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The inversion of a spindle torus. If the inversion center lies on the torus, then the spindle cyclide degenerates to a parabolic spindle cyclide.

A fractal composed of repeated copies of a pentagram or other polygon. The above figure shows a generalization to different offsets from the center.

The resultant of the vectors represented by the three radii from the center of a triangle's circumcircle to its polygon vertices is the segment extending from the ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

The circumcircle of an ellipse, i.e., the circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse's semimajor axis.

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 ...

The equilateral cevian triangle point of a triangle is the unique point P such that the Cevian triangle of P is equilateral. This point is Kimberling center X_(370).

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...