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Fermat's spiral, also known as the parabolic spiral, is an Archimedean spiral with m=2 having polar equation r^2=a^2theta. (1) This curve was discussed by Fermat in 1636 ...

The gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

Guilloché patterns are spirograph-like curves that frame a curve within an inner and outer envelope curve. They are used on banknotes, securities, and passports worldwide for ...

A heart-shaped surface given by the sextic equation (x^2+9/4y^2+z^2-1)^3-x^2z^3-9/(80)y^2z^3=0 (Taubin 1993, 1994). The figures above show a ray-traced rendering (left) and ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...

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 ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

A plot of a function expressed in polar coordinates, with radius r as a function of angle theta. Polar plots can be drawn in the Wolfram Language using PolarPlot[r, {t, tmin, ...