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Fibonacci Rectangles

Louis H. Kauffman
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Abstract

Is there any other proportion for a rectangle, other than the Golden Proportion, that will allow the process of cutting off successive squares to produce an infinite paving of the original rectangle by squares of different sizes? The answer is: No. The only proportion that allows this pattern is the Golden Ratio. Two proofs are given.

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Louis H. Kauffman. 2004-05-04. Fibonacci Rectangles. https://arxiv.org/abs/math/0405048

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