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Rectangle Squaring


RectangleSquaring

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which passes through the semicircle at H. Then  square EKLH has the same area as BCDE. This can be shown as follows:

A(BCDE)=BE·ED
(1)
=BE·EF
(2)
=(a+b)(a-b)
(3)
=a^2-b^2
(4)
=c^2.
(5)

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References

Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 13-14, 1990.

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Rectangle Squaring

Cite this as:

Weisstein, Eric W. "Rectangle Squaring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RectangleSquaring.html

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