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Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

The quartic surface obtained by replacing the constant b in the equation of the Cassini ovals with b=z, obtaining [(x-a)^2+y^2][(x+a)^2+y^2]=z^4. (1) As can be seen by ...

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 Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

A point of discontinuity, also called a leap.

The pedal curve to the Tschirnhausen cubic for pedal point at the origin is the parabola x = 1-t^2 (1) y = 2t. (2)

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

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 ...