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The (m,n)-windmill graph is the graph obtained by taking m copies of the complete graph K_n with a vertex in common (Gallian 2011, p. 16). The (m,n)-windmill graph is ...

Geometry

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

Checkers is a two-player game with the most common variant played on an 8×8 checkerboard with each player starts with twelve pieces of a fixed color on opposite sites of the ...

The Costa surface is a complete minimal embedded surface of finite topology (i.e., it has no boundary and does not intersect itself). It has genus 1 with three punctures ...

A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place. For example, the only derangements of {1,2,3} are {2,3,1} and ...

A digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...