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Given a Schwarz triangle (p q r), replacing each polygon vertex with its antipodes gives the three colunar spherical triangles (p q^' r^'),(p^' q r^'),(p^' q^' r), (1) where ...

A mensuration formula is simply a formula for computing the length-related properties of an object (such as area, circumradius, etc., of a polygon) based on other known ...

If, in a plane or spherical convex polygon ABCDEFG, all of whose sides AB, BC, CD, ..., FG (with the exception of AG) have fixed lengths, one simultaneously increases ...

Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

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 regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent ...