A derived polygon with side ratios chosen as so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle , the midpoint-inscribed polygons , , ... are similar triangles. For a quadrilateral , the midpoint-inscribed polygon is a parallelogram known as the Varignon parallelogram, and , , , ... are similar parallelograms, as are , , , ....
Midpoint Polygon
See also
Derived Polygon, Midpoint, Varignon Parallelogram, Varignon's TheoremExplore with Wolfram|Alpha
References
Tischel, G. "Ein Konvergenzsatz für Mittenpolygone." Mitt. Math. Ges. Hamburg 18, 169-184, 1999.Referenced on Wolfram|Alpha
Midpoint PolygonCite this as:
Weisstein, Eric W. "Midpoint Polygon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MidpointPolygon.html