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The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as ...

An octic graph is a regular graph of degree eight. The numbers of simple octic graphs on n=9, 10, 11, ... nodes are 1, 6, 94, 10786, 3459386, ... (OEIS A014378). Examples are ...

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

An integer sequence whose terms are defined in terms of number-related words in some language. For example, the following table gives the sequences of numbers having digits ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...