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The equation of the curve of intersection of a torus with a plane perpendicular to both the midplane of the torus and to the plane x=0. (The general intersection of a torus ...

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.

A modular form which is not allowed to have poles in the upper half-plane H or at iinfty.

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.