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For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

An arrangement of points with no three collinear, or of lines with no three concurrent.

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

A similarity transformation which preserves orientation, also called a homothety.

The metric ds^2=(dx^2+dy^2)/((1-x^2-y^2)^2) for the Poincaré hyperbolic disk, which is a model for hyperbolic geometry. The hyperbolic metric is invariant under conformal ...

A bistable eight-sided polyhedron discovered by Wunderlich and Schwabe (1986).

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.