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The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

A map projection in which areas on a sphere, and the areas of any features contained on it, are mapped to the plane in such a way that two are related by a constant scaling ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

The Euler-Gergonne-Soddy circle, a term coined here for the first time, is the circumcircle of the Euler-Gergonne-Soddy triangle. Since the Euler-Gergonne-Soddy triangle is a ...

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

The Evans conic is the conic section passing through the Fermat points X and X^', the inner and outer Napoleon points N and N^', and the isodynamic points S and S^' of a ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

On a Lie group, exp is a map from the Lie algebra to its Lie group. If you think of the Lie algebra as the tangent space to the identity of the Lie group, exp(v) is defined ...