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A pivot point of a curve is a fixed point Q such that points P lying on the curve and their (isogonal, isotomic, etc.) conjugates are collinear with Q.

A Julia set with c=-0.390541-0.586788i. The fractal somewhat resembles the better known Mandelbrot set.

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

The point of concurrence of the six planes in Monge's tetrahedron theorem.

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

A point where a curve intersects itself along four arcs. The above plot shows the quadruple point at the origin of the quadrifolium (x^2+y^2)^3-4x^2y^2=0.

A point where a curve intersects itself along three arcs. The above plot shows the triple point at the origin of the trifolium (x^2+y^2)^2+3x^2y-y^3=0.

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

The fixed point with respect to which a pedal curve or pedal triangle is drawn.