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A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

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 ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

The Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble ...

The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions alpha = a(b^2+c^2) (1) alpha = sin(A+omega), (2) where ...

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

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.