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A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

A mensuration formula is simply a formula for computing the length-related properties of an object (such as area, circumradius, etc., of a polygon) based on other known ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

If lim_(z->z_0)(f(z)-f(z_0))/(z-z_0) is the same for all paths in the complex plane, then f(z) is said to be monogenic at z_0. Monogenic therefore essentially means having a ...

The Peano-Gosper curve is a plane-filling function originally called a "flowsnake" by R. W. Gosper and M. Gardner. Mandelbrot (1977) subsequently coined the name Peano-Gosper ...

A phase portrait is a plot of multiple phase curves corresponding to different initial conditions in the same phase plane (Tabor 1989, p. 14). Phase portraits for simple ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

Consider n intersecting circles. The maximal number of regions into which these divide the plane are N(n)=n^2-n+2, giving values for n=1, 2, ... of 2, 4, 8, 14, 22, 32, 44, ...

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...