik, Matemáticas, Mathématiques, Matematica, Mathematics
Angewandte Mathematik, Matemáticas aplicadas, Mathématiques appliquées, Matematica applicata, Applied mathematics
Geschichte der Mathematik, Historia de la matemática, Histoire des mathématiques, Storia della matematica, History of mathematics
Philosophie der Mathematik, Filosofía de la matemática, Philosophie des mathématiques, Filosofia della matematica, Philosophy of mathematics
Browse Topic: Math Help and Tutorials | Math Formulas | Math Lesson Plans | Arithmetic | Glossary of Terms | Math Stumpers | Calculators | Math Worksheets | Mathematicians | Books, Resources, DVDs | Recreational Math
The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
Jump to one of the galleries
2011 Mathematical Art Exhibition
Edmund Harriss:: Shapes and Tilings
2010 Mathematical Art Exhibition
Simulated Snowflakes
Crocheted Lorenz Manifolds
2009 Mathematical Art Exhibition
Jean-Francois Colonna :: A Gateway Between Art and Science
Gwen L. Fisher :: Woven Beads
Dejenie A. Lakew :: Hyper Symmetries
Nathan Selikoff :: Algorithmic Artwork
Chaim Goodman-Strauss :: Symmetries
Robert J. Lang :: Origami
Carlo Séquin :: Mathematical Images
Anne M. Burns :: Gallery of "Mathscapes"
George Hart :: Geometric Sculptures
Fractal Art :: Beauty and Mathematics
Seifert Surfaces
Robert Straight :: Toroids and Plaids
Quilts
Mike Field :: Realizations
Bradford Hansen-Smith :: Wholemovement
Knots
3D-XplorMath
Thomas Hull :: The mathematics of origami
Notices of the American Mathematical Society :: Cover Art
Neben der grossen Übersicht an bereits benannten Zahlenfolgen (siehe "Index"), ist die Suchfunktion sehr schön. Man gibt eine Zahlenfolge ein und erhält die definierte Zahlenfolge (sofern es sie gibt) mit vielen Informationen zurück. Diese Seite gefällt meinem Mathematikergehirn.
In der Datenbank befanden sich 2004 ca. 90.000 Zahlenfolgen.
My Favorite Integer Sequences - N. J. A. Sloane:
Hard sequences
Projective planes
The Poincaré conjecture
Dedekind's problem
The Hadamard maximal determinant problem
Enumerating Hadamard matrices
The kissing number problem
Sorting by prefix reversal
Recursive sequences
Differences = complement
Golomb's sequence
Wilson's primeth recurrence
Recamán's sequences
The $10,000 sequence
The Prague clock sequence
Cayley's mistake
Meanders and stamp-folding
Extremal codes and lattices
Levine's sequence
Arrays of Numbers
Gilbreath's conjecture
The Wythoff array
The Boustrophedon transform
Tchoukaillon solitaire (or Mancala, or Kalahari)
The alphabetical sections of the Index are created "on the fly" from the following plain text file.
This file is useful if you want to search the whole Index, or suggest additions or changes.
jeep problem | abelian numbers | absolute primes | abundant numbers | Ackermann function | addition chains | additive bases | Aho-Sloane paper | Airey's converging factor | Aitken's array | Alcuin's sequence | Alekseyev's problem | algebras, Jordan | aliquot trajectories for certain initial values | almost primes | almost-natural numbers | alphabetical order, numbers in | alternating bit sets | alternating bit sum | alternating permutations | alternating sign matrices | amicable numbers | Andrews-Mills-Robbins-Rumsey numbers | Apery numbers | Apery's number zeta(3) | Apocalyptic powers | Apollonian ball packings | Apollonian circle packings | ApSimon mints problem | arborescences | arc-cotangent reducible numbers | arccos(x) | arccosec(x) | arccosech(x) | arccosh(x) | arcos and arccos are both used in the OEIS! | arcosh and arccosh are both used in the OEIS! | arcsec(x) | arcsech(x) | arcsin(x) | arcsinh(x) | arctangent numbers, triangle of | ARIBAS | arithmetic means | arithmetic numbers | arithmetic progressions | Armstrong numbers | Aronson's sequence | Artin's conjecture | Artin's constants
B-trees | Baby Monster simple group | backgammon | Baker-Campbell-Hausdorff expansion | balanced numbers | Balancing weights | ballot numbers | balls into boxes | balls on the lawn | Barker sequences (or Barker codes) | Barnes-Wall lattices | barriers for omega(n) | baseball | Batcher parallel sort | Baxter permutations | Beans-Don't-Talk | Beanstalk | Beatty sequences | Beethoven | beginning with t | Bell numbers | Bell's formula | Benford numbers | Benny, Jack | Berlekamp's switching game | Bernoulli numbers | Bernoulli polynomials | Bernoulli twin numbers | Bernstein squares | Berstel sequence | Bertrand's Postulate | Bessel function | Bessel numbers | Bessel polynomial | Bessel triangle | Board of Directors Problem | Bode's law | Bohr radius | Bokmal | Bond percolation | Boolean functions | Boolean lattices | Braille | Bravais lattices | Brazilian Portuguese | Brun's constant | Buffon's needle | Burnside's problem in group theory | Busy Beaver problem
C(n,2) | C(n,3) | C(n,4) | C(n,k) | cab-taxi numbers | Cahen's constant | Cald's sequence | Cantor set | Cantor's sigma function | Carmichael numbers | Carmichael's lambda function | Catalan constant | Catalan numbers | Catalan triangle | Catalan's conjecture | Catalan | Cauchy numbers | Cayley's mistake | Cebychev is spelled | Chacon sequences | Chains | Champernowne constant | Champernowne sequence | Chebycheff is spelled | Chebychev is spelled | Chebyshev function theta(n) | Chebyshev polynomials | Chernoff sequence | Chinese | Chowla sequence | Chowla's function | Chvatal conjecture | Class numbers | Clifford group, | Cluster series | Clusters | coconut problem |
| Coefficients | Collatz problem | Colombian numbers | coloring a cube | coloring a map | coloring a triangle | colorings | Congruence property | Congruences | congruent numbers | Connell sequence | Consecutive | Consistent | Convolutions | Conway group Con.0 | Conway sequences | Conway-Guy sequence | Coprime sequences | cos(nx) | cos(x) | cosec(x), Taylor series for | cosecant numbers | cosh x / cos x, Taylor series for | cosh(x) | Costas arrays | cot(x), Taylor series for | cotangent numbers | Cotes numbers | Cotesian numbers | cototient(n) | Coxeter-Todd 12-dimensional lattice | Critical exponents | Croatian | Crystal classes | crystallographic groups | cube numbers, centered | Cube roots | Cubes | Cubic curves | Cubic fields | cuboctahedral numbers | Cullen numbers | Cullen primes | Cycles | cyclic group | cyclic numbers | Cyclic | Czech
J-function | J2 simple group | Jack Benny | Jacobi elliptic function sn | Jacobi nome | Jacobi symbol | Jacobi theta series | Jacobi triple product identity | Jacobsthal sequence | Jacobsthal-Lucas numbers | Japanese | join points around circle | joke numbers | Jordan algebras | Josephus problem | Josephus's sieve | Joyce, James, "Ulysses" |
| jumping champions | jumping problem | junction numbers | Justified arrays
L-series | L.C.M. | labeled partitions | lacing a shoe | Laguerre polynomials, | Lah numbers | LambertW function | laminated lattices, numbers of | Landau approximation | Landau's function g(n) | Langford-Skolem problem of arranging 11223344...nn | language, words in a certain | largest factors of various numbers | largest prime dividing n | last digits | last occurrence | Latin (the language) | Latin cubes | Latin rectangles | Latin squares | Latin | Lazy Caterer sequence | LCM(x,y) | least common multiple | Least number of powers to represent n | least significant bit (lsb) | Leech lattice | Leech triangle | Leech's path-labeling problem | left factorials | Legendre polynomials | Legendre's conjecture | LEGO blocks | Lehmer's constant | Lehmer's polynomial | Leibniz's triangle | lemniscate function | Lemoine's conjecture | Leonardo logarithms | Les Marvin sequence | Levenshtein distance | Levine's sequence | Levy's conjecture | Li(n) | Lie algebras | light, speed of | light-bulb game of Berlekamp | light-bulbs | linear codes | linear extensions | linear forms | linear inequalities | linear orders | Linear spaces | Linus sequence | Liouville's constant | Liouville's function L(n) | Liouville's function lambda(n) | Liouville's number | list manipulation functions of Lisp | ln | locks | Loeschian numbers | log 10, decimal expansion of | log 2, decimal expansion of | log 3, decimal expansion of | log 5, decimal expansion of | log 7, decimal expansion of | log(3/2) | log(cos(x)) | log(n)*2^n/n | log(n) | log(sin(x)/x) | logarithmic integral | logarithmic numbers | log_10 e, decimal expansion of | log_2 3 | log_2(n) | long but finite sequences | longest common subsequences, most | longest common substrings, most | look and say sequences | loops, Moufang | Losanitsch's triangle | loxodromic sequence of spheres | Loxton-van der Poorten sequence | Loyd's 15-Puzzle | LS ("Look and Say") | lsb = least significant bit | Lucas numbers | Lucas polynomials | Lucas pseudoprimes | Lucas, Theorie des Nombres | Lucas-Carmichael numbers | Lucasian primes | lucky numbers | Lukasiewicz words | Lyndon words | L_infinity norms in lattices
M-sequences | M-trees | magic numbers | magic series | magic squares | magnetization coefficients | Mahler's number | Mahonian numbers | Mancala solitaire (generalized) | Mandelbrot set | Mangoldt function | Manhattan lattice | Manhattan subways | map, 3x+1 | map, coloring | maps, folding | Maps, Hamiltonian | Maris-McGwire numbers | Markoff numbers | Markov numbers | Matchings | mathematical symbols in OEIS | matrices, (+1,-1) | matrices, (0,1) | matrices, alternating sign | matrices, anti-Hadamard | matrices, binary, n X n | matrices, Hadamard | Matrices, Hilbert | Matrices, Pascal | Matrices, Schur | Matrices, stochastic | matrices, ternary, n X n | matroids , | Maundy cake | Max Alekseyev's problem | max(x,y) | McKay-Thompson sequences for Monster simple group | McKay-Thompson series for Monster simple group (start) | meanders | Meeussen sequences | menage numbers | mens-room permutations | merge sort | Mertens's conjecture | Mertens's function | Mian-Chowla sequences | Miller-Rabin primality test | Mills primes | Mills's constant | min(x,y) | Minkowski's question mark function | mobiles | Mobius | Mock theta numbers | mod(x,y) | models (in statistics) | modest numbers | Moebius (or Mobius) function mu(n) | Moebius function | Moebius transforms | Molecular species | Molien series | money | monoids | Monster simple group, McKay-Thompson series for | months | Montreal solitaire | Moon (1987), "Some enumerative results on series-parallel networks" | Moran numbers | mosaic numbers | Moser-de Bruijn sequence | most significant bit (msb) | motifs | Motzkin numbers | Motzkin triangle | mousetrap game | Mozart | Mrs Perkins's quilt | msb = most significant bit | Mu Torere | mu(n) | MU-numbers | mult | multigraphs | Multinomial coefficients | Multiplication-cost | Multiplicative encodings | multiplicative order of 2 mod n, ord(2,n) | multiplicative order of x mod y, ord(x,y), sequences related to | multiplicatively perfect numbers | multiply-perfect numbers | musical scales | mutinous numbers
n -> 3n - sigma(n) | n appears n times | n divides concatenation of all numbers up through n | n reversed, R(n) | n!+1 | n!-1 | n!/2 | n! | n# (1st definition of primorial numbers) | N-free graphs | n-phi-torial | Narayana triangle (also called Catalan triangle) | Narayana-Zidek-Capell numbers | narcissistic numbers | natural numbers, in base 2 | natural numbers, in bases 1 through 10 | natural numbers, rearrangement of (conjectured or otherwise)(1) | near-rings | necklaces | necklaces, aperiodic | necklaces, asymmetric | necklaces | negative numbers | Negative pseudo-squares | neofields | Nets | Networks | next prime after terms of various sequences | nexus numbers | Niemeier lattices | nilpotent numbers | Nim-addition | Nim-multiplication | Nim-multiplication in Maple | Nim-products | Nim-sums | Nim-sums in Maple | Nim | Niven numbers | Niven's constant | no-three-in-line problem | Noergaard, Per | nome | non-collinear points in cube | Non-Hamiltonian | non-mathematical sequences
| Non-separable | noncubes | nonpositive integers | nonprimes | nonrepetitive sequences | nonsquares | nontotients | Norgard, Per | Norwegian | not always integral | notation in OEIS | noughts and crosses | NSW numbers | number of positive integers | number of syllables to represent n | number of ways the set (1^k, 2^k, ..., n^k) can be partitioned into two sets of equal sums | number of words to represent n | number theory, unsolved problems in | numbers n such that 2^k + n is prime for all k | numbers n such that n*2^k + 1 is composite for all k | numbers n such that n*2^k + 1 is prime for all k | numbers of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i >= 1 | numbers, automorphic | numbers, Bernoulli | numbers, Euler | numbers, feral | numbers, octal | numbers, tri-perfect | numbers, triperfect | numbers, triply perfect | numbers, wild | numeri idonei | numerus idoneus | n^(n+1) | n^(n-1) | n^(n-2) | n^(n-3) | n^2-n+41 is prime | n^n
O'Nan group | octagonal numbers | octahedral numbers | octahedron, truncated | octal numbers | octupi | odd numbers, fake | odious numbers | omega(n), number of distinct primes dividing n | Omega(n), total number of primes dividing n | one local maximum, arrays with | one odd, two even, etc. | one puddle | ones-counting sequence | operational recurrences | optimal rulers | OR(x,y) | orchard problem | ord(x,y) | order, binary | order, multiplicative order of 2 mod n | ordered factorizations | ordered partitions | orders | ordinals | Ore numbers | orthogonal arrays, number of | orthogonal groups | out-points
