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For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

A set S with a single point P removed is called a punctured set, written S\{P}.

A field F in which any Pythagorean extension of F coincides with F.

The positive rational numbers, denoted Q^+.

One of the four regions of the plane defined by the four possible combinations of signs (+,+), (+,-), (-,+), and (-,-) for (x,y).

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...

The analog of trilinear coordinates for tetrahedra.

One of the operations exists exists (called the existential quantifier) or for all forall (called the universal quantifier, or sometimes, the general quantifier). However, ...

V=100(Q_3-Q_1)/(Q_3+Q_1), where Q_1 and Q_3 are the first and third quartiles and Q_3-Q_1 is the interquartile range.

In the classical quasithin case of the quasithin theorem, if a group G does not have a "strongly embedded" subgroup, then G is a group of Lie-type in characteristic 2 of Lie ...