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Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

The application of an apodization function.

The Diophantine equation x^2+k=y^3, which is also an elliptic curve. The general equation is still the focus of ongoing study.

Let P be a polynomial of degree n with derivative P^'. Then ||P^'||_infty<=n||P||_infty, where ||P||_infty=max_(|z|=1)|P(z)|.

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

The boundary of complex hyperbolic 2-space.

A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.