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An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...

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 ...

An extension of an arbitrary field F of the form F(sqrt(1+lambda^2)), where lambda in F.

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 ...

A Pythagorean triangle is a right triangle with integer side lengths (i.e., whose side lengths (a,b,c) form a Pythagorean triple). A Pythagorean triangle with GCD(a,b,c)=1 is ...

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

The positive rational numbers, denoted Q^+.

The doublestruck capital letter Q, Q, denotes the field of rationals. It derives from the German word Quotient, which can be translated as "ratio." The symbol Q first ...