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Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

The configuration formed by two curves starting at a point, called the vertex V, in a common direction. Horn angles are concrete illustrations of non-Archimedean geometries.

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

Shapes such as segments or angles appear larger when placed inside a larger angle.

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

Two lines or plane congruent geometric figures which lie on top of each other are said to be coincident.

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

A plane curve of the form y=x^n. For n>0, the curve is a generalized parabola; for n<0 it is a generalized hyperbola.

The plane through the midpoint of a line segment and perpendicular to that segment, also called a mediating plane. The term "mediator" was introduced by J. Neuberg ...

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...