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The polygon formed by the lines tangent to the circumcircle of a polygon. The tangential polygon of an n-gon is itself an n-gon.

A point at which two polygon edges of a polygon meet.

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

The number q in a star polygon {p/q}.

A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than 180 degrees. An example of a non-simple ...

Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The ...

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 ...