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The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

A generalization of the polyominoes using a collection of equal-sized equilateral triangles (instead of squares) arranged with coincident sides. Polyiamonds are sometimes ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...