Saturday, March 17, 2012

1737 Geometrical Construction Error

I have just started reading “Architecture and Geometry in the Age of the Baroque” by George L. Hersey, which was recommended as another good book into the theoretical mind of the time -- connecting music and architecture.

In the book, on pg 16, is Guarino Guarnini’s scheme for drawing a Golden-section rectangle, published in 1737.

There was a clear typo in the text, where


should have read


Or at least it seemed obvious to me, then I wasn’t so sure, so I thought, heck, I’ll just do the construction, then measure and calculate the resulting ratios. I tried it 3 or 4 times. Expecting to get 1.618, I was surprised to get 1.73 or 1.74. What the heck is going on? So I did the quick theoretical calculation -- maybe where I should have started -- and found that the ratio from this construction is actually the square root of 3, or about 1.73.

Guarnini’s method is/was wrong. And here it was being presented in an architecture text written in 2000 as being correct. And then, perhaps, in a subsequent edition, there is a footnote (14) that presents the error, though it is not corrected in the text itself.

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