p-adic square roots in PARI | p-adic valuations | packing squares | Packings | Padovan sequence | Pair-coverings |
| panarithmic numbers | pancake numbers | paper-folding sequences | paradoxical sequences | parentheses, ways to arrange | parenthesized in 2 ways | PARI code | parity sequence | partially ordered sets | partition function for lattices | partition numbers, prime | partitions, binary | partitions, graphical | partitions, into even number of parts | partitions, into odd number of parts | partitions, into odd parts | partitions, into parts 5k+-1 | partitions, into parts 5k+-2 | partitions, into primes | partitions, into relatively prime parts | partitions, into triangular numbers | partitions, m-ary | partitions, odd | partitions, of a polygon | partitions, of n into 4 squares | partitions, of n into 4th powers | partitions, perfect | Partitions, planar | partitions, protruded | partitions, square | partitions, total number of parts | partitions, total | partitions, wide | Pascal triangle | Pascal's rhombus | Pascal's square | Paths in plane | paths in square grid | Paths through arrays | patience | Patterns | pay-phones | Peaks | Peanuts cartoon sequences | pedal triangles | peeling rinds | Pell numbers | Pell's equation | Pellian equation x^2 - D*y^2 = 1 | Pellian equation | Pennies | pentagonal numbers | pentagonal pyramidal numbers | Pentagonal Theorem |
| percolation series (1) | perfect lattices | perfect numbers | perfect partitions | perfect powers | perfect rulers | perfect years | period of reciprocal of n | period of reciprocal of nth prime | Periodic differences | Periodic sequences | periodic table | Periods | Permanents | Permutation arrays | permutation groups | Permutations, alternating | permutations, asymmetric | Permutations, Baxter | permutations, bitriangular | Permutations, by cycles | Permutations, by descents | Permutations, by distance | Permutations, by inversions | Permutations, by length of runs | Permutations, by number of peaks | Permutations, by number of runs | Permutations, by number of sequences | Permutations, by order | Permutations, by rises | Permutations, by spread | Permutations, by subsequences | permutations, connected | Permutations, cycles in | Permutations, descending subsequences of | Permutations, discordant | permutations, even | permutations, graceful | permutations, indecomposable | Permutations, inequivalent | Permutations, inversions in | Permutations, isolated reformed | Permutations, key | Permutations, necklace | Permutations, odd | permutations, of n letters | permutations, of order 2 | permutations, of order dividing k, for k=2,3,4,5,... (1) | permutations, of the positive (or nonnegative) integers | permutations, of the integers, induced by Catalan rerankings, each paired with its inverse | permutations, of the integers, signature-permutations induced by Catalan automorphisms, | Perrin sequence | persistence (additive) | persistence (multiplicative) | Phi(n) | phi(n) | pi(10^n) | pi(x), number of primes | Pi, continued cotangent for | Pi, continued fraction for | Pi, convergents to | Pi, decimal expansion of | Pi, strings of digits in | piano keyboard | picture-perfect numbers | pieces | Pierce expansions | Pierpont primes | Pisano numbers | Pisano periods | Pisot sequences, definition | Pisot sequences, warning about recurrences for | Pisot sequences | planar graphs | planar vs plane | Planck's constant | plus perfect numbers | Poincare conjecture | Poincare series | pointed objects | Points on surface of various polyhedra | poker | Polish | Polya's conjecture | polyaboloes | polyares | polycubes | polygamma function | polygonal numbers | polygons (1) | polygons constructible with ruler and compass | polygons inscribed in a circle | polygons with all diagonals drawn | polyhedra (1) | polyhedra, allomorphic | polyhedra, regular | polyhedra | polyhes | polyhexes | polyiamonds | polyknights | polynomial identities | Polynomials, Bell | polynomials, Bernoulli | Polynomials, Bessel | Polynomials, by height | Polynomials, characteristic | Polynomials, Chebyshev | Polynomials, cyclotomic | polynomials, cyclotomic, inverse, Phi(1..9) | polynomials, cyclotomic | Polynomials, discriminants of | polynomials, divisors of x^n-1 | polynomials, Euler | Polynomials, Gandhi | Polynomials, Hammersley | polynomials, Hermite | Polynomials, hit | polynomials, irreducible over a finite field | polynomials, irreducible over GF(q), q >= 4 | polynomials, irreducible, binary, degree divides n | polynomials, irreducible, binary, degree n | polynomials, irreducible, over GF(3), degree divides n | polynomials, irreducible, over GF(3), degree n | polynomials, irreducible, over GF(4), degree divides n | polynomials, irreducible, over GF(4), degree n | polynomials, irreducible, over GF(5) | polynomials, irreducible, over GF(7) | polynomials, irreducible | polynomials, Laguerre | polynomials, Legendre | polynomials, monic irreducible over finite fields | Polynomials, m\'{e}nage | Polynomials, orthogonal | Polynomials, period | polynomials, primitive | Polynomials, relatively prime | Polynomials, rook | polynomials, Shapiro | polyominoes | polyominoes, 3-dimensional | polyominoes, hexagonal | polyominoes, indecomposable | polyominoes, rotationally symmetric | polyominoes, triangular | polytans | polytopes, regular | polytopes | Poonen-Rubinstein paper | Popes | porisms | Portuguese | posets | posets | posets, chains in | posets, connected | posets, forbidden | posets, graded | posets, increasing | posets, irreducible | posets, N-free | posets, reduced | posets, series-parallel | positive integers | Post functions | postage stamp problem | Potts model | power set, chains in | power train | power-sum numbers | powerful numbers | powers (1) | powers of 10 | powers of 11 | powers of 12 | powers of 13 | powers of 14 | powers of 15 | powers of 16 | powers of 17 | powers of 18 | powers of 19 | powers of 20 | powers of 21 | powers of 22 | powers of 23 | powers of 24 | powers of 25 | powers of 26 | powers of 27 | powers of 28 | powers of 29 | powers of 2 | powers of 30 | powers of 31 | powers of 32 | powers of 33 | powers of 34 | powers of 35 | powers of 36 | powers of 37 | powers of 38 | powers of 39 | powers of 3 | powers of 40 | powers of 41 | powers of 42 | powers of 43 | powers of 44 | powers of 45 | powers of 46 | powers of 47 | powers of 48 | powers of 4 | powers of 5 | powers of 6 | powers of 7 | powers of 8 | powers of 9 | powers of a prime but not prime | powers of e rounded up | powers of Pi rounded upwards | powers that be | powers, not the difference of two | powers, perfect | powers, the difference of two | powertrain function | practical numbers | Prague clock sequence | preferential arrangements | preorders | previous prime and next prime etc. for terms of various sequences | previous prime, next prime etc. NP...PP...NPMPP...nMPP...NPMn...MIN | prime factorizations of important sequences | prime factors of n, number of A001222
| prime plus twice a square | prime powers | prime pyramid | Prime quadruplets | Prime races | prime signature | prime triplets | prime(2^n) | prime(n) == +/-k (mod n) | prime, largest dividing n | prime, smallest whose product of digits is (something) | PRIMEGAME | Prime Pi(x), number of primes | primes | primes involving quasi-repdigits D(R)nE | primes involving repunits | primes of the form binomial(k*n, n) ? 1, k=2..6 | primes p such that x^k = 2 has a solution mod p, | primes such that the sum of the predecessor and successor primes is divisible by k | primes with X as smallest positive primitive root | primes, absolute | primes, additive | primes, almost | primes, approximations to | primes, automorphic | primes, balanced | primes, Bertrand | Primes, by class number | primes, by Erdos-Selfridge class n+ | primes, by Erdos-Selfridge class n- | Primes, by number of digits | primes, by order | Primes, by period length | primes, by primitive root | Primes, chains of | primes, characteristic function of | Primes, compressed | Primes, consecutive | primes, cuban | primes, Cullen | primes, deceptive | Primes, decompositions into | primes, differences between | primes, dihedral calculator
| primes, dividing n | primes, doubled | primes, duodecimal | primes, Euclid-Pocklington | primes, Euclidean | primes, even | primes, Fermat | primes, final digits of | primes, fortunate | primes, from Euclid's proof | primes, gaps between | primes, Germain | primes, good | primes, half-quartan | primes, happy | primes, Higgs | primes, home | primes, Honaker | primes, iccanobiF | primes, in arithmetic progressions | primes, in decimal expansion of Pi | Primes, in intervals | Primes, in number fields | Primes, in residue classes | Primes, in sequences | Primes, in ternary | primes, in various ranges | Primes, inert | primes, irregular | primes, isolated | Primes, largest | primes, left-truncatable | primes, lonely | primes, long period | primes, Lucas numbers | primes, Lucasian | primes, Mersenne | primes, Mills's | primes, minus a constant | primes, multiplicative and additive | primes, multiplicative | primes, next | primes, number of less than n*10^k | primes, octavan | primes, of a particular form, number that are less than or equal to 10^n | primes, of form n! +- 1 | primes, of form x^2 + kxy + y^2 | primes, of form x^2+27y^2 | primes, of form x^2+y^2 | primes, order of
| primes, Pierpont | Primes, primitive roots of | primes, products of | primes, pseudo | primes, quadratic form, discriminant | Primes, quadratic partitions of | Primes, quadratic residues of | primes, quartan | primes, quintan | primes, reciprocals of, periods | primes, regular | Primes, represented by quadratic forms | primes, repunit | primes, right-truncatable | primes, safe | primes, sextan | primes, short period | Primes, single | primes, Sophie Germain | Primes, special sequences of | Primes, square roots of | primes, Stern | primes, strobogrammatic | primes, strong | primes, subsets in range 2^n,2^(n+1), | primes, sum of the first k^n primes, k=2,3,5,6,7,10 | Primes, sums of digits of | Primes, supersingular | primes, that divide sum of all primes | Primes, to odd powers only | primes, transformed by cellular automata | Primes, transforms of | primes, truncatable | primes, truncated | primes, twin primes conjecture | primes, twin | primes, undulating | primes, various subsets in range 2^n,2^(n+1) | primes, weak | primes, which are average of their neighbors | Primes, whose reversal is a square | primes, Wilson | Primes, with consecutive digits | primes, with first digit 1 (or 2, 3, etc.) | Primes, with large least nonresidues | Primes, with prime subscripts | primes, Woodall | primeth recurrence | primitive (1) | Primitive factors | primitive polynomials | primitive roots | primorial numbers | primorial primes | primorials | principal character | prism numbers | probability difference equation | probability orderings | problimes | product_{k >= 1} (1-x^k)^m (1) | profiles | projective planes of order n | projective planes, maps on | projective planes, permanent of | projective planes | promic numbers | pronic numbers | Proth numbers | proton mass | proton-to-electron mass ratio | Prufer codes for trees | pseudo Q-numbers | pseudo-bricks | pseudo-Galois numbers | pseudo-lines | pseudo-powers to base 3 | pseudo-random numbers | pseudo-random numbers | pseudo-Smarandache numbers | pseudo-squares | pseudo-wild numbers | pseudoperfect numbers | pseudoprimes | pseudoprimes, Carmichael numbers | pseudoprimes, Euler-Jacobi | pseudoprimes, Lucas | pseudoprimes, Miller-Rabin primality test | psi function | puzzle sequences (01) | pyramidal numbers (1) | Pythagoras' theorem | Pythagorean triples |
q-factorials | Q-graphs | quadrangulations | quadratic character, sequences with prescribed | quadratic fields, | quadratic fields, Euclidean | quadratic fields, genera of | quadratic fields, imaginary, by class numbers | quadratic fields, real, by class numbers | quadratic fields, real, discriminants | quadratic fields, simple | quadratic fields, totally real of degree n | quadratic fields, unique factorization domains | quadratic forms, binary | quadratic forms, extreme | quadratic forms, genera of | quadratic forms, minimal norm of | quadratic forms, one class per genus | quadratic forms, perfect | quadratic forms, populations of | quadratic forms, ternary | Quadratic invariants | quadratic nonresidues, consecutive | quadratic residues, consecutive | Quadrilaterals | quadrinomial coefficients | quadruple factorial numbers | quarter-squares | quasi-amicable numbers | quasi-orders | quasigroups, asymmetric | quasigroups, by idempotent | quasigroups, commutative | quasigroups, self-converse | quasigroups, with identity | quasigroups | quaternions, Hurwitz, prime | Quebbemann 32-dimensional lattice | queens problem | Quet transform | quilt, Mrs. Perkins's
