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Wednesday, June 18, 2014

Mona Phi-sa

By now you know that this number 'phi', which emerges as you look further down the list of Fibonacci numbers, explains some really unexpected relationships, from geometry to architecture, to the animal kingdom (Fibonacci Zoo, notwithstanding) and in the human body. One particular human, and technically, we aren't actually talking about a human, but a painting of a human, stands out as perhaps the most perfect of them all - Mona Lisa.

The Mona Lisa

This painting is arguably the most famous one ever made, certainly the most famous one Leonardo da Vinci (not OUR Leonardo!) painted. We aren't talking scupltures, so David is not in the conversation, by the way. The Mona Lisa hangs in the world-famous Louvre museum, and has captivated art buffs and casual fans for centuries. You can learn more about the painting at this Khan academy site.

So what makes this painting so famous? I've not had the chance to see it, but I understand it is actually quite small, and viewing it is a little stressful, with crowds gathering around it, cameras snapping right and left, and I am left to wonder, what's the big deal?

Well, I'm not going to make any claims about my art history credentials (which are none). Instead, I want to look at her face. Lisa, it is believed, was the wife of a man who asked da Vinci to paint her. That's it. But what makes her so interesting from a mathematical standpoint is that the dimensions of her face are nearly perfect. I guess maybe it's from one Italian Leonardo (Pisano) to another (da Vinci), but a close look at Mona Lisa reveals that her facial dimensions very closely match the Fibonacci spiral we saw in a previous post.
The Fibonacci Spiral in the painting of Mona Lisa

It turns out that some faces just look nicer than others, much like those rectangles we saw whose 'perfection' was hard to describe, but we knew it when we saw it. Facial recognition experts have long found the value of phi in faces that are widely accepted as being beautiful. Sample faces include Angelina Jolie, Jennifer Aniston, Beyonce, Johnny Depp, and Jessica Simpson, to name a few. At the Math of Beauty web site, you can see a little more into this phenomenon. And wouldn't you know it? Even Oprah got into the act on an episode that dealt with something called "The Beauty Equation.

So is it real? Do men and women with 'perfect' facial dimensions really look more attractive? I'll leave that to you to decide for yourself. As for me, my wife thinks so, and that's all that matters. Try searching for 'golden ratio' and 'beauty' and see what you find.

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