Portal:Mathematics/Did you know

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Instructions

1. Add new items at the first redlink in the section below
2. Update the main page so that the {{Did you know|total=12|show=9}} has the "total" parameter equal to the number of non-empty subpages. The "show" paramter must not be more than 20.

If you have any difficulty, problems or questions relating to the technical side of this sub-page, ask at the Portal's talk page.

Current DYKs

1. 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?
2. 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?
3. 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?
4. 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?
5. Portal:Mathematics/Did_you_know/5: ...that a sphere can be cut up and reassembled into two spheres the same size as the original (Banach-Tarski paradox)?
6. 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?
7. 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?
8. Portal:Mathematics/Did_you_know/8: ...that you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.
9. Portal:Mathematics/Did_you_know/9: ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?
10. 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?
11. Portal:Mathematics/Did_you_know/11: ...that every natural number can be written as the sum of four squares?
12. Portal:Mathematics/Did_you_know/12: ...that the largest known prime is over 9 million digits long?
13. 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?
14. 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.
15. Portal:Mathematics/Did_you_know/15: ...that it is unknown whether π and e are algebraically independent?
16. Portal:Mathematics/Did_you_know/16: ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
17. 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.
18. Portal:Mathematics/Did_you_know/18: ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
19. Portal:Mathematics/Did_you_know/19: ...that the primality of a number can be determined using only a single division using Wilson's Theorem?
20. 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.
21. 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.
22. Portal:Mathematics/Did_you_know/22: Portal:Mathematics/Did you know/22