Midpoint Polygon


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 midpoint-inscribed polygons P_1, P_2, ... are similar triangles. For a quadrilateral P, the midpoint-inscribed polygon P_1 is a parallelogram known as the Varignon parallelogram, and P_1, P_3, P_5, ... are similar parallelograms, as are P_2, P_4, P_6, ....

See also

Derived Polygon, Midpoint, Varignon Parallelogram, Varignon's Theorem

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Tischel, G. "Ein Konvergenzsatz für Mittenpolygone." Mitt. Math. Ges. Hamburg 18, 169-184, 1999.

Referenced on Wolfram|Alpha

Midpoint Polygon

Cite this as:

Weisstein, Eric W. "Midpoint Polygon." From MathWorld--A Wolfram Web Resource.

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