Beauty is in the Eye of the Beholder...or is it?


Today's blog is a little bit about maths.

Let me ask you a question...



Now, I am betting that most of you said rectangle B. Apparently this is no coincidence. This is to do with something called the golden ratio.
The golden ratio is a special number that appears in art, architecture and nature; it has a value of approximately 1.618 - and is also known as phi. If you take a line a divide it into two parts so that the longer part divided by the shorter part is equal to the whole length divided by the longer part. This is the golden ratio.


If you put this into a rectangle you get this, the golden rectangle;

http://en.wikipedia.org/wiki/Golden_rectangle

Phi can be calculated by looking at Fibbonacci's sequence, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... Etc. can you spot the pattern?

If you then find the ratio of a number and the number that proceeds it in the sequence you get the following;

1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538, 34/21 = 1.61905 55/34 = 1.161764, 89/55 = 1.61861.

Keep going and you get the irrational number that is phi, 1.6180339887.....

The golden ratio and the golden rectangle appear in many places - take a look at the video below from Good Morning America, try to spot the golden rectangles...

http://abcnews.go.com/blogs/lifestyle/2012/04/britains-most-beautiful-face-reveals-beauty-secrets/

When you start looking for it you can find these golden ratios everywhere;

Leonardo Da Vinci's Viturian Man highlights the ratio;


http://creativesagest.blogspot.co.uk/2009/03/golden-ratio-secret-to-aesthetics.html
 

and maybe the Mona Lisa's attractiveness is not all that surprising after all?


http://library.thinkquest.org/05aug/01274/phibeauty3.htm
 

So do we find things attractive if they fit contain the golden ratio? Maybe, but I think that beauty is much more than simple mathematics.
If you are interested in more check out the following websites;

http://www.goldennumber.net/architecture/

http://www.guardian.co.uk/artanddesign/2009/dec/28/golden-ratio-us-academic

http://35.9.122.184/goldenratio.pdf (a very interesting academic study)

Comments

  1. Anonymous21 July 2012 at 22:54

    A very intellectual blog Ed. I like your dessert ones best!

    ReplyDelete

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