Being a physical science major, it is extremely fascinating to explore the connections between mathematics, science, and art. I know that a lot of modern art has begun to use advanced technology, but I had no idea that even Leonardo DaVinci integrated mathematics into his art. One mathematical term in familiar is very fascinating to me: psi. Psi, also known as the golden ratio, is a number encountered when taking ratios of distances in simple geometric figure. The number turns out to be 1.618034…. At first glance, this would appear to be irrelevant in art, but it can actually be found in architectural masterpieces created in Ancient Greece. The Parthenon is famous for its use of the golden ratio in its construction; even the Greeks knew that the golden ratio was visually pleasing. Another ancient example of the use of the Golden ratio is the Great Pyramid of Giza.

This pyramid was built circa 2560 BC and the length of the base divided by the height is very near the Golden Ratio (1.5717…). Euclid also speaks of the Golden Ratio; Plato dabbled in the area as well. Plato philosophized that if a line were divided into two equal segments so that each would be related to the whole in the same way, then a special proportional relationship would result. Plato, as we know now, was quite correct.

So how, exactly, is the golden ratio derived? It turns out that there are multiple ways to do so. One is the Fibonacci sequence.

Here is a ‘Fibonacci series’.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..

If we take the ratio of two successive numbers in this series and divide each by the number before it, we will find the following series of numbers.

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.6666…

8/5 = 1.6

13/8 = 1.625

21/13 = 1.61538…

34/21 = 1.61904…

The ratio seems to be settling down to a particular value, which we call the golden ratio(Phi=1.618..). (http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html)

The Fibonacci Sequence is even more intimately related to the Golden Ratio: shapes exist such as the Golden Rectangle and the Golden Spiral which combine these two concepts in different ways. The Golden Rectangle is a shape formed using proportions that are two sequential numbers in the Fibonacci Sequence. It has been theorized that this shape is one of the most appealing shapes to the eye. It seems like no large coincidence then that it is precisely this shape that Leonardo DaVinci used in his very famous Mona Lisa.

The Golden Ratio is also found in more modern artwork. The Sacrament of the Last Supper, by Salvadore Dali, is actually painted on a canvas matching the proportions of the Golden Rectangle.

Clearly, the Golden Ratio has stood the test of time. Its usage has spanned centuries upon centuries, and it has been utilized by dozens of artists and architects. Personally, I think this is a part of its appeal. The Golden Ratio and the Fibonacci sequence are found so often, in both math, art, and nature, but both concepts still remain largely a mystery. Why are shapes created by these mathematical concepts so visually pleasing? Did the ancient architects realize the aesthetics of these ratios and implement them on purpose, or was it just a coincidence? Personally, I think there is still a lot to learn about the use of the Golden ratio in history, but the ratio does serve one very important purpose: it shows another way that math and art are intimately connected.

http://www.youtube.com/watch?v=fmaVqkR0ZXg

P.S.–sorry this is late, I didn’t join the class until 3rd week so I had some catching up to do.

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