2013년 10월 24일 목요일

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=BE·EF
(1)
= (a+b)(a-b)=a^2-b^2=c^2.
(2)
Wolfram

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