Search Results for ""

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

If the cusp of the cardioid is taken as the inversion center, the cardioid inverts to a parabola.

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

An example of a subspace of the Euclidean plane that is connected but not pathwise-connected with respect to the relative topology. It is formed by the ray y=0, x<=0 and the ...

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the negative pedal curve with respect to the pedal point (x_0,y_0)=(0,0) is the circle ...

The negative pedal curve of a line specified parametrically by x = at (1) y = 0 (2) is given by x_n = 2at-x (3) y_n = ((x-at)^2)/y, (4) which is a parabola.

The pedal curve to the Tschirnhausen cubic for pedal point at the origin is the parabola x = 1-t^2 (1) y = 2t. (2)

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 = ...

Given a parabola with parametric equations x = at^2 (1) y = 2at, (2) the negative pedal curve for a pedal point (x_0,0) has equation x_n = (at^2[a(3t^2+4)-x_0])/(at^2+x_0) ...

The inverse curve of the Archimedean spiral r=atheta^(1/n) with inversion center at the origin and inversion radius k is the Archimedean spiral r=k/atheta^(-1/n).