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The pedal curve of a sinusoidal spiral r=a[cos(nt)]^(1/n) with pedal point at the center is another sinusoidal spiral with polar equation r=a[cos(nt)]^(1+1/n). A few examples ...

A "squashed" spheroid for which the equatorial radius a is greater than the polar radius c, so a>c (called an oblate ellipsoid by Tietze 1965, p. 27). An oblate spheroid is a ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...

An Archimedean spiral is a spiral with polar equation r=atheta^(1/n), (1) where r is the radial distance, theta is the polar angle, and n is a constant which determines how ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...