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An involution of a set S is a permutation of S which does not contain any permutation cycles of length >2 (i.e., it consists exclusively of fixed points and transpositions). ...

The triangle DeltaA^*B^*C^* obtained by reflecting the vertices of a reference triangle DeltaABC about the opposite sides is called the reflection triangle (Grinberg 2003). ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

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.

A number taken to the power 3 is said to be cubed, so x^3 is called "x cubed." This terminology derives from the fact that the volume of a cube of edge length x is given by ...

The symbol used in continental Europe, most of North and South America (with the exception of the United States and Canada), and most of Africa to denote a decimal point, for ...