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Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

A polyomino is a generalization of the domino to a collection of n squares of equal size arranged with coincident sides. Polyominos were originally called "super-dominoes" by ...

Riemann defined the function f(x) by f(x) = sum_(p^(nu)<=x; p prime)1/nu (1) = sum_(n=1)^(|_lgx_|)(pi(x^(1/n)))/n (2) = pi(x)+1/2pi(x^(1/2))+1/3pi(x^(1/3))+... (3) (Hardy ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...

Two fractions are said to be adjacent if their difference has a unit numerator. For example, 1/3 and 1/4 are adjacent since 1/3-1/4=1/12, but 1/2 and 1/5 are not since ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

A node which is one graph edge further away from a given node in a rooted tree.