R(n), or n reversed | rabbits, dying | rad(n) | RADD sequences (Reverse then add something) | Radon function | Radon theorem | Ramanujan approximation | Ramanujan numbers tau(n) | Ramanujan's Lost Notebook | Ramsey numbers | random numbers | random sequences | Raney numbers | rapidly growing sequences | rational numbers | Rational points on curves | rationals, enumerating | RATS | Raymond strings | reachable configurations on circles | read n backwards | rebasing notation b[n]q | Recaman's sequence | Recaman's sequence, addition steps | Recaman's sequence, condensed version | Recaman's sequence, heights | Recaman's sequence, quotients and remainders | Recaman's sequence, records for a(n)/n | Recaman's sequence, segments in | Recaman's sequence, simplified version | Recaman's sequence, steps to hit n | Recaman's sequence, subtraction steps | Recaman's sequence, transforms based on | Recaman's sequence, two-dimensional versions | Recaman's sequence, variations on | reciprocal of n, decimal expansion of | reciprocals of primes | rectilinear crossing number of complete graph | recurrences over rings | recurrences, of the form a(n) = k*a(n - 1) +/- a(n - 2), | recurrences, of the form a(0) = 2; a(1) = k; a(n) = k*a(n - 1) + a(n - 2) | reduced residue system | reduced totient function psi | refactorable numbers | reflection coefficients | regions formed by lines in plane | regions formed by spheres in space | regions in regular polygon | regular n-gon with all diagonals drawn | regular primes | regular sequences | relations on n points | relations, antisymmetric transitive | relations, antisymmetric | Relations, connected | Relations, dissimilarity | Relations, reflexive | relations, self-converse | relations, symmetric reflexive | relations, symmetric | relations, transitive | Relations, ultradissimilarity | Relations, vacuously transitive | relations, without symmetry | relations | relatively prime pairs of numbers | relatively prime triples of numbers | remove 2's from n | remove squares! | rencontres numbers, triangle of | repdigit (repeated digit) numbers | repeating substrings | repfigit or Keith numbers | Representation degeneracies | Representations as sums of increasing powers | Representations as sums of Lucas numbers | Representations as sums of squares | Representations as sums of triangular numbers | Representations of 0 | Representations of 1 | Representations of symmetric group | repunit primes | repunits | residues, cubic | Residues | resistances | Reverse Add Then Sort | Reverse and Add! | reversion of series | REVERT transform | rhombic dodecahedral numbers | rhyme schemes | Riemann hypothesis, | Riemann hypothesis, sequences equivalent to | Riemann hypothesis, sequences related to | Riemann zeta function | Riesel numbers | Riesel problem | riffle shuffling | rings (in graph-theoretic sense) | rings, commutative | rings, enumeration of | rings, nonassociative | rings, nonisomorphic and nonantiisomorphic | rings, self-converse | rings, semisimple | rings, with unit | rings | Riordan numbers | Robbins constant | Robbins numbers | Robbins triangle | Robinson's constant | Rogers-Ramanjuan continued fraction | Rogers-Ramanujan identities | Roman numerals for n | Ron's sequence | rook tours | rook walks | Rooks | rooted trees , | rooted trees, achiral | rooted trees, asymmetric (1) | rooted trees, AVL | rooted trees, B-trees | rooted trees, binary (1) | rooted trees, boron | rooted trees, by generators | rooted trees, by internal nodes | rooted trees, carbon | rooted trees, chiral planted | rooted trees, codes for | rooted trees, composite binary | rooted trees, constant | rooted trees, directed | rooted trees, evolutionary | rooted trees, fixed points in | rooted trees, game | rooted trees, genealogical | rooted trees, Greg | rooted trees, Husimi | rooted trees, hybrid binary | rooted trees, identity | rooted trees, increasing | rooted trees, involution | rooted trees, lableling (Goebel) | rooted trees, leaves | rooted trees, M-type | rooted trees, matched | rooted trees, nodes | rooted trees, noncrossing | rooted trees, normalized total height | rooted trees, of subsets | rooted trees, oriented | rooted trees, partially labeled | rooted trees, permutation | rooted trees, phylogenetic | rooted trees, planar | rooted trees, planar, planted | rooted trees, plane, encodings of | rooted trees, plane, encoded as totally balanced binary strings | rooted trees, planted | rooted trees, pointed | rooted trees, powers of enumerator | rooted trees, prime binary | rooted trees, projective plane | rooted trees, quartic planted | rooted trees, red-black | rooted trees, search | rooted trees, series-reduced planted (1) | rooted trees, series-reduced | rooted trees, spanning | rooted trees, steric planted | rooted trees, symmetries in planted | rooted trees, ternary | rooted trees, triangle | rooted trees, trimmed | rooted trees, unary-binary | rooted trees, with a forbidden limb | rooted trees, with(out) a primary branch | rooted trees | rotation distance | royal paths in a lattice | Rubik cube | Rudin-Shapiro word | ruler and compass | ruler function | rulers, complete | rulers, Golomb | rulers, optimal | rulers, perfect | runs in binary expansion | runs, lengths of | Russian | Ruth-Aaron numbers
safe primes | SAGE program | Salie numbers | Sally sequence | Sam Loyd's 15-Puzzle | same upside down | Sarrus numbers | scheduling | Scheme (programming language) | Schroder is spelled Schroeder in the OEIS | Schroeder numbers | Schroeder's 1st problem | Schroeder's 2nd problem | Schroeder's 3rd problem | Schroeder's 4th problem | Schroeder's problems | Scott, Dana, sequences | Scrabble | sec(x), Taylor series for | secant numbers | secant-tangent numbers | Second moment | segmented numbers | Self numbers | Self-contained numbers | self-describing numbers | Self-dual | Self-generating sequences | semigroups | semigroups, asymmetric | semigroups, by idempotents | semigroups, commutative | semigroups, idempotent | semigroups, inverse | semigroups, non-commutative | semigroups, numerical | semigroups, regular | semigroups, relation | semigroups, self-converse | semigroups, with identity | semiorders | semiperfect numbers | semiprimes (or semi-primes) | semiprimes | separating families | sequence and first differences include all numbers | sequences by number of increases | sequences depending on A-numbers in OEIS | Sequences of prescribed quadratic character | sequences offering a monetary reward | sequences that contain every finite sequence of nonnegative integers | sequences that need extending | sequences which agree for a long time but are different | sequences whose extension requires factoring large numbers | sequences with a gap (some later term is known) (1) | sequences with a large but finite number of terms | Serbian | series-parallel networks | series-parallel numbers | set partitions | sets of lists | sets | sexy prime pairs | shadow of constants | Shannon switching function | Shell sort | shift registers, enumeration of output sequences | shift registers, enumeration of | shift registers, periods | Shifts left when transformed | shoe lacing | shoelaces | shogi (Japanese chess) | shuffle groups | shuffling (1) |
| Sierpinsky | sieve, | sieve, badly sieved numbers | sieve, binary | sieve, Eratosthenes | sieve, even | sieve, Flavius Josephus | sieve, generated by a | sieve, golden | sieve, Madore's | sieve, multilevel | sieve, Smarandache | sieve, spiral | sieve, square | sieve, ternary | sigma(n) = sum of divisors of n | sigma_0(n) | sigma_1(n) | sigma_k(n), the sum of the k-th powers of the divisors of n | signature sequences (1) | signature | silver mean, 1+sqrt(2) | silver number | Silverman's sequence | simple cubic lattice, theta series of | simple groups | simplex, barycentric subdivision of | simplices in a cube | Simplices | simplicial arrangements of lines | simplicial polyhedra | sin(x) | sinh(x) | siteswaps (or site swaps) | skat | skeins | skip 1, take 2, etc | slicing a cake | slicing a torus | slicing space | sliding block puzzles | Slowly converging series
| smallest number not a product of earlier terms | Smarandache numbers | Smarandache-Wagstaff function | Smarandache-Wellin numbers and primes | Smith numbers | sn | snake-in-box problem | Snoopy cartoon sequences | sociable numbers, infinitary | sociable numbers, unitary | sodalite | Soddy | solid partitions | solitary numbers | Solovay-Strassen primality test | solutions of x^k = 1 in symmetric group, for k=2,3,4,... | solutions to x+y=z | solvable numbers | Somos sequences | songs, popular, sequences from | sopf(n), sum of primes dividing n (without repetition) | sopfr(n), sum of primes dividing n (with repetition) | Sophie Germain primes | sorting, Batcher parallel sort | sorting, bridge hands | sorting, by block moves | sorting, by list merging | sorting, by prefix reversal | sorting, merge sort | sorting, networks | sorting, Shell sort | sorting | spaces, linear | spaces | Spanish | special numbers | specific heat | spectral arrays | spectrum of a number | speed of light | spelling and notation | spelling | Sperner families | Sperner's theorem | sphere, surface area of n-dimensional | sphere, vector fields on | sphere, volume of n-dimensional | spherical designs | Spheroidal harmonics | spirals, enumeration of | spirals, sequences from | split numbers | sqrt(2), continued cotangent for | sqrt(2), continued fraction convergents to | sqrt(2), decimal expansion of | sqrt(3), decimal expansion of | sqrt(n), length of period of continued fraction for | sqrt(n), nearest integer to, etc. | sqrt(p), length of period of continued fraction for | SQS | square arrays, indexing | square lattice (1) | square lattice, polygons on | square lattice, sublattices of | square lattice, theta series of | square lattice, walks on | square numbers | square pyramidal numbers | square root of pi | square roots of integers ( 1) | square roots, functional | square roots, of numbers | square roots, of primes | square, truncated | square-free graphs | square-free numbers, gaps between | square-free numbers | square-free sequences | square-free words | square-full numbers | squared rectangles and squared squares | squared squares | squarefree | squarefull numbers | squares, magic | squares, packing
| squares, undulating | Squares | stacking boxes | stacks | stamp-folding | Standard deviation | Stanley | stapled intervals | stapled sequences | star numbers | stars in sky | statistical models | Stechkin's function | Steiner systems, quadruple (SQS's) | Steiner triple systems (STS's) | stella octangula numbers | Stern's sequences | Stern's diatomic sequence | Stern's sequence | Stern's and Stern-Brocot sequences | Stern-Brocot tree | Stirling numbers, associated | Stirling numbers, generalized | Stirling numbers, of 1st kind | Stirling numbers, of 2nd kind | Stirling transform | Stirling's formula | Stolarsky array | Stopping times | Storage systems | Stormer numbers | Strobogrammatic numbers | strongly multiplicative means that a(m*n) = a(m)*a(n) for all m and n >= 1 | structure constants | structures, differential | STS | subfactorial numbers | sublattices | Subsequences of [1 ... n] | subset sums | subtract if you can else add | subtract-a-prime | subtract-a-square | subway stops | subwords | Such sequence | suitable numbers | sum of digits in powers of m | sum of digits, n times | sum of digits | sum of first n squares equals a triangular number | sum-free subsets | sum-full subsets | summarize previous term | sums of squares and sums of cubes , | sums of 16 squares, number of ways of writing as | sums of 2 cubes | sums of 2 squares | sums of 3 cubes | sums of 3 squares | sums of 3 squares | sums of 4 cubes | sums of 4 squares | sums of 4th powers needed to represent n | sums of 5 cubes | sums of 6 cubes | sums of 7 cubes | sums of 8 cubes | sums of 8 or 9 cubes | sums of consecutives squares give squares | sums of distinct cubes | sums of distinct squares | Sums of divisors | Sums of powers | sums of squares needed to represent n | sums of squares, sequences related to (01) | sums of tetrahedral numbers | sums of two distinct prime cubes | Sum_{k = 0..n} f(k) is standard OEIS notation (rather than sum_k^n, sum for k from 0 to n, etc.) | super-abundant numbers | superabundant numbers | superfactorials | superior highly composite numbers | Superpositions of cycles | superqueens | supersingular primes |
| supertough | Surfaces | susceptibility (1) | Swedish | switchboard problem | switching classes | switching networks | Sylvester's sequence | Sym, game of | symbols in OEIS | symmetric functions of noncommuting variables | symmetric functions | symmetric group S_n, character table | symmetric group S_n, order of | symmetric group S_n | symmetric numbers | S_n
t is the first... | T-coordinates for arrays | t-designs, spherical | table (or triangle) of (1) | take 1, skip 2, etc. | take-a-factorial | take-a-prime | take-a-square | take-a-triangle | tan(x), Taylor series for | tan(x) | tangent numbers, generalized | tangent numbers, triangle of | tangent numbers
