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Divide the sides of a quadrilateral into three equal parts. The figure formed by connecting and extending adjacent points on either side of a polygon vertex is a ...

A p-elementary subgroup of a finite group G is a subgroup H which is the group direct product H=C_n×P, where P is a p-group, C_n is a cyclic group, and p does not divide n.

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

Champernowne's constant C=0.12345678910111213... (1) (OEIS A033307) is the number obtained by concatenating the positive integers and interpreting them as decimal digits to ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...