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The evolute of a circle is a degenerate point at the origin.

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 ...

For a unit circle with parametric equations x = cost (1) y = sint, (2) the negative pedal curve with respect to the pedal point (r,0) is x_n = (r-cost)/(rcost-1) (3) y_n = ...

The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

A circular pattern obtained by superposing parallel equally spaced lines on a set of concentric circles of increasing radii, then coloring the regions in chessboard fashion. ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

The circum-medial triangle DeltaA^'B^'C^' is the circumcevian triangle of a reference triangle DeltaABC with respect to the triangle centroid G of DeltaABC (Kimberling 1998, ...

The circum-orthic triangle DeltaA^'B^'C^' is the circumcevian triangle of a triangle DeltaABC with respect to the orthocenter H (Kimberling 1998, p. 163). The circum-orthic ...

The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle. Its trilinear vertex matrix is ...