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The bifoliate is the quartic curve given by the Cartesian equation x^4+y^4=2axy^2 (1) and the polar equation r=(8costhetasin^2theta)/(3+cos(4theta))a (2) for theta in [0,pi]. ...

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...

The circumcircle of the Cevian triangle DeltaA^'B^'C^' of a given triangle DeltaABC with respect to a point P. The following table summarizes a number of named Cevian circles ...

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

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 circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...