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Fundamental Theorem of Directly Similar Figures


Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define F_r={(1-r)P_0+rP_1:P_0 in F_0,P_1 in F_1}. Then F_r is also directly similar to F_0.


See also

Directly Similar, Finsler-Hadwiger Theorem

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References

Detemple, D. and Harold, S. "A Round-Up of Square Problems." Math. Mag. 69, 15-27, 1996.Eves, H. Solution to Problem E521. Amer. Math. Monthly 50, 64, 1943.

Referenced on Wolfram|Alpha

Fundamental Theorem of Directly Similar Figures

Cite this as:

Weisstein, Eric W. "Fundamental Theorem of Directly Similar Figures." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FundamentalTheoremofDirectlySimilarFigures.html

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