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The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

Consider a quadratic equation x^2-sx+p=0 where s and p denote signed lengths. The circle which has the points A=(0,1) and B=(s,p) as a diameter is then called the Carlyle ...

The digon is the degenerate polygon (corresponding to a line segment) with Schläfli symbol {2}.

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

A 100-sided polygon, virtually indistinguishable in appearance from a circle except at very high magnification.

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...