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Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

An equivalence class is defined as a subset of the form {x in X:xRa}, where a is an element of X and the notation "xRy" is used to mean that there is an equivalence relation ...

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each ...

Each of the sacred unit fractions which the ancient Egyptians attributed to the six parts of the eye of the god Horus: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions, ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

An (n,k) fountain is an arrangement of n coins in rows such that exactly k coins are in the bottom row and each coin in the (i+1)st row touches exactly two in the ith row. ...

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental domain of G in S if S is the union of conjugates of F, i.e., S= union _(g ...