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Let t, u, and v be the lengths of the tangents to a circle C from the vertices of a triangle with sides of lengths a, b, and c. Then the condition that C is tangent to the ...

A pyritohedron is an irregular dodecahedron composed of identical irregular pentagons. The name "pyritohedron" derives from that fact that a common crystal form in pyrite has ...

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

Given a Pythagorean triple (a,b,c), the fractions a/b and b/a are called Pythagorean fractions. Diophantus showed that the Pythagorean fractions consist precisely of ...

The notation Q^_ denotes the algebraic closure of the rational numbers Q. This is equivalent to the set of algebraic numbers, sometimes denoted A.

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...

A quadratic polynomial is a polynomial of degree 2. A univariate quadratic polynomial has the form f(x)=a_2x^2+a_1x+a_0. An equation involving a quadratic polynomial is ...

A quadratic recurrence is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a second-degree polynomial in x_k with k<n. For example, x_n=x_(n-1)x_(n-2) ...

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 catacaustic of the quadrifolium with arbitrary radiant point is a complicated function. A few example are illustrated above.