| tanh(x), Taylor series for | tanh(x) | tatami mats | tau(n), number of divisors | tau | tau_k or d_k numbers, number of ordered n-factorizations of n | taxi-cab numbers | taxicab numbers | Tchebycheff is spelled | Tchebychev is spelled | Tchoukaillon (or Mancala) solitaire | telephone country codes | tennis ball problem (1) | tensors | terminology in OEIS | ternary continued fractions | ternary quadratic forms | ternary representation | ternary words | tetrahedral lattice | tetrahedral numbers, sums of | tetrahedral numbers | tetrahedron, coloring a | tetrahedron, truncated | tetrahedron |
| theta series of A_3 lattice | theta series of b.c.c. lattice | theta series of Coxeter-Todd lattice | theta series of cubic lattice | theta series of diamond lattice | theta series of D_3 lattice | theta series of f.c.c. lattice | theta series of h.c.p. | theta series of hexagonal lattice | theta series of hexagonal net | theta series of laminated lattices | theta series of Leech lattice | theta series of P_{10b} packing | theta series of square lattice | theta series of Z lattice | theta series | theta(n) | theta_2(q) | theta_3(q) | theta_4(q) | Third One Lucky game | three-way splitting of integers | threshold functions | threshold graphs | Thue-Morse sequence | Thue-Morse ternary sequences (closed under a->abc, b->ac, c->b) | tic-tac-toe | tie, tying a | tiered orders | topologies | topologies, connected | torus, cubes in | torus, slicing a | total height of rooted trees | total orders | total partitions | totative | totient function phi(n) | totient function phi(n), does not take these values | totient function phi(n), half-totient function | totient function phi(n), inverse to | totient function phi(n), iterating | totient function phi(n), values of | tough polyhedra | tournaments, automorphism groups of | tournaments, number of different tournament graphs | tournaments, outcomes of | tournaments, rigid | tournaments, round-robin | tournaments, score sequences in | tournaments, tournament sequences | tournaments | tours, rook | Tower of Hanoi | Towers of Hanoi | traffic light problem | trailing zeros in n! | trails | transform, hyperbinomial | transformations on unit interval | translation planes | transpositions | tree, unary-binary, definition | trees | trees, 2-colored | trees, achiral | trees, alternating | trees, asymmetric | trees, automorphism group of | trees, average height of rooted labeled | trees, balanced ordered | trees, balanced | trees, bicentered | trees, binary rooted | trees, binary | trees, bisectable | trees, boron | trees, by diameter | trees, by height | trees, by stability index | trees, by valency | trees, carbon | trees, centered | trees, chiral | trees, codes for | trees, complexity | trees, constant | trees, coordination sequence | trees, diameter 3 | trees, diameter 4 | trees, diameter 5 | trees, diameter 6 | trees, diameter 7 | trees, diameter 8 | trees, diameter of | trees, directed | trees, E-type | trees, endpoints | trees, evolutionary | trees, exchange | trees, exponentiation of e.g.f. | trees, fat | trees, fixed points in | trees, free | trees, graceful | trees, Greg
| trees, heap ordered | trees, hexagon | trees, homeomorphically irreducible | trees, Husimi | trees, identity | trees, in wheel | trees, indecomposable | trees, intransitive | trees, labeled | trees, leaves | trees, Leech labeling problem | trees, leftist | trees, log of e.g.f. | trees, M-type | trees, matched | trees, nodes | trees, of subsets | trees, oriented | trees, partially labeled | trees, path length | trees, permutation | trees, phylogenetic | trees, planar | trees, plane | trees, planted | trees, powers of g.f. | trees, projective plane | trees, quartic | trees, Ramsey theorem for | trees, reversion of g.f. | trees, rooted | trees, rotation distance between | trees, Schroeder | trees, series-reduced | trees, shapes of | trees, signed | trees, spanning (1) | trees, spectra of | trees, squares of | trees, stability index of | trees, stable | trees, Steiner | trees, steric | trees, symmetries in | trees, ternary | trees, triangle of | trees, trimmed | trees, two-colored | trees, Weiner index | trees, with a forbidden limb | trees, with bicentroid | trees, with centroid | trees | tri-perfect numbers | triangle of x+y, etc. | triangle, coloring a | Triangles | triangles, by perimeter | triangular arrays of integers, enumeration of special | triangular arrays, indexing | triangular lattice | triangular numbers, partitions into | triangular numbers, sums of three | triangular numbers, sums of two | triangular numbers | triangular square numbers | triangular triples | triangulations (1) | tribulations game, remoteness numbers | tribulations | tricapped prism | trigonometric functions which either increase or decrease monotonically | trinomials over GF(2) , | triperfect numbers | triple factorial numbers
| triply perfect numbers | truncatable primes | truncated cube | truncated octahedron | truncated square numbers | truncated tetrahedron | Turing machines which halt | Turing machines | Turkish | twin primes conjecture | twin primes constant | twin primes | two consecutive residues | two-way infinite sequences (01) | two-way splittings of integers | twopins positions
U-coordinates for arrays | ugly numbers | Ulam numbers | Ulam-type sequences | unary representations | unary-binary tree, definition | undecagon is spelled 11-gon in the OEIS | undulating numbers | undulating squares | unexplained differences between partition generating functions | unhappy numbers | unidecagon is spelled 11-gon in the OEIS | Unions and sums | unique factorization domains | unit fractions | unit interval graphs | unitary amicable numbers | unitary divisors of n, number of | unitary divisors of n, sum of | unitary divisors | unitary perfect numbers | unitary phi (or unitary totient) function uphi | unpredictable sequence | unsolved problems in number theory | untouchable numbers | up-down permutations | urinals | urns | usigma(n)
vampire numbers | Van der Pol numbers | Van der Waerden numbers | Van Lier sequences | Vassiliev invariants | vector fields | vertex diagrams | vertex operator algebras (1) | very rapidly growing sequences | Von Staudt-Clausen representation | voting schemes
walk, longest, on cube | Walks, on b.c.c. lattice | Walks, on cubic lattice | Walks, on diamond lattice | Walks, on hexagonal lattice | Walks, on honeycomb | Walks, on Kagom\'{e} lattice | Walks, on Manhattan lattice | Walks, on n-cube | Walks, on square lattice | Walks, on square lattice | Walks, on tetrahedral lattice | walks, on tetrahedron | walks, on triangle | walks, random | walks, rook | Wallis pairs | Wallis' number | Waring's problem | Weak Macdonald Conjecture | Weber functions | Wedderburn-Etherington numbers | Weierstrass P-function | Weigh transform | weight distributions of codes (1) | weight enumerators | weight of n | weird numbers | Welsh | Weyl group W(E7) | Weyl group W(E_8), Molien series for | white numbers | Whitney numbers | whole numbers | Width | Wieferich primes | wild and pseudo-wild numbers | Wilson primes | Wilson primeth recurrence | Wilson quotients | Wilson remainders | windmills | wire, folding a piece of | Wirsing constant | witnesses | Witt vectors, dimensions | Witt vectors, reduced | Witt vectors | Wolstenholme numbers | wonderful Demlo numbers | Woodall numbers n*2^n-1 | Woodall numbers | Woodall primes | word, Thue-Morse | Words in certain languages | World Geodetic System 1984 Ellipsoid | worst cases | Wyt queens game | Wythoff array | Wythoff game (1) | Wythoff game, 3-pile | Wythoff game | Wythoff sequence, lower ([n*tau]) | Wythoff sequence, upper ([n*tau^2])
x in S implies 2x not in S | x*ceiling(x), iterating (1) | x*floor(x), iterating | x/(1-rx-sx^2) | XOR(x,y) | x^2+xy+y^2, of form | x^2+y^2 | x^2+y^2+2z^2, of form | x^4+y^4+z^4 = t^t | x^x, derivative of
years, perfect | years | yoke-chains | Young tableaux
Z-channel, codes for | Z2[X]-polynomials | zag numbers | Zarankiewicz's problem | Zeckendorf expansion | zero sequence |
| zeros in n!, trailing | zeta function | zeta(2) | zeta(3) | zig numbers | Z^1, theta series of | Z^2 lattice | Z^3 lattice | Z^4, theta series of | Z^4, walks on
(+1,-1)-matrices | (+1,0,-1)-matrices | (-1)-Sigma(n) | (-1)-sigma(n) | (-1)sigma(n) | (-1)Sigma(n) | (-1)sigma(n) | (-1)^n | (0,1)-matrices | (2-rx)/(1-rx-sx^2) | 0,1 then repeat | 0^n | 1's in binary expansion | 1's sequence | 1-factorizations | 1/(1-rx-sx^2) | 1/n , | 1/n, decimal expansion of | 1/n, period of expansion of (in various bases) | 1/p (p prime), number of cycles | 1/p (p prime), period of decimal expansion =(p-1)/k | 1/p (p prime), period of decimal expansion of | 1/p (p prime), sum of | 10*n^2 + 2 | 10-gonal numbers | 10^n | 11-gonal numbers | 11-gonal pyramidal numbers | 11-smooth numbers | 111...111, primes of form | 12-gonal numbers | 12-gonal pyramidal numbers | 13-gonal numbers | 13-smooth numbers | 14-dimensional lattices | 14-gonal numbers | 15 puzzle | 15-gonal numbers | 16-gonal numbers | 17-gonal numbers | 17-smooth numbers | 18-gonal numbers | 19-gonal numbers | 19-smooth numbers | 196, trajectory of
2 is a 4th power residue mod p | 2 is a cubic residue mod p | 2 is a square mod p | 2 is an mth power residue mod p | 2-adic valuation | 2-graphs | 2-plexes | 20-gonal numbers | 21-gonal numbers | 22-gonal numbers | 23-gonal numbers | 23-smooth numbers | 2^2^n | 2^n + 1, primes dividing | 2^n + 2 is divisible by n | 2^n - 1 | 2^n/n | 2^n | 2^p - 1
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In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven Prize Problems. The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. During the Millennium Meeting held on May 24, 2000 at the Collège de France, Timothy Gowers presented a lecture entitled "The Importance of Mathematics", aimed for the general public, while John Tate and Michael Atiyah spoke on the problems. The CMI invited specialists to formulate each problem.
One hundred years earlier, on August 8, 1900, David Hilbert delivered his famous lecture about open mathematical problems at the second International Congress of Mathematicians in Paris. This influenced our decision to announce the millennium problems as the central theme of a Paris meeting.
The rules for the award of the prize have the endorsement of the CMI Scientific Advisory Board and the approval of the Directors. The members of these boards have the responsibility to preserve the nature, the integrity, and the spirit of this prize.
Paris, May 24, 2000
Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier-Stokes Equations
P vs NP
Poincaré Conjecture
Riemann Hypothesis
Yang-Mills Theory
cut-the-knot
Interactive Mathematics Miscellany and Puzzles
Mathematic Glossary
Mathematics as a Language
Math Glossary, Math Terms
This site is for teachers, parents and students who seek engaging mathematics. Many of the topics are accompanied by Java illustrations. There are more than 900 Java applets. The applets can be licensed by teachers for inclusion in their own pages.
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Arithmetic
Base Conversion | Divisibility Criteria | Euclid's Game | Fast Arithmetic Tips | Hour glass timing | Magic in Square | Make an Identity | Napier Bones | Number Guessing Game | Arithmetic Word Problems | Online practice | And much much more ...
Math Games & Puzzles
Three Jugs Problem | Box Labels | Fish Soup game | Goat, Cabbage and Wolf | Josephus Flavius' problem | Mastermind Variants | Peg Solitaire | Scoring | Toads And Frogs Puzzle | Toads And Frogs in 2D | Tower of Hanoi | Tromino Puzzle | And much much more ...
Logic
Lewis Carroll's Logic Game | Logic Word Problems | And more ...
Fractals & Chaos
Color Cycling on Mandelbrot | Cantor sets | Pascal Triangle | Fractal Curves and Dimension
Iterated Function Systems | Iterations in Mandelbrot Set | Julia Sets | Logistic Model | Plane Filling Curves | Toying with Tremas | And more ...
Fallacies
Curry's Paradox | Delian Problem Solved | A Faulty Dissection | Langman's Paradox | Sam Loyd's Son's Dissection | Rouse Ball's Fallacy | And more ...
Calculus
Equations of the Straight Line | Function, Derivative and Integral | Lagrange Interpolation | Riemann Sums | Rolle's and Mean Value | Taylor Series for Cosine | And more ...
Combinatorial Games
Date Game | Grundy's Game | Kayles | Nim | Nimble | Northcott's game | One Pile | Plainim Misère | Subtraction Game | Take-Away Games | Turning Turtles | Wythoff's Nim | And much more ...
Algebra
3-Term Arithmetic Series | Binary Color Device | Candy Game | Chebyshev polynomials | Counting Triangles | Averages | Heads and Tails | Multiplication Table | Interest Calculations | Letter Counting | Merlin's Magic Squares | Proizvolov's Identity | Pythagorean Triples | Self-documenting Sentences | What's next? | Word Problems | Online practice | And much more ...
Visual Illusions
Balls and Shadows Illusion | Bulging lines illusion | Gerbino's Illusion | Heaver: A Visual Illusion | Hering Illusion | Judd Illusion | Kanizsa Triangle | Müller-Lyer Illusion | Necker Cube | Perspective Illusion | Poggendorff Illusion II | Ponzo Illusion | Revolving Circles Illusion | Twisted Cord Illusion | Wundt Block Illusion | Zöllner's Illusion | And much much more ...
Probability
Birds On a Wire | Buffon's Noodle | Misuse of Statistics | Monty Hall Dilemma | Parrondo's Paradox | Probability and Infinity | And much more ...
