Monday, February 11, 2008

I'll tell you what's truly fascinating. The dimensions of our modern page were finalized in the 12th century. Before that, it was a gradual shift from the square pages of the scroll to the familiar rectangular ones we have in our books now. In a sense, then, the page as we know it has been around since the 12th century, and it hasn't changed significantly since then.

Now the fascinating part. Fibonacci lived from the late 12th to early 13th centuries. He, and other Medieval mathematicians and architects and scribes, had a rekindled interest in Classical Greek geometry, such as the Golden Section. The ratio of the page that was born in the 12th century is about 0.7:1, which is almost the perfect rectangle produced by the Golden Section. The shape of our paper is governed by ancient geometry. The spiral really is everywhere.

(P.S. I might be speculating a little.)


Blake said...

There are so many other geometries that show up in nature, I've always wondered why people focus on this one. Stars are spherical, sugar crystals are cubic , snow flakes form in hexagonal patterns. Nature is chock full of symmetries. I would think it would just be a statistical fact of nature that some shapes will have approximately the "Golden Ratio" if you are allowed to subjectively choose which dimensions of a random object produce some arbitrary number.

Though it is curious why they chose the rectangle for paper size. Why does Europe use A4 and North America 8x11?

Anonymous said...

That is truly fascinating.

After doing a bit of reading on Wikipedia ....

Apparently people incorporated it so widely in architecture and design because they thought it had divine or aesthetic properties. It seems unclear whether people really do find it inherently aesthetic, or whether it really is innate in nature (although logarithmic spirals certainly are, of which the golden spiral is one example).

Neither 8.5/11 nor .7 are particularly close to the golden ratio, but:

European paper sizes are apparently very meticulously designed:
Their ratio is 1:sqrt(2)