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When referring to a planar object, "fixed" means that the object is regarded as fixed in the plane so that it may not be picked up and flipped. As a result, mirror images are ...

The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let f be a function over the reals" means "Let f be a ...

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

The symbol v variously means "disjunction" (i.e., OR in logic) or "join" (for a lattice).

Pre-Algebra

The altitudes of a triangle are the Cevians A_iH_i that are perpendicular to the legs A_jA_k opposite A_i. The three altitudes of any triangle are concurrent at the ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...