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A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

3 is the only integer which is the sum of the preceding positive integers (1+2=3) and the only number which is the sum of the factorials of the preceding positive integers ...

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...

A number n is called an Egyptian number if it is the sum of the denominators in some unit fraction representation of a positive whole number not consisting entirely of 1s. ...

The exponential factorial is defined by the recurrence relation a_n=n^(a_(n-1)), (1) where a_0=1. The first few terms are therefore a_1 = 1 (2) a_2 = 2^1=2 (3) a_3 = ...

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits of its distinct prime factors (excluding 1). ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...