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The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

An object is amphichiral (also called reflexible) if it is superposable with its mirror image (i.e., its image in a plane mirror).

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

The intercept form of a line in the Cartesian plane with x-intercept a and y-intercept b is given by x/a+y/b=1.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

An algorithm which isolates roots in the complex plane by generalizing one-dimensional bracketing.