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Math and…Art??

As a huge math nerd and art hobbyist (especially photography), I get really excited when the two overlap. Have you ever heard of the Fibonacci sequence? It starts with 0, 1, then continues with each term equaling the sum of the previous two:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.

What’s fascinating about the Fibonacci sequence is that it appears everywhere in nature in the form of the golden ratio.  Dividing a number in the sequence by the preceding number approximates the golden ratio (the approximation becomes more accurate the further down the sequence the numbers are and approaches ~1.618).  This ratio is expressed in the dimensions of conch shell spirals, the arrangement of branches on trees, the formation of petals on flowers, and even in proportions of the human body.

The golden ratio is used in art because shapes which express the ratio are more appealing to the eye–more beautiful.  In photography, a common composition technique is the “rule-of-thirds” in which the subject or horizon line is placed a third of the way from the frame.  This makes more interesting photographs than if the subject were in the center, and it works because it was derived from the golden ratio.

I think it’s incredible that this simple mathematical pattern seems to govern nature and even how we perceive beauty!

  1. leimaf
    April 26, 2012 at 2:05 pm

    Yes!! I was going to make a post about the link between face proportion and sexual attraction. Apparently many studies have reached the same conclusion: that people are attracted to more symmetrical faces, which denote better genes, because they will make better mates with which to reproduce the healthiest offspring. It is interesting to also note how this emphasis on symmetry extends further onto plants and art. Perhaps beauty really is just, in essence, mathematics.

  2. anthonypribadi
    April 27, 2012 at 2:28 pm

    wow this is a good post! and look, you got 6 likes! haha. I knew about this Golden Ratio thing before and I thought it is pretty cool too. The exact Golden Ratio is (1+squareroot(5))/2 which is 1.618 accurate to 3 decimal places. And it is derived by a simple math equation. Let’s say we have two variables, x and y, where x is smaller than y. And so, the so called Golden Ratio is just the ratio where y/x is the same as (x+y)/y. Solving the equation, it turns out that y/x is (1+squareroot(5))/2.

    Parts of human body often follow this Golden Ratio, for instance the span of the whole arm divided by the distance from elbow to the end of one’s fingers follows Golden Ratio too. But I didn’t know about the Fibonacci part, that the division of any 2 neighbors approximate Golden Ratio. So I thought that is pretty cool too.

    And for those who are interested, this youtube video shows some cool explanations and demonstrations, too. Only 3 minutes. Enjoy. http://www.youtube.com/watch?v=fmaVqkR0ZXg

  3. zmackay
    April 28, 2012 at 6:47 am

    This is an incredible phenomenon, and actually brings to mind the idea of bio-mimicry which I was reading about the other day. It never fails to amaze me how many mathematic equations and feats of masterful engineering point straight back to the most natural occurrences; much like the conch-shells and aspects of human physiology you mentioned. There is a certain arrogance that humans seem to inherently possess which can be both negative and at time ingenious. Although we put man-made technological developments on an infallible pedestal, many people have little to no regard of the planet we inhabit and the millennia before our existence that it has had to solve many of the mysteries we grapple with today. This golden ratio is an aesthetically elegant reminder of that, and makes me wonder what other connections we can make to, and conclusions we can draw from our environment. Although there is a massive movement towards conservation taking place, I think we could also be a little humbled and inspired by the planet that has sustained a virtually unfathomable degree of existence for so long.

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