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An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_(175) (Kimberling 1994) and has equivalent ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

The Gewirtz graph, sometimes also called the Sims-Gewirtz graph (Brouwer), is an integral graph on 56 nodes and 280 edges that is also a regular graph of order 10. It is ...

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...

The line L^' through a triangle polygon vertex obtained by reflecting an initial line L (also through a polygon vertex) about the angle bisector. If three lines from the ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...