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For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the involute is given by x_i = 2a+3acostheta(1-costheta) (3) y_i = ...

A Cartesian curve is a curve specified in Cartesian coordinates. The term "Cartesian curve" is sometimes also used to refer to the Cartesian ovals.

Let P=alpha_1:beta_1:gamma_1 and Q=alpha_2:beta_2:gamma_2 be points, neither of which lie on a sideline of the reference triangle DeltaABC. The P-Ceva conjugate X of Q is ...

Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

An ellipse intersects a circle in 0, 1, 2, 3, or 4 points. The points of intersection of a circle of center (x_0,y_0) and radius r with an ellipse of semi-major and ...

The orthotomic of the unit circle represented by x = cost (1) y = sint (2) with a source at (x,y) is x_o = xcos(2t)-ysin(2t)+2sint (3) y_o = -xsin(2t)-ycos(2t)+2cost. (4)

Given two closed curves, the circuminscribed curve is simultaneously inscribed in the outer one and circumscribed on the inner one.

A geometric figure which touches only the vertices (or other extremities) of another figure.

If the cusp of the cissoid of Diocles is taken as the inversion center, then the cissoid inverts to a parabola.

An equation of the form y=ax^3+bx^2+cx+d where only one root is real.