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Finsler-Hadwiger Theorem

\begin{figure}\begin{center}\BoxedEPSF{FinslerHadwingerTheorem.epsf}\end{center}\end{figure}

Let the Squares $\vbox{\hrule height.6pt\hbox{\vrule width.6pt height6pt \kern6.4pt \vrule width.6pt}
\hrule height.6pt}ABCD$ and $\vbox{\hrule height.6pt\hbox{\vrule width.6pt height6pt \kern6.4pt \vrule width.6pt}
\hrule height.6pt}AB'C'D'$ share a common Vertex $A$. The midpoints $Q$ and $S$ of the segments $B'D$ and $BD'$ together with the centers of the original squares $R$ and $T$ then form another square $\vbox{\hrule height.6pt\hbox{\vrule width.6pt height6pt \kern6.4pt \vrule width.6pt}
\hrule height.6pt}QRST$. This theorem is a special case of the Fundamental Theorem of Directly Similar Figures (Detemple and Harold 1996).

See also Fundamental Theorem of Directly Similar Figures, Square


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.




© 1996-9 Eric W. Weisstein
1999-05-26