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A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

A figure formed by taking a series of steps of length 1, 2, ..., n, with an angle theta turn after each step. The symbol for a spirolateral is ^(a_1,...,a_k)n_theta, where ...

A swirl is a generic word to describe a function having arcs which double back around each other. The plots above correspond to the function f(r,theta)=sin(6cosr-ntheta) for ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

A triangle in which all three angles are acute angles. A triangle which is neither acute nor a right triangle (i.e., it has an obtuse angle) is called an obtuse triangle. ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

A demiregular tessellation, also called a polymorph tessellation, is a type of tessellation whose definition is somewhat problematical. Some authors define them as orderly ...