Let the squares and share a common polygon vertex . The midpoints and of the segments and together with the centers of the original squares and then form another square . This theorem is a special case of the fundamental theorem of directly similar figures (Detemple and Harold 1996).
Finsler-Hadwiger Theorem
See also
Directly Similar, Fundamental Theorem of Directly Similar Figures, SquareExplore with Wolfram|Alpha
References
Detemple, D. and Harold, S. "A Round-Up of Square Problems." Math. Mag. 69, 15-27, 1996.Finsler, P. and Hadwiger, H. "Einige Relationen im Dreieck." Comment. Helv. 10, 316-326, 1937.Fisher, J. C.; Ruoff, D.; and Shileto, J. "Polygons and Polynomials." In The Geometric Vein: The Coxeter Festschrift. New York: Springer-Verlag, 321-333, 1981.Referenced on Wolfram|Alpha
Finsler-Hadwiger TheoremCite this as:
Weisstein, Eric W. "Finsler-Hadwiger Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Finsler-HadwigerTheorem.html