Portal:Mathematics/Did you know
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Current DYKs
‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/1: ...that outstanding mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/2: ...that a regular heptagon is the regular polygon with the fewest number of sides which is not constructible with a compass and straightedge?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/3: ...that the Gudermannian function relates the regular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/4: ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/5: ...that a ball can be cut up and reassembled into two balls the same size as the original (Banach-Tarski paradox)?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/6: ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/7: ...that Euler found 59 more amicable numbers while for 2000 years, only 3 pairs had been found before him?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/8: ...that you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/9: ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/10: ...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/11: ...that every natural number can be written as the sum of four squares?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/12: ...that the largest known prime number is over 22 million digits long?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/13: ...that the set of rational numbers is equal in size to the subset of integers; that is, they can be put in one-to-one correspondence?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/14: ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/15: ...that it is unknown whether π and e are algebraically independent?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/16: ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/17: ...that it is possible for a three dimensional figure to have a finite volume but infinite surface area? An example of this is Gabriel's Horn.‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/18: ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/19: ...that the primality of a number can be determined using only a single division using Wilson's Theorem?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/20: ...that the line separating the numerator and denominator of a fraction is called a solidus if written as a diagonal line or a vinculum if written as a horizontal line?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/21: ...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/22: ... that there are 115,200 solutions to the ménage problem of permuting six female-male couples at a twelve-person table so that men and women alternate and are seated away from their partners?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/23: ... that mathematician Paul Erdős called the Hadwiger conjecture, a still-open generalization of the four-color problem, "one of the deepest unsolved problems in graph theory"?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/24: ...that the six permutations of the vector (1,2,3) form a regular hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/25: ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/26: ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/27: ...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/28: ...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/29: ...the Piphilology record (memorizing digits of Pi) is 70000 as of Mar 2015?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/30: ...with a Perrin number denoted P(i), i=1,2,3..., when i is prime then P(i) is composite, being divisible by i?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/31: ...that Auction theory was successfully used in 1994 to sell FCC airwave spectrum, in a financial application of game theory?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/32: ...properties of Pascal's triangle have application in many fields of mathematics including combinatorics, algebra, calculus and geometry?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/33: ...work in artificial intelligence makes use of Swarm intelligence, which has foundations in the behavorial examples found in nature of ants, birds, bees, and fish among others?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/34: ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/35: ...that Modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/36: ... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat if and only if the sum of every other angle between consecutive creases is 180º?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/37: ... that, in the Rule 90 cellular automaton, any finite pattern eventually fills the whole array of cells with copies of itself?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/38: ... that, while the criss-cross algorithm visits all eight corners of the Klee–Minty cube when started at a worst corner, it visits only three more corners on average when started at a random corner?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/39: ...that in senary, all prime numbers other than 2 and 3 end in 1 or a 5?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/40: ... if the integer n is prime, then the nth Perrin number is divisible by n?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/41: ...that it is impossible to trisect a general angle using only a ruler and a compass?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/42: ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/43: ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/44: ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/45: ... that economists blame market failures on non-convexity?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/46: ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/47: ... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/48: ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/49: ... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/50: ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/51: ... that the Hadwiger conjecture implies that the external surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/52: ... that an equitable coloring of a graph, in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/53: ... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/54: ...that it is possible to stack identical dominoes off the edge of a table to create an arbitrarily large overhang?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/55: ...that in Floyd's algorithm for cycle detection, the tortoise and hare move at very different speeds, but always finish at the same spot?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/56: ...that in graph theory, a pseudoforest can contain trees and pseudotrees, but cannot contain any butterflies, diamonds, handcuffs, or bicycles?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/57: ...that it is not possible to configure two mutually inscribed quadrilaterals in the Euclidean plane, but the Möbius–Kantor graph describes a solution in the complex projective plane?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/58: ...that the six permutations of the vector (1,2,3) form a hexagon in 3D space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/59: ...that the Rule 184 cellular automaton can simultaneously model the behavior of cars moving in traffic, the accumulation of particles on a surface, and particle-antiparticle annihilation reactions?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/60: ...that a cyclic cellular automaton is a system of simple mathematical rules that can generate complex patterns mixing random chaos, blocks of color, and spirals?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/61: ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/62: ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/63: ...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a right-angled triangle?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/64: ...that the orthocenter, circumcenter, centroid and the centre of the nine-point circle all lie on one line, the Euler line?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/65: ...that an arbitrary quadrilateral will tessellate?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/66: ...that it has not been proven whether or not every even integer greater than two can be expressed as the sum of two primes?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/67: ...that the sum of the first n odd numbers divided by the sum of the next n odd numbers is always equal to one third?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/68: ...that i to the power of i, where i is the square root of -1, is a real number?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/69: ...an infinite, nonrepeating decimal can be represented using only the number 1 using continued fractions?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/70: ...there are 19 consecutive prime numbers ending in the digit 1, starting from 253931039382791?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/71: ...that the Electronic Frontier Foundation funds awards for the discovery of prime numbers beyond certain sizes?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/72: ...that pi can be computed using only the number 2 by the work of Viète?‹The template Exists is being considered for deletion.›
- Portal:Mathematics/Did_you_know/73: … that the Riemann Hypothesis, one of the Millennium Problems, depends on the asymptotic growth of the Mertens Function?‹The template Exists is being considered for deletion.› ‹The template Exists is being considered for deletion.›
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