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The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...

The Wormald graph is a unit-distance 4-chromatic graph with girth 5 on 13+5(13; 5)=6448 vertices.

cos(pi/(30)) = 1/4sqrt(7+sqrt(5)+sqrt(6(5+sqrt(5)))) (1) cos((7pi)/(30)) = 1/4sqrt(7-sqrt(5)+sqrt(6(5-sqrt(5)))) (2) cos((11pi)/(30)) = 1/4sqrt(7+sqrt(5)-sqrt(6(5+sqrt(5)))) ...

The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron of unit edge length by ...

cos(pi/(15)) = 1/8(sqrt(30+6sqrt(5))+sqrt(5)-1) (1) cos((2pi)/(15)) = 1/8(sqrt(30-6sqrt(5))+sqrt(5)+1) (2) cos((4pi)/(15)) = 1/8(sqrt(30+6sqrt(5))-sqrt(5)+1) (3) ...

Values of the trigonometric functions can be expressed exactly for integer multiples of pi/20. For cosx, cos(pi/(20)) = 1/4sqrt(8+2sqrt(10+2sqrt(5))) (1) cos((3pi)/(20)) = ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

A block matrix is a matrix that is defined using smaller matrices, called blocks. For example, [A B; C D], (1) where A, B, C, and D are themselves matrices, is a block ...