Portal : Mathematics/Did you know archive
Portal:Mathematics/Did_you_know/1 : ...that the mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture , which he declined?Portal:Mathematics/Did_you_know/2 : ...that a regular heptagon is the regular polygon with the fewest sides which is not constructible with a compass and straightedge ?Portal:Mathematics/Did_you_know/3 : ...that the regular trigonometric functions and the hyperbolic trigonometric functions can be related without using complex numbers through the Gudermannian function ?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?Portal:Mathematics/Did_you_know/5 : ...that a ball can be cut up and reassembled into two balls, each the same size as the original (Banach-Tarski paradox )?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 ?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?Portal:Mathematics/Did_you_know/8 : ...that you cannot knot strings in 4 dimensions, but you can knot 2-dimensional surfaces , such as spheres ?Portal:Mathematics/Did_you_know/9 : ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?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?Portal:Mathematics/Did_you_know/11 : ...that every natural number can be written as the sum of four squares ?Portal:Mathematics/Did_you_know/12 : ...that the largest known prime number is nearly 25 million digits long?Portal:Mathematics/Did_you_know/13 : ...that the set of rational numbers is equal in size to the set of integers ; that is, they can be put in one-to-one correspondence ?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 .Portal:Mathematics/Did_you_know/15 : ...that it is unknown whether π and e algebraically independent ?Portal:Mathematics/Did_you_know/16 : ...that a nonconvex polygon with three convex vertices is called a pseudotriangle ?Portal:Mathematics/Did_you_know/17 : ...that it is possible for a three-dimensional figure to have a finite volume but infinite surface area , such as Gabriel's Horn ?Portal:Mathematics/Did_you_know/18 : ... that as the dimension of a hypersphere tends to infinity, its "volume " (content) tends to 0?Portal:Mathematics/Did_you_know/19 : ...that the primality of a number can be determined using only a single division using Wilson's Theorem ?Portal:Mathematics/Did_you_know/20 : ...that the line separating the numerator and denominator of a fraction is called a solidus vinculum 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?Portal:Mathematics/Did_you_know/22 : ... that there are 115,200 solutions to the ménage problem permuting six female-male couples at a twelve-person table so that men and women alternate and are seated away from their partners?Portal:Mathematics/Did_you_know/23 : ... that mathematician Paul Erdős called the Hadwiger conjecture four-color problem , "one of the deepest unsolved problems in graph theory "?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 Portal:Mathematics/Did_you_know/25 : ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram ?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?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 ?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 Portal:Mathematics/Did_you_know/29 : ...the Piphilology record (memorizing digits of Pi ) is 70000 as of Mar 2015?Portal:Mathematics/Did_you_know/30 : ...that people are significantly slower to identify the parity of zero than other whole numbers, regardless of age, language spoken, or whether the symbol or word for zero is used?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 ?Portal:Mathematics/Did_you_know/32 : ...properties of Pascal's triangle have application in many fields of mathematics including combinatorics , algebra , calculus and geometry ?Portal:Mathematics/Did_you_know/33 : ...work in artificial intelligence makes use of swarm intelligence , which has foundations in the behavioral examples found in nature of ants, birds, bees, and fish among others?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?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?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?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?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 corneron average when started at a random cornerPortal:Mathematics/Did_you_know/39 : ...that in senary , all prime numbers Portal:Mathematics/Did_you_know/40 : ...that, for all prime numbers p , the p th Perrin number is divisible by p ?Portal:Mathematics/Did_you_know/41 : ...that it is impossible to trisect a general angle ruler and a compass ?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 ?Portal:Mathematics/Did_you_know/43 : ...that the 1966 publication disproving Euler's sum of powers conjecture , proposed nearly 200 years earlier, consisted of only two sentences?Portal:Mathematics/Did_you_know/44 : ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions ?Portal:Mathematics/Did_you_know/45 : ... that economists blame market failures on non-convexity ?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?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 ?Portal:Mathematics/Did_you_know/48 : ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle ?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?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 ?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?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?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 ?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?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?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?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 ?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 ?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?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?Portal:Mathematics/Did_you_know/61 : ...that a nonconvex polygon with three convex vertices is called a pseudotriangle ?Portal:Mathematics/Did_you_know/62 : ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory ?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?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 Portal:Mathematics/Did_you_know/65 : ...that an arbitrary quadrilateral will tessellate ?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 ?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?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?Portal:Mathematics/Did_you_know/69 : ...an infinite, nonrepeating decimal can be represented using only the number 1 using continued fractions ?Portal:Mathematics/Did_you_know/70 : ...that 253931039382791 and the following 18 prime numbers all end in the digit 1?Portal:Mathematics/Did_you_know/71 : ...that the Electronic Frontier Foundation funds awards for the discovery of prime numbers beyond certain sizes?Portal:Mathematics/Did_you_know/72 : ...that pi can be computed using only the number 2 by the work of Viète ?Portal:Mathematics/Did_you_know/73 : … that the Riemann Hypothesis , one of the Millennium Problems , depends on the asymptotic growth of the Mertens Function ?Portal:Mathematics/Did_you_know/74 : … that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater?Portal:Mathematics/Did_you_know/75 : … that the best known lower bound for the length of the smallest superpermutation was first posted anonymously to the internet imageboard 4chan ?Portal:Mathematics/Did_you_know/76