Computer Math Magic
Arithmetic magic matrix | Bachet's Magic Trick | Calendar Magic | Gergonne's Magic Trick | Hummer's Mind Reader | Magic in Square | Number Guessing Game | Guessing Two Numbers
Combinatorics
Bicolor Tower of Hanoi | Art Gallery Theorem | Coin change | Critical Path | Latin Squares | Listing all permutations | Monotone Sequences | A Pigeonhole Problem | Project Scheduling | Scrub Tile Puzzle | Shuttle Puzzle | Tower of Hanoi | And much more ...
Miscellaneous
Disappearing Rectangles | Impossible Fork | Projectile Trajectory | Random Dot Stereograms | Ratchet Effect | And more ...
Geometry
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| Pascal Triangle and the Tower of Hanoi |
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| Prime |
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Where is your Birthday in PI?
Mein Geburtstag steht an der 500.112sten Stelle innerhalb der Zahl PI: I found 080257 starting at this location in PI: 500112
Word Combinations
This script reads a series of alphanumeric characters, and calculates how many unique ways those characters can be rearranged. If desired, it will display all of the combinations.
J
jeff560
Earliest Known Uses of Some of the Words of Mathematics
Earliest Uses of Various Mathematical Symbols
Mathematical Words
These pages show the names of the individuals who first used various common mathematical symbols, and the dates the symbols first appeared. The most important written source is the definitive A History of Mathematical Notations by Florian Cajori.
Zu jedem der folgenden Punkte gibt es eine eigen Seite mit ausführlichen Erklärungen:
Symbols of operation, including +, -, X, division, exponents, radical symbol, dot and vector product
Grouping symbols, including (), [], {}, vinculum
Symbols of relation, including =, >, <
Fractions, including decimals
Symbols for various constants, such as pi, i, e, 0
Symbols for variables
Symbols to represent various functions, such as log, ln, absolute value; also the f(x) notation
Symbols used in geometry
Symbols used in trigonometry; also symbols for hyperbolic functions
"subtract" - When Fibonacci (1201) wishes to say "I subtract," he uses some of the various words meaning "I take": "tollo", "aufero", or "accipio". Instead of saying "to subtract" he says "to extract".
In English, Chaucer used "abate" around 1391 in "Treatise on the Astrolabe": "Abate thanne thees degrees And minutes owt of 90" (OED2).
In a manuscript written by Christian of Prag (c. 1400), the word "subtraction" is at first limited to cases in which there is no "borrowing". Cases in which "borrowing" occurs he puts under the title "cautela" ("caution"), and gives this caption the same prominence as "subtractio".
In "Practica" (1539) Cardano used "detrahere" ("to draw from" or "to take from").
In 1542 in the "Ground of Artes" Robert Recorde used "rebate": "Than do I rebate 6 out of 8, & there resteth 2".
In 1551 in "Pathway to Knowledge" Recorde used "abate": "Introd., And if you abate euen portions from things that are equal, those partes that remain shall be equall also" (OED2).
Digges (1572) writes "to subduce or substray any sume, is wittily to pull a lesse fro a bigger number."
Schoner, in his notes on Ramus (1586 ed., p. 8), uses both "subduco" and "tollo" for "I subtract".
In his arithmetic, Boethius uses "subtrahere", but in geometry attributed to him he prefers "subducere".
The first citation for "subtract" in the OED2 is in 1557 by Robert Recorde in "The whetstone of witte": "Wherfore I subtract 16. out of 18".
Hylles (1592) used "abate", "subtact", "deduct", and "take away" (Smith vol. 2, pages 94-95).
From Smith (vol. 2, page 95): The word "subtract" has itself had an interesting history. The Latin "sub" appears in French as "sub", "soub", "sou", and "sous", "subtrahere" becoming "soustraire" and "subtractio" becoming "soustraction". Partly because of this French usage, and partly no doubt for euphony, as in the case of "abstract", there crept into the Latin works of the Middle Ages, and particularly into the books printed in Paris early in the 16th century, the form "substractio". From France the usage spread to Holland and England, and form each of these countries it came to America. Until the beginning of the 19th century "substract" was a common form in England and America, and among those brought up in somewhat illiterate surroundings it is still to be found. The incorrect form was never popular in Germany, probably because of the Teutonic exclusion of international terms.
K
Krohn-Rhodes (W3)
Die Doppelbezeichnung "Krohn-Rhodes" geht zurück auf die beiden Mathematiker/Informatiker Kenneth Krohn (Harvard) und John Rhodes (MIT).
"LaTeX" steht für "Lamport TeX". "LaTeX" ist ein Textsatzsystem von Leslie Lamport, das eine Vereinfachung bzw. Spezialisierung des von D. Knuth entwickelten Textsatzsystems "TeX" darstellt. "LaTeX" ermöglicht wie "TeX" unter anderem das Setzen von komplizierten Formeln der Mathematik, Chemie etc.
Das Textsatzsystem "TeX" wurde seit 1977 von Prof. Donald E. Knuth (*1938) in Stanford (USA) entwickelt wurde, um insbesondere wissenschaftliche, mathematische und technische Textdokumente druckfertig zu machen. Die erste Version, der im Lauf der Zeit einige Verbesserungen folgten, wurde 1982 vorgestellt.
TeX (bzw. das dazu entwickelte Makropaket LaTeX, s. u.) entwickelte sich schnell zum De-facto-Standard für die Verarbeitung naturwissenschaftlicher Texte und wird auch noch heute in diesem Bereich eingesetzt.
Zur Aussprache ist zu sagen, daß "TeX" als "tech", "TEKH" ausgesprochen wird. Das zu Grunde liegende griech. "techne" = dt. "Kunst", "Handwerk", "Technik" enthält den griechischen Buchstabe "Chi", der wie ein lateinisches X geschrieben wird.
Die Weiterentwicklung für mathematische Texte, "LaTeX", wird entsprechend "lah-tech", "lah-TEKH", "Lej-tech" ausgesprochen.
"LaTeX" vereinfacht den Umgang mit "TEX", indem es entsprechend der logischen Struktur des Dokuments auf vorgefertigte Layout-Elemente zurückgreift.
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Important : Le "Χ" à la fin du mot LaTeX n'est pas un x majuscule mais la lettre grecque "Chi" (dont le code HTML est Χ). LaTeX se prononce donc "lateck" et non "latecs".
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Der Code dazu: Eine bekannte Summenformel lautet und man erzählt dazu eine Anekdote von Carl-Friedrich Gauss. Wenn man möchte kann man diese Formel auch im Displaystyle schreiben, nämlich
\displaystyle\sum_{k=1}^n k = \frac{n\cdot(n+1)}{2}
Dieser Text beschreibt in Form eines Kochbuches LaTeX-Textteile. In einem gewöhnlichen Kochbuch ermitteln Sie, worauf Sie in etwa Appetit haben, indem Sie die Seiten des Kochbuches überfliegen, bis ein Rezept mit reizvollem Titel Ihre Aufmerksamkeit erregt. Das Rezept enthält dann eine Zutatenliste und einen Text, der Ihnen erklärt, wie und in welcher Reihenfolge Sie diese Zutaten verarbeiten müssen, um das betreffende Gericht zuzubereiten, das durch den Titel benannt ist. Dieses Kochbuch funktioniert in ähnlicher Weise, nur daß Sie hier keine Angst haben müssen, an Gewicht zuzunehmen.
Der wesentlichste Unterschied zu einem normalen Kochbuch ist der, daß Sie hier gleich mit dem Kochen anfangen können.
Ja, Sie haben richtig gelesen. Hier wird Ihnen nicht nur ein Kochbuch zu Verfügung gestellt, sondern eine ganze, vollausgestattete Küche mit dazu. Und Sie müssen am Ende noch nicht einmal abwaschen.
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(E?)(L1) http://www.math.com/
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Neben dem umfassenden Mathematik-Glossar findet man weiterhin die Schwerpunktthemen:
Cantor's Theorem | Cantor Set | Carroll's Paradox | Conics | Dandelin's Spheres | Differentiation Rules | Fallacies | Gödel's Theorems | Greek Alphabet | Hempel's Ravens Paradox | Integration Forms | Irrationality of the Square Root of 2 | Kepler's Laws | Latin Terms and Phrases | Limits | Platonic Solids | Series | Sid's Paradox | Solving Story Problems | Trig Functions and Identities | Von Neumann Heirarchy | Zeno's Paradox of the Tortoise & Achilles
Number Theory | Combinatorics | Geometry | Algebra | Calculus & Diff Eqs | Probability & Statistics | Set Theory & Foundations | Reflections on Relativity | History | Physics | Music | Animated Illustrations | Combined List of Articles | Quotations
Number Theory | Symmetric Pseudoprimes | Is e Normal? | Identities for Linear Recurring Sequences | The Half-Totient Tree | Limit Cycles of xy (mod x+y) | A Knot of Congruences | Rounding Up to PI | Fermat's Last Theorem for Cubes |
| Self-Similar Reverse-Sum Sequences | The Sum of the Prime Factors of N | Sequence Partitionable Into Powers of 2 or 3 | Iterated Sum-of-Digits Function | If ab+1, ac+1, bc+1 are squares,... | Zeisel Numbers | The Jewel of Arithmetic: Quadratic Reciprocity | Highly Wilsonian Primes | Quadratic Congruences | Squares in Arithmetic Progression (mod p) | Numeri Idonei | Sequences With No Arithmetic Progressions | A Primality Criterion | Can n Divide !n ? | Diophantine Walk-a-thon | Barlow's Observation | Divisors of an n-term Geometric Series | More Results on the Form xy (mod x+y) | Sums of Three Cubes | Congruences Involving the Totient Function | Infinitely Many Rhondas | Why z Is Not a Prime Power in z^p = x^p + y^p | Summations and Recurrences | Evidence for Goldbach | Miscellaneous Diophantine Equations | No Four Squares In Arithmetic Progression | Minimum Difference Function | Gauss' Lemma Without Divisibility Arguments | Product Divisible By Sum of Squares | Lucas and Perrin Pseudoprimes | Pseudoprimes For x^2 - 4x - 9 | Primitive Roots and Exponential Iterations | Sums of Consecutive Nth Powers Equal to an Nth Power | On Case 1 of Fermat's Last Theorem | A Mersenne Coincidence | Coprime Partitions | The 450 Pound Problem (x^3 + y^3 = 6z^3) | Is This a Prime? | Reverse Greed for Unit Fractions | The Amanda Arrangement | Sum of Divisors Equals a Power of 2 | Sublime Numbers | On x^2 + y^3 = z^6 | A Method Of Factoring Based On 1/N | The Distribution of Perfection | Fermat's Last Theorem for Quadratic Integers | Square Triangular Numbers | Differences Between Powers | Recurrences and Pell Equations | In Defense of Base-Related Problems | On x^3 - x + y^3 - y = z^3 - z | On the Density of Some Exceptional Primes | Double Equations from Triangles in Squares | Differently Perfect | A Special Property of 151 | Simple Complex Quadratic Fields |
| Casting Out Nines | Detecting Squares | Numbers Expressible As (a^2 - 1)(b^2 - 1) | Concordant Forms | Solving Magic Squares |
| Cyclic Divisibility | Waring's Problem | The 2 Ohm Problem | Reflective and Cyclic Sets of Primes | Unit Fraction Partitions | N = (x^2 + y^2)/(1+xy) Is A Square | Perrin's Sequence | Proof of Generalized Little Theorem of Fermat | Minimizing the Denominators in Unit Fraction Expansions |
| Pythagorean Graphs | Series Within Parallel Resistor Circuits | Sequences Based On Continued Fraction For PI | Smallest Quadrilateral With Distinct Integer Sides | Mock-Rational Numbers | Coherent Arrays of Squares | Anti-Carmichael Pairs | Magic Square of Squares | Orthomagic Square of Squares | Automedian Triangles and Magic Squares | Continued Fractions and Characteristic Recurrences | One In The Chamber |
| Average of Sigma(n)/n | Lucas's Primality Test With Factored N-1 | Highly Heronian Ellipses | How Leibniz Might Have Anticipated Euler | Odd Greedy Unit Fraction Expansions | Factoring Zeta | Accidental Melodies | Some Properties of the Lucas Sequence | Four Squares From Three Numbers | Meandering Convergence of a Dirichlet Series | Geodesic Diophantine Boxes | Least Significant Non-Zero Digit of n! | Discordance Impedes Square Magic | No Progression of Four Rectangles On A Conic? | Whole Permutation Fractions | A Unique Intersection Pattern for Plane Curves
