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The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first ...

The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

An arrangement of overlapping circles which cover the entire plane. A lower bound for a covering using equivalent circles is 2pi/sqrt(27) (Williams 1979, p. 51).

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...

The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function (1) which is not a Kimberling center. Its radius is ...

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The Dou circle is the circle cutting the sidelines of the reference triangle DeltaABC at A^', A^(''), B^', B^(''), C^', and C^('') such that ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...