This paper suggests that via Varignon's theorem the area of an arbitrary quadrilateral is twice that of the parallelogram created by the mid points of the edges of the quadrilateral. However, if we take a bowtie s.t. (x, y) = (0, 0), (1, 1), (0, 1), (1, 0), then the area of the parallelogram created by the mid points is zero whilst the area of the bowtie is a half. Have I missed something?
2026-04-04 06:09:53.1775282993
Varignon's Parallelogram Area For "Square" Bow-tie
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