Combinatorics | Partitions into Distinct Parts | Dedekind's Problem | On Eulerian Numbers | Permutation Loops | The Four Color Theorem | Polyomino Enumerations | Powers of Primes Dividing Factorials | The Dartboard Sequence | Meeting Combinations and Interval Graphs | Binary Games | Additive and Multiplicative Partitions | 414298141056 Quarto Draws Suffice! | Coloring The Edges of an Icosahedron | Uniform Squares | Cumulative Permutation Sequences | Center of Gravity With Integer Coordinates | The Factorial Number System | Sums and Differences of Discrete Functions | The Statistics of Counterintelligence | Partition Transform Cycles | Clouds, Shy Squares, and Diophantus | Computing the Partitions of n | Solving Magic Squares | Generating the Monotone Boolean Functions | Meeting Probabilities | The Determinants of 4x4 Magic Squares | Discrete Circular Distributions | Balls In Bins With Limited Capacities | The Importance of Being Urnest (B Balls, K Colors, N Urns) | Sequences of Characters in Random Strings | Complete Bit-Cubes | A Procrustean Protocol | Partitions into Consecutive Integers | Tables of 1 to N with Equal Columns | Regular Polygonal Arrangements | The Pigeon Hole Principle | Two Proofs of Impossibility for Five-Point Star | Golf Tournaments, Polyhedra, and Latin Squares | Generating Functions for Point Set Distances | Derangements and Generalizations | Round-Robin Ties | The Coin in Three Fountains | Impossible Strings for Cellular Automata | Hamilton Cycles on McCauley Graphs | Permutation Puzzles | Collecting k Complete Sets of Coupons | Christmas Ornaments | Pythagorean Graphs | Ringing of the Changes (The Shape of 4!) | f(f(x))=exp(x) Generates the Multinomials | Progress on Dedekind's Problem | Electoral Draws | On Euler's Pentagonal Theorem | Generating Functions and Recurrence Relations
Geometry | The Five Squarable Lunes | Constructing the Heptadecagon | Generalizing Pythagoras and Carnot | Iterative Isoscelizing | Parabola Through Four Points | Euclid's Proposition III,20 and its Converse | Sphere Packing In Curved Space | Pascal's Mystic Hexagram | Min-Energy Configurations of Electrons On A Sphere | Generating Functions for Point Set Distances | Curvature of Linear Interpolation | Gravity Sextant | An Optical Illusion | Platonic Solids and Plato's Theory of Everything | Euclid's Plan and Proposition 6 | What Mirrors Do | Volume of n-Spheres and the Gamma Function | Ptolemy's Orbit | The Golden Pentagon | Apollonius' Tangency Problem | Loci of Equi-angular Points | Heron's Formula and Brahmagupta's Generalization | Heron's Formula for Tetrahedrons | The Orbit of Triangles | Perpendicular Regression Of A Line | Rolling Spheres and Cones | Cramer's Paradox | The Lemniscate and Spacetime | Factoring Convex Figures | Smallest Quadrilateral With Distinct Integer Sides | Mean Distance from Vertex to Interior of Plane Figures | The Mystery of the Grazing Goat | Old Notes on Curvature | Did Archimedes Know Gauss-Bonnet? | Leaning Ladders | Pent Up Ratios | Thinking Outside the Triangle | On the Ellipse | The Shape of Coincidence | Double Equations from Triangles in Squares | Main Diagonal Passing Through Interior | Distances In Bounded Regions | Embedding Non-Euclidean Within Euclidean Geometry | On de Bruijn Grids and Tilings | Archimedes on Spheres and Cylinders | Trees on a Complex Plain | Pappus' Theorem | Acute Problem | Quintisecting an Angle | Quadrilateral In a Circle | Volume Under a Triangle | Constructible Points and Coverable Points | A Quarky Formula for Volume of Parallelpiped | Piero della Francesca's Tetrahedron Formula | Automedian Triangles | Piano Keys | On Ptolmey's Theorem | N-Fold Polygonal Spirals | Equal Bisectors and Isosceles Triangles | Equation of a Triangle | Highly Heronian Ellipses | No Equilateral Triangles on a Chess Board | Net Area and Green's Theorem | Ringing of the Changes (The Shape of 4!) | The Resultant and Bezout's Theorem | Stochastic Rhombic Tiling | Diophantine Geodesic Boxes | Angular Angst | Random Tiling of a Sphere | Zeno's Mice and the Logarithmic Spiral | Path Lengths and Coordinates | The Cube Unfolded | Revisiting the Four-Point Parabola | Morley's Trisection Theorem | Isospectral Point Sets in Higher Dimensions | Exponential Spiral Tilings | Harmonia Mensurarum | Constant Headings and Rhumb Lines | Enveloping Circular Arcs | Normals From A Point To An Ellipse | Cutting Self-Similar Pentagons | The Tetratorus and Other Multi-Layered Polyhedra | The Curvatures of Hypersurfaces | Menelaus and Ceva | Carnot, Organizer of Transversals | Non-Periodic Tilings With N-fold Symmetry | Aperiodic Tilings | Tilings Based on Perrin's Sequence | Routh's Theorem by Cross Products
Algebra | Multiple Linear Regression | Kummer's Objection | Irreducibility Criteria | Proving Algebraic Inequalities | Bit-String Orbits Under Rotate-XOR | Piano Keys | The Crystallographic Restriction | Polynomials For Sums of Square Roots | Leaning Ladders | On Ptolmey's Theorem | Machin's Merit | The Twelve-Step Cycle of 1/(sin(x)cos(x)) | Finite Subgroups of the Mobius Group | The Fundamental Theorem of Algebra | String Algebra | Apollonius' Tangency Problem | Asymptotic Approach to 2D Arrays | Iterated Logarithmic Functions | Eigenvalue Problems and Matrix Invariants | Iterated Means |
| Square Roots by Pencil and Paper | A Quasi-Periodic Sequence | Sums of Powers in Terms of Symmetric Functions | Self-Similar Reverse-Sum Sequences | Generalized Mediant | Tangents, Exponentials, and PI | Recurrences For Harmonic Sums | Bernoulli Numbers and Harmonic Series | Quasi-Groups | Laminar Transformations | Ancient Square Roots | Pythagoras On Dot and Cross Products | Infinite Products and a Tangent Fan | Exponential Partitions | Geometric Dot Products and Digit Reversals | Radical Expression For cos(2pi/7) | On f(x^2+y^2) = f(x)^2 + f(y)^2 | Series Solution of Non-Linear Equation | Compressor Stalls and Mobius Transformations | Convoluting Arrays | Harmonic Sums of Integers with k Binary 1's |
| Gauss' Lemma Without Divisibility Arguments | Mnemonic Coins and Pattern Avoidance | The Shortest Path To Trigonometric Identities | Polynomials From Pascal's Triangle | Bras, Kets, and Matrices | Decimal Representations as Power Series | Reflecting on the Geometric Mean | Sums of Powers | Trees on a Complex Plain | Inverse Square Weighted Interpolation |
| Reducing Quartics to Cubics | Platonions | Annuities With Inflation | On Eulerian Numbers | Intersections of Polynomials | Angular Angst | Quarky Vector Triple-Product | From the Geometric Series to Stirling Numbers | Orthomagic Square of Squares | Automedian Triangles and Eigen Vectors | Continued Fractions and Characteristic Recurrences | On the Solution of the Cubic | Phased Summations | Arranging the Solutions of f(x+y+z)=xyz | Tangent To PI | Cross-Linear Interpolation | The Super-Symmetric Mean | Rational Sines of Rational Multiples of PI | Cyclic Redundancy Checks | Permutation Loops | Loxodromic Aliasing | Determining the Galois Group of a Polynomial | Formal-Numeric Series | Discrete Fourier Transforms | Continuous From Discrete Transfer Functions | Expulsion Sets | Bi-Rational Substitutions Giving Squares | Cyclic Divisibility | The Tetratorus and Other Multi-Layered Polyhedra | Maxwell and Second-Degree Commutation | Inverse-Square Forces and Orthogonal Polynomials | Harmonia Mensurarum | Iterative Isoscelizing | Galois Groups | Hermitian Matrices | An Algebraic Duality | Linear Fractional Transformations | The Resultant and Bezout's Theorem | Isospectral Point Sets in Higher Dimensions | Rotation Matrices | Iterative Solutions of Homogeneous Linear Systems | Binary Reverse-Sum Automata | The Cayley-Hamilton Theorem
Calculus and Differential Equations | The Laplace Equation and Harmonic Functions | Fractional Calculus | Analytic Functions, The Magnus Effect, and Wings | Fourier Transforms and Uncertainty | Propagation of Pressure and Waves | The Virial Theorem | Causality and the Wave Equation | Integrating the Bell Curve | Compressor Stalls and Mobius Transformations | Dual Failures with General Densities |
| Series Solutions of the Wave Equation | The Limit Paradox | Proof That PI is Irrational | Simple Proof that e is Irrational | The Filter Of Observation | Eigenvalue Problems and Matrix Invariants | Root-Matched Recurrences For DiffEQs | Why Calculus? | High Order Integration Schemes | Do We Really Need Eigen Values? | Markov Models with Aging Components | Leibniz's Rule | A Removable Singularity in Lead-Lag Coefficients | Convergence of Series (How NOT to Prove PI is Irrational) | Sum of n^2 / (n^3 + 1), n=1 to inf | Tilting Pencils | Continuous From Discrete Transfer Functions | Ptolemy's Orbit | Distances In Bounded Regions | Rolling Spheres and Cones | Integrating Factors | Series Solution of Non-Linear Equation | Volume of n-Spheres and the Gamma Function | Choice Without Context? | Infinite Products and a Tangent Fan
| Cylinders with Cylindrical Holes | Markov Models with Variable Transition Rates | Age Distributions in Continuous Markov Models | Analytic Continuation | Ratio Populations | Newton's Proposition LXXI | Harmonic Sums of Integers with k Binary 1's | An Infinite Wall | Perpendicular Regression Of A Line | The Prismoidal Formula | On Random Chords | Potential Flow and d'Alembert's Paradox | Curvature of Linear Interpolation | Round-Robin Ties | Irrationality of Quadratic Sums | Time for a Rocking Chair | Net Area and Green's Theorem | How Leibniz Might Have Anticipated Euler | Meandering Convergence of a Dirichlet Series | Mean Distance from Vertex to Interior of Plane Figures | Aliasing and Uncertainty | Frequency Response of First-Order Lag | Mean Partial Sums of Non-Convergent Series | Constant Headings and Rhumb Lines | Inverse-Square Forces and Orthogonal Polynomials | Did Archimedes Know Gauss-Bonnet? | Enveloping Circular Arcs | Laplace Transforms | The Wave Equation and Permutation of Rays | Huygens' Principle | Recurrence Relations for Ordinary Differential Equations | The Curvatures of Hypersurfaces | Poisson Processes and Queues | Lagrangian and Hamiltonian Mechanics | Lead-Lag Frequency Response | Differential Operators and the Divergence Theorem | Precession in a Circle | Higher-Order Wave Equations and Matter Waves | Complete Solutions of Linear Systems | Noether's Theorem | Color Space, Physical Space, and Fourier Transforms | Series Solution of Relativistic Orbits | Geodesics by Differentiation | Inverse Functions | The Euler-Maclaurin Formula | Change of Variables in Multiple Integrals
Probability and Statistics | Evaluating Probabilities of Boolean Events | The Gambler's Ruin | Integrating the Bell Curve | Poisson Processes and Queues | Ratio Populations | Failure Rates, MTBFs, and All That | Boolean Expansion as Linear Interpolation | At Least One Girl | The Collector's Problem | Periodic and Continuous Repair Models | Collecting k Complete Sets of Coupons | Generalized Birthday Problem (N Items in M Bins) | Independence and Negation | Probabilities With Renaming | Dice Rolling A Given Sum | Redundant Systems With A Common Threat | Meeting Probabilities | A Better Lottery? | Bayesian Balls | Random High-Low Searching | Hierarchial Repair and Quantum State Reduction | Mnemonic Coins and Pattern Avoidance | Reliability with Mixed Periodic Repairs | Balls In Bins | Choice Without Context? | Combining Probabilities | A Barrel of Colors and Null Outcomes | Open-Loop and Closed-Loop Markov Models | The e in Petersburg | Weibull Analysis | Two Properties of Markov Models | Hail Encounters | Dual Failures with General Densities | Optimizing Your Wife | Complete Markov Models and Reliability | Probabilities and Velocities | Two In the Shop | Differences Between Normal Samples | Benford's Law | Perpendicular Regression Of A Line | On 13 Bridges | Random Triangles | The Complex Domain of Probability | Infinite Parallel Redundancy | N Points On Sphere Fall In One Hemisphere | Bernoulli Trials | Two-Dimensional Runs in Bernoulli Trials | Reliability of Series-Parallel Systems | Sequences of Characters in Random Strings | Botches, Failures, and Successes | Undetected Failures of Threat Protection | A Random Walk Through PI | The Shape of Coincidence | Markov Models with Boolean Transition Logic | The Expectation of Posterior Beliefs | Markov Models of Dual-Redundant Systems | Then There Were None | Generating Random Numbers In Order | Biased and Anti-Biased Variance Estimates | Markov's Marbles | The Y10K Problem, Pascal's Wager, and Petersberg | Expected Area of Random Polygon in a Circle | World's Oldest Man Dies | Asymptotic Rate of an Open Loop Markov Model | Probability of Intersecting Intervals | Timed Markov Models
