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The parallel curves of a circle with radius a with offset k are given by the parametric equations x_p(t) = (a+k)cost (1) y_p(t) = (a+k)sint (2) and are therefore themselves ...

The radial curve of a unit circle from a radial point (x,y) and parametric equations x = cost (1) y = sint (2) is another circle with parametric equations x_r = x-cost (3) ...

The strophoid of a circle with pole at the center and fixed point on the circumference is a Freeth's nephroid.

Gradshteyn and Ryzhik (2000) define the circulant determinant by (1) where omega_j is the nth root of unity. The second-order circulant determinant is |x_1 x_2; x_2 ...

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.

A triangle DeltaA^'B^'C^' is said to be circumscribed in a triangle DeltaABC if A lies on B^'C^', B lies on C^'A^', and C lies on A^'B^' (Kimberling 1998, p. 185). Examples ...

For the parametric representation x = (2t^2)/(1+t^2) (1) y = (2t^3)/(1+t^2), (2) the catacaustic of this curve from the radiant point (8a,0) is given by x = ...

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

The pedal curve of the cissoid, when the pedal point is on the axis beyond the asymptote at a distance from the cusp which is four times that of the asymptote is a cardioid.