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Determined the possible values of r and n for which there is an identity of the form (x_1^2+...+x_r^2)(y_1^2+...+y_r^2)=z_1^2+...+z_n^2.

A polynomial with real positive coefficients and roots which are either negative or pairwise conjugate with negative real parts.

Two lines in hyperbolic geometry which diverge from each other in both directions.

A space having dimension n>3.

A 32-sided polygon. The regular icosidodecagon is a constructible polygon, and the regular icosidodecahedron of side length 1 has inradius r, circumradius R, and area A r = ...

A 24-sided polygon. The regular icositetragon is constructible. For side length 1, the inradius r, circumradius R, and area A are given by r = 1/2(2+sqrt(2)+sqrt(3)+sqrt(6)) ...

A type of point at infinity in which parallel lines in the hyperbolic plane intersect at infinity in one direction, while diverging from one another in the other.

A "line" having imaginary coefficients in its equations which can arise in algebraic geometry.

Definitions about a set which depend on the entire set.

A word or string which is not admissible.