Set Theory and Foundations | Representing Sets of Pure Order | Color Space, Physical Space, and Fourier Transforms | Global Reversibility of Cellular Automata | Guessing Faster Than Light | Hierarchial Repair and Quantum State Reduction | Spiritualism and Electromagnetism | The Necessity of the Quantum | Maxwell's Paradox of Attraction | Fuzzy Logic | Continuous Turing Machines | Fractal Logic | On Olber's Paradox | Hawking Radiation and Super-Acoustic Diffusion | Generalized Lorentz Transformations and Relative Rotation | Zeno and Uncertainty | Is Arithmetic Consistent? | Reconstructing Brouwer | The 3m Halo | Euclid's Plan and Proposition 6 | Constructible Points and Coverable Points | Round Trips and One-Way Speeds | A Mirror To Physics | Cantor's Diagonal Proof | Conditions for Relativity | Expansion as Gravity and Many Worlds | Function 34776 | An Infinite Wall | Omni-Directional Flux | Interfering With PI | Choice Without Context? | The Shortest Path To Trigonometric Identities | Reflections on The Mirror Question | Certainty In Math and Physics | Dialogue On Mathematical and Physical Knowledge | Is Mathematical Knowledge Cumulative? | Are All Triangles Isosceles? | Higher Order Dynamics | Dialogue on the Foundations of String Theory | Controversies Over the Equivalence Principle | On the Origins of Quantum Mechanics | Lorentz Boosts and the Electromagnetic Field | Did Poincare Anticipate Godel? | Attractive Forces From Quantum Exchanges | Weighing the Evidence | Something Like Quantum Mechanics | Marginalia | Timely Confessions | What is an Inertial Coordinate System? | If the Sun Were Suddenly to Explode | Is the World Provably Indeterminate? | Gamaliel's Principle | Preserving the Wave | This Business of Interpretation | Unreasonable Effectiveness | MathPages Wanted List | Newtonian Gravity In Closed or Curved Space | The Y10K Problem, Pascal's Wager, and Petersberg | Infinite Descent versus Induction | Newtonian and Relativistic Conservation Laws | Expulsion Sets | Interleaving Ad Infinitum | White Ravens and Black Swans | Spacetime Coordinates and Frames | Continuity and the Void | Potential Energy, Inertia, and Quantum Coherence | Cellular Automata | Harmonia Praestabilita | Central Forces from Retarded Action | Pitch and Color Recognition | General Relativity and the Principle of Inertia | Efficient and Final Causes | Feynman's Ants | Another Derivation of Mass-Energy Equivalence | Hawking Radiation as Delayed Choice | Null Cones in Cylindrical Dimensions | On Relativistic Precession | The Spacetime Hole and the EPR Arguments | Benevolent Design and the Anthropic Principle | Causality and the Wave Equation | Dirac's Belt | On The Many Principles of Equivalence | Curved Coordinate Systems and Fictitious Forces | Eigen Duality and Quasi-Eigen Systems
Reflections on Relativity | | Preface 1 | | 1. First Principles | 1.1 Experience and Spacetime 3 | 1.2 Systems of Reference 9 | 1.3 Inertia and Relativity 16 | 1.4 The Relativity of Light 23 | 1.5 Corresponding States 33 | 1.6 A More Practical Arrangement 44 | 1.7 Staircase Wit 58 | 1.8 Another Symmetry 65 | 1.9 Null Coordinates 72 | | 2. A Complex of Phenomena | 2.1 The Spacetime Interval 81 | 2.2 Force Laws and Maxwell's Equations 88 | 2.3 The Inertia of Energy 98 | 2.4 Doppler Shift for Sound and Light 111 | 2.5 Stellar Aberration 118 | 2.6 Mobius Transformations of the Night Sky 131 | 2.7 The Sagnac Effect 140 |
| 2.9 Accelerated Travels 159 | 2.10 The Starry Messenger 173 | 2.11 Thomas Precession 183 | | 3. Several Valuable Suggestions | 3.1 Postulates and Principles 192 | 3.2 Natural and Violent Motions 202 | 3.3 De Mora Luminis 209 | 3.4 Stationary Paths 218 | 3.5 A Quintessence of So Subtle a Nature 224 | 3.6 The End of My Latin 230 | 3.7 Zeno and the Paradox of Motion 238 | 3.8 A Very Beautiful Day 245 | 3.9 Constructing the Principles 251 | | 4. Weighty Arguments | 4.1 Immovable Spacetime 256 | 4.2 Inertial and Gravitational Separations 265 | 4.3 Free-Fall Equations 270 | 4.4 Force, Curvature, and Uncertainty 274 | 4.5 Conventional Wisdom 280 | 4.6 The Field of All Fields 292 | 4.7 The Inertia of Twins 297 | 4.8 The Breakdown of Simultaneity 301 | | 5. Extending the Principle | 5.1 Vis Inertiae 308 | 5.2 Tensors, Contravariant and Covariant 313 | 5.3 Curvature, Intrinsic and Extrinsic 323 | 5.4 Relatively Straight 340 | 5.5 Schwarzschild Metric from Kepler's 3rd Law 349 | 5.6 The Equivalence Principle 354 | 5.7 Riemannian Geometry 359 | 5.8 The Field Equations 370 | | 6. Ist Das Wirklich So? | 6.1 An Exact Solution 382 | 6.2 Anomalous Precession 389 | 6.3 Bending Light 400 | 6.4 Radial Paths in a Spherically Symmetrical Field 408 | 6.5 Intersecting Orbits 413 | 6.6 Ideal Clocks in Arbitrary Motion 419 |
| 6.8 Sources in Motion 431 | | 7. Cosmology | 7.1 Is the Universe Closed? 438 | 7.2 The Formation and Growth of Black Holes 449 | 7.3 Falling Into and Hovering Near A Black Hole 458 | 7.4 Curled-Up Dimensions 468 | 7.5 Packing Universes In Spacetime 472 | 7.6 Cosmological Coherence 478 | 7.7 Boundaries and Symmetries 486 | 7.8 Global Interpretations of Local Experience 493 | | 8. The Secret Confidence of Nature | 8.1 Kepler, Napier, and the Third Law 505 | 8.2 Newton's Cosmological Queries 510 | 8.3 The Helen of Geometers 518 |
| 8.5 Scholium 531 | 8.6 On Gauss' Mountains 536 | 8.7 Strange Meeting 541 | 8.8 Who Invented Relativity? 548 | 8.9 Paths Not Taken 559 | | 9. The Relativistic Topology | 9.1 In The Neighborhood 567 | 9.2 Up To Diffeomorphism 576 | 9.3 Higher-Order Metrics 579 | 9.4 Spin and Polarization 584 | 9.5 Entangled Events 587 | 9.6 Von Neumann's Postulate and Bell's Freedom 593 | 9.7 The Gestalt of Determinism 599 | 9.8 Quaedam Tertia Natura Abscondita 602 | 9.9 Locality and Temporal Asymmetry 606 | 9.10 Spacetime Mediation of Quantum Interactions 611 | | Conclusion 618 | | Appendix: Mathematical Miscellany 620 | | Bibliography 633
History | Mercurius in Sole Visus | The Thought of a Thought - Edgar Allan Poe | The Prismoidal Formula | Gerber's Gravity | Harmonia Mensurarum | Carnot, Organizer of Transversals | Roemer's Hypothesis | Magnetism and Earnshaw's Theorem | Nicolas Fatio and the Cause of Gravity | Dialogues | Stokes' Mistake | Timely Confessions | Conquering the Perihelion | Wonder En Is Gheen Wonder | The Quantity of Motion | Historical Assessments of the Fatio-Lesage Theory | Archimedes and the Square Root of 3 | Bertelsen's Number | Euclid's Plan and Proposition 6 | Mayan Numeration | Saturnday, Sunday, Moonday | The Dullness of 1729 | Berkeley and the Infidel | Newton's Birth Date and the Anni Mirabiles | Whittaker and the Aether | Franklin's Magic Squares | Fatio, Lesage, and the Camisards | Ancient Square Roots | Fermat's Infinite Descent | Negative Numbers | Hold Your Horses | Did Archimedes Know Gauss-Bonnet? | Herbert Dingle and the Twins | Egyptian Unit Fractions | The Metamorphosis of Judas Iscariot | Catch of the Day (153 Fishes) | The Guest Star | From Euclid to Gregory | What Happened to Dingle? | Guillaume, Guillaume, and Einstein | Eccentrics, Deferents, Epicycles, and Equants | Why Was Michelson Surprised? | The Most Teachable of Mortals | Zulu Hitler | Hipparchus on Coumpound Statements | Piero della Francesca's Tetrahedron Formula | Omar Khayyam On Cubics | The Ten Means of Ancient Greece | Heron's Formula and Brahmagupta's Generalization | Gravitational and Inertial Mass in Newton's Principia | Continuity and the Void |
| Galois's Analysis of Analysis | How Leibniz Might Have Anticipated Euler | Fermat's Fallibility | Adam's Gold | Constructing the Heptadecagon | The Moszkowski Affair | Prisca Sapientia | Harmonia Praestabilita | Einstein on the Inertia of Energy | Accidental Melodies | The Portraits of Emilie | Poincare Contemplates Copernicus | The Five Squarable Lunes | Reflections on Relativity | Archimedes on Spheres and Cylinders | Newton's Proposition LXXI | Platonic Solids and Plato's Theory of Everything | Lesage's Shadows | Remembering Socrates | The Bulging Earth | Translating Aristotle | The Longitude of Lewis and Clark | An Anomaly In Translation | Galileo's Law of Planetary Motion | Maxwell's Displacement and Einstein's Trace | Zur Farbenlehre | Kinetic Pressure and Tetrode's Star | Did Einstein Misunderstand Aberration? | The Doctrine of Chance
Animated (Java) Illustrations
Here are a few animated illustrations that are discussed in one or more notes on this site.
The Stars In The Sky
This applet shows the positions of all 297 stars with magnitudes less than 3.5, projected onto a sphere like a planetarium, and identifies all those of the first magnitude.
Kinematics of a Hypocycloidal Engine
This applet illustrates the workings of an unconventional internal combustion engine.
24 Electrons on a Sphere
This shows the minimum energy configuration of 24 charged particles on the surface of a sphere. The colors of the edges denote their lengths. Notice that the surface of this solid consists of 24/4 perfect squares, 24/3 perfect triangles, 24/2 additional "bi-gons", and of course 24/1 vertices, all arranged so that each vertex is identical. In addition, the vertices have a "handedness", so there are really two distinct versions of this solid.
Bell-Ringing Solid
This shape is what's called a "truncated octahedron", one of the 13 Archimedian solids. It has six square faces and eight hexagonal faces, making a total of 14 faces. The number of edges is 36, as required by Euler's formula F + V - E = 2. There is an interesting connection between this solid and the patterns of bell ringing.
Kepler's Rhombic Dodecahedron
This is one of the most fascinating of the simple solids, with an interesting correspondence to "the shape of coincidences".
The above illustrations are discussed in the notes
The Stars In The Sky
Hypocycloidal Engine
Min-Energy Configurations of Electrons on a Sphere
Ringing of the Changes (The Shape of 4!)
Meeting Probabilities and The Shape of Coincidence
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The Mathematical Atlas
INDEX USING MATHEMATICS SUBJECT CLASSIFICATION
The Divisions of Mathematics
In order to find one's way around the collection of mathematical ideas, it is useful to organize them and classify them in some way into parts.
...
How many parts of mathematics -- Two? Eight? Sixty-three?
...
The image at right shows a "map" of the subfields of mathematics. These are the major classification groupings used at this site and by most research mathematics projects. The sizes and positions of the "bubbles" are computed to reflect the sizes and relatedness of the various disciplines. On our tour, we'll highlight some of the main groupings of these areas (the different color groups).
...
