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A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...

A k×n Latin rectangle is a k×n matrix with elements a_(ij) in {1,2,...,n} such that entries in each row and column are distinct. If k=n, the special case of a Latin square ...

If there is no integer 0<x<p such that x^2=q (mod p), i.e., if the congruence (35) has no solution, then q is said to be a quadratic nonresidue (mod p). If the congruence ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...