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Any continuous function G:B^n->B^n has a fixed point, where B^n={x in R^n:x_1^2+...+x_n^2<=1} is the unit n-ball.

For a unit circle with parametric equations x = cost (1) y = sint, (2) the negative pedal curve with respect to the pedal point (r,0) is x_n = (r-cost)/(rcost-1) (3) y_n = ...

The strophoid of a circle with pole at the center and fixed point on the circumference is a Freeth's nephroid.

A family of subsets of a topological space such that every point has a neighborhood that intersects only one of them.

The Euler infinity point is the intersection of the Euler line and line at infinity. Since it lies on the line at infinity, it is a point at infinity. It has triangle center ...

A topological space in which every point has a countable neighborhood system base for its neighborhood system.

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

A stable fixed point of a map which, in a dissipative dynamical system, is an attractor.