Partial Differential Equations (Methods of Integrations) [322]
Partial Differential Equations (Initial Value Problems) [321]
Partial Differential Equations of First Order [324]
Monge-Ampère Equations [278]
Partial Differential Equations of Elliptic Type [323]
Partial Differential Equations of Hyperbolic Type [325]
Partial Differential Equations of Parabolic Type [327]
Partial Differential Equations of Mixed Type [326]
Green's Functions [188]
Green's Operators [189]
Integral Equations [217]
Integrodifferential Equations [222]
Special Functional Equations [388]
Pseudodifferential Operators [345]
Special Functions
Special Functions [389]
Generating Functions [177]
Elliptic Functions [134]
Gamma Function [174]
Hypergeometric Functions [206]
Spherical Functions [393]
Functions of Confluent Type [167]
Bessel Functions [039]
Ellipsoidal Harmonics [133]
Mathieu Functions [268]
Numerical Analysis
Numerical Methods [300]
Interpolations [223]
Error Analysis [138]
Numerical Solutions of Linear Equations [302]
Numerical Solutions of Algebraic Equations [301]
Numerical Computations of Eigenvalues [298]
Numerical Integration [299]
Numerical Solutions of Ordinary Differential Equations [303]
Numerical Solutions of Partial Differential Equations [304]
Analog Computation [019]
Evaluation of Functions [142]
Computer Science and Combinatorics
Automata [031]
Computers [075]
Coding Theory [063]
Cybernetics [095]
Random Numbers [354]
Simulations [385]
Data Processing [096]
Mathematical Models in Biology [263]
Complexity of Computations [071]
Combinatorics [066]
Latin Squares [241]
Graph Theory [186]
Probability Theory
Probability Theory [342]
Probability Measures [341]
Limit Theorems in Probability Theory [250]
Stochastic Processes [407]
Markov Processes [261]
Markov Chains [260]
Brownian Motion [045]
Diffusion Processes [115]
Additive Processes [005]
Branching Processes [044]
Martingales [262]
Stationary Processes [395]
Gaussian Processes [176]
Stochastic Differential Equations [406]
Ergodic Theory [136]
Stochastic Control and Stochastic Filtering [405]
Probabilistic Methods in Statistical Mechanics [340]
Statistics
Statistical Data Analysis [397]
Statistical Inference [401]
Statistic [396]
Sampling Distributions [374]
Statistical Models [403]
Statistical Decision Functions [398]
Statistical Estimation [399]
Statistical Hypothesis Testing [400]
Multivariable Analysis [280]
Robust and Nonparametric Methods [371]
Time Series Analysis [421]
Design of Experiments [102]
Sample Survey [373]
Statistical Quality Control [404]
Econometrics [128]
Biometrics [040]
Psychometrics [346]
Insurance Mathematics [214]
Mathematical Programming and Operations Research
Mathematical Programming [264]
Linear Programming [255]
Quadratic Programming [349]
Nonlinear Programming [292]
Network Flow Problems [281]
Integer Programming [215]
Stochastic Programming [408]
Dynamic Programming [127]
Game Theory [173]
Differential Games [108]
Control Theory [086]
Information Theory [213]
Operations Research [307]
Inventory Control [227]
Scheduling and Production Planning [376]
Mechanics and Theoretical Physics
Systems of Units [414]
Dimensional Analysis [116]
Variational Principles [441]
Mechanics [271]
Spherical Astronomy [392]
Celestial Mechanics [055]
Orbit Determination [309]
Three-Body Problem [420]
Hydrodynamics [205]
Hydrodynamical Equations [204]
Magnetohydrodynamics [259]
Turbulence and Chaos [433]
Wave Propagation [446]
Oscillations [318]
Geometric Optics [180]
Electromagnetism [130]
Networks [282]
Thermodynamics [419]
Statistical Mechanics [402]
Boltzman Equation [041]
Relativity [359]
Unified Field Theory [434]
Quantum Mechanics [351]
Lorentz Group [258]
Racah Algebra [353]
Scattering Theory [375]
Second Quantization [377]
Field Theory [150]
S-Matrices [386]
Feynman Integrals [146]
Elementary Particles [132]
Renormalization Group [361]
Nonlinear Lattice Dynamics [287]
Solitons [387]
Approximation Methods in Physics [025]
Inequalities in Physics [212]
History of Mathematics
Ancient Mathematics [024]
Greek Mathematics [187]
Roman and Medieval Mathematics [372]
Arab Mathematics [026]
Indian Mathematics [209]
Chinese Mathematics [057]
Japanese Mathematics (Wasan) [230]
Renaissance Mathematics [360]
Mathematics in the 17th Century [265]
Mathematics in the 18th Century [266]
Mathematics in the 19th Century [267]
Abel, Niels Henrik [001]
Artin, Emil [028]
Bernoulli Family [038]
Cantor, Georg [047]
Cartan, Élie [050]
Cauchy, Augustin Louis [053]
Dedekind, Julius Wilhelm Richard [098]
Descartes, René [101]
Dirichlet, Peter Gustav Lejeune [119]
Einstein, Albert [129]
Euler, Leonhard [141]
Fermat, Pierre de [144]
Fourier, Jean Baptiste Joseph [158]
Galois, Évariste [171]
Gauss, Carl Friedrich [175]
Gödel, Kurt [184]
Hilbert, David [196]
Jacobi, Carl Gustav Jacob [229]
Klein, Felix [233]
Kronecker, Leopold [236]
Lagrange, Joseph Louis [238]
Laplace, Pierre Simon [239]
Lebesgue, Henri Leon [244]
Leibniz, Gottfried Wilhelm [245]
Lie, Marius Sophus [247]
Newton, Isaac [283]
Pascal, Blaise [329]
Poincaré, Henri [335]
Riemann, Georg Friedrich Bernhard [363]
Takagi, Teiji [415]
Viète, François [444]
Von Neumann, John [445]
Weierstrass, Karl [447]
Weyl, Hermann [448]
Erstellt: 2011-11
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Rhonda Number (W3)
Wie der Zufall so spielt. Der (vermutlich) Mathematiker "K. S. Brown" hatte einen Bekannten namens "Rhonda", der in einem Haus/Anwesen/Wohnblock mit der Nummer "25662" wohnte. Und diese Nummer erfüllte just die Anforderung an eine "Rhonda-Nummer".
A positive integer n is called a "base-b Rhonda number" if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by "K. S. Brown" after an acquaintance of his whose residence number 25662 satisfies this property. The etymology of the term is therefore similar to the Smith numbers.
25662 is a Rhonda number to base-10 since its prime factorization is
25662 = 2*3*7*13*47
and the product of its base-10 digits satisfies
2*5*6*6*2 = 720 = 10*(2+3+7+13+47)
The Rhonda numbers to base 10 are 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, ... (Sloane's A099542). The corresponding sums of prime factors are 24, 24, 28, 30, 54, 72, 32, 24, 48, 72, ... (Sloane's A099543).
Rhonda numbers exist only for bases that are composite since there is no way for the product of integers less than a prime b to have b as a factor.
The first few Rhonda numbers for small composite bases b are summarized in the following table.
...
JsMath is a means of including mathematical notation in web pages. It interprets TeX code within your document and uses JavaScript, CSS and unicode fonts to typeset the resulting formulas. It works across multiple browsers and platforms, without MathML
TEX-Dateien und -Tools
Dieses Verzeichnis listet nützliche kleine TeX-Dateien auf, deren Makros man bei dem ein oder anderen mathematischen Dokument, wie z.B. einem Vorlesungsskrip oder einem Versuchsprotokoll (in Physik) nicht jedesmal von neu in seinen Editor hämmern möchte.
First published Thu Jul 11, 2002
Set Theory is the mathematical science of the infinite. It studies properties of sets, abstract objects that pervade the whole of modern mathematics. The language of set theory, in its simplicity, is sufficiently universal to formalize all mathematical concepts and thus set theory, along with Predicate Calculus, constitutes the true Foundations of Mathematics. As a mathematical theory, Set Theory possesses a rich internal structure, and its methods serve as a powerful tool for applications in many other fields of Mathematics. Set Theory, with its emphasis on consistency and independence proofs, provides a gauge for measuring the consistency strength of various mathematical statements. There are four main directions of current research in set theory, all intertwined and all aiming at the ultimate goal of the theory: to describe the structure of the mathematical universe. They are: inner models, independence proofs, large cardinals, and descriptive set theory. See the relevant sections in what follows.
1. The Essence of Set Theory
2. Origins of Set Theory
3. The Continuum Hypothesis
4. Axiomatic Set Theory
5. The Axiom of Choice
6. Inner Models
7. Independence Proofs
8. Large Cardinals
9. Descriptive Set Theory
Bibliography
Other Internet Resources
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...
straightdope
A simpler value for pi
Indiana wollte einst den Wert von "Pi" per Gesetz auf den Wert 3 festlegen.
Did a state legislature once pass a law saying pi equals 3?
February 22, 1991
Dear Cecil:
In Science magazine a while back an article about the latest attempts to calculate pi to the umpteen zillionth decimal place made a passing reference to a curious Oklahoma law. It said Oklahoma legislators had passed a law making pi equal to 3.0. I also remember Robert Heinlein in one of his novels mentioning that Tennessee had passed a similar law. Did either of these states ever pass such a law? Are they still on the books? What are the penalties if I proclaim that pi equals 3.14159...?
— Wulf Losee, Andover, Connecticut
Dear Wulf:
Cecil had heard this story too, only the state in question was Kansas, leading him to believe the whole thing was made up by big-city sharpies having a little fun at the expense of the rustics. However, with the help of Joseph Madachy, editor of the Journal of Recreational Mathematics, I've learned the story does have a germ of truth to it.
...
(E?)(L?) http://archives.math.utk.edu/topics/
In these pages, you will find links to various WWW resources on Mathematics. They are organized by topics.
Abstract Algebra | Algebra | Analysis | Applied Mathematics | Arithmetic | Art & Music | Calculus | Cellular Automata | Combinatorics | Complex Analysis | Computational Geometry | Computational Science | Computer Algebra / Cryptology |
| Differential Geometry | Discrete Mathematics | Dynamical Systems | Fluid Dynamics | Fourier Analysis & Wavelets | Fractals | Geometry | History of Mathematics | Industrial Mathematics | Linear and Matrix Algebra | Linear & Nonlinear Programming | Logic & Set Theory | Mathematics Education | Mathematical Biology | Miscellaneous | Multivariable Calculus | Nonlinear Dynamics | Number Theory | Numerical Analysis | Ordinary Differential Equations | Partial Differential Equations | Pre-Calculus | Probability Theory | Statistics | Topology | Trigonometry
uvic
The (Combinatorial) Object Server
(E?)(L?) http://www.theory.csc.uvic.ca/~cos/
What is it?
The idea is that you specify a type of combinatorial object, together with specific parameter values, and COS will return to you a list of all such objects. COS can generate permutations, combinations, various types of trees, unlabelled graphs, linear extensions of posets, pentomino puzzle solutions, numerical partitions, and a host of other combinatorial objects.
In some instances you may specify the order in which the objects are generated (such as lexicographic or a Gray code order). Almost always the output may be presented in a variety of formats which you may specify. These different formats include well-known correspondences and representations of the objects. For example, permutations may be ouput in one-line notation, in cycle notation, or as a pair of Standard Young Tableau under the Schensted correspondence.
Quick jump to math help:
Calculus, Derivatives Calculus, Integration Calculus, Quotient Rule Coins, Counting Combinations, Finding all Complex Numbers, Adding of Complex Numbers, Calculating with Complex Numbers, Multiplying Complex Numbers, Powers of Complex Numbers, Subtracting Conversion, Area Conversion, Lengths Conversion, Mass Conversion, Power Conversion, Speed Conversion, Temperatures Conversion, Volume Data Analysis, Finding the Average Data Analysis, Finding the Standard Deviation Data Analysis, Histograms Decimals, Convert to a fraction Electricity, Cost of Factoring, Integers Factors, Greatest Common Factors, Least Common Fractions, Adding Fractions, Comparing Fractions, Converting Fractions, Convert to a decimal Fractions, Dividing Fractions, Multiplying Fractions, Reducing Fractions, Subtracting Fractions, What are they Geometry, Boxes Geometry, Circles Geometry, Cylinders Geometry, Rectangles Geometry, Right Triangles Geometry, Spheres Geometry, Squares Graphing, Lines Graphing, Any function Graphing, Circles Graphing, Ellipses Graphing, Hyperbolas Graphing, Inequalities Graphing, Polar Plot Graphing, (x,y) point Inequalities, Graphing Inequalities, Solving Interest, Compound Interest, Simple Lines, The Equation from point and slope Lines, The Equation from slope and y-int Lines, The Equation from two points Loan, Payment Schedule Lottery, Finding odds Math, Practicing Polynomials Math, Practicing the Basics Metric system, Converting Numbers, Adding Numbers, Calculating with Numbers, Calculating with variables Numbers, Dividing Numbers, Multiplying Numbers, Number line comparing Numbers, Number line Numbers, Place Value Numbers, Pronouncing Numbers, Rounding Numbers, Subtracting Parabolas, Graphing Polynomials, Adding/Subtracting Polynomials, Completing the Square Polynomials, Dividing Polynomials, Factoring Difference of Squares Polynomials, Factoring Trinomials Polynomials, Factoring with GCF Polynomials, Multiplying Polynomials, Raising to a power Practice, Math problems Proportions, What are they Quadratic Equations, Quadratic Formula Quadratic Equations, Solve by Factoring Radicals, Other Roots Radicals, Square Roots Ratios, What are they Retirement, Saving for Sale Price, Calculating Scientific Notation, Converting Scientific Notation, Dividing Scientific Notation, Multiply Shapes, Rectangles Simplifying, Anything Simplifying, Exponents Simplifying, Like Terms Simplifying, Products Time, Thinking about Tip, Figuring a Trigonometry, Expressions Trigonometry, Right Triangles Windchill, Figuring
MathWorldTM is the web's most complete mathematical resource, assembled over more than a decade by internet encyclopedist Eric W. Weisstein with assistance from the mathematics and internet communities.
MathWorld is a comprehensive and interactive mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. Like the vibrant and constantly evolving discipline of mathematics, this site is continuously updated to include new material and incorporate new discoveries.
INDEX: Algebra | Applied Mathematics | Calculus and Analysis | Discrete Mathematics | Foundations of Mathematics | Geometry | History and Terminology | Number Theory | Probability and Statistics | Recreational Mathematics | Topology | Animations | Live 3D Graphics
Eine Spitzensite mit vielen Erklärungen zu mathematischen Begriffen.
