The Golden Ratio and Beauty

Beauty is in the eye of the beholder, but why do we find certain things more beautiful than others? In some regard, it can all be boiled down to a little bit of math.

Now, for those of you that aren’t interested in a math lesson, please scroll down past the equations for how one ratio is hidden in our daily lives. For those dying for the explanation behind the golden ratio, prepare to be blown away.

The Greek letter phi (Φ) is most commonly associated with collegiate Greek life, but as someone with a math degree it has a bit of a different meaning. Phi also represents the golden ratio in mathematics, and is equal to 1.618.

Start with a 1×1 square and add another 1×1 square. Follow that with a 2×2 square, and now you have a rectangle whose longest side is 3. Add a 3×3 square and the longest side becomes 5. Pretty elementary, right?

golden-ratio

Now, start writing down the length of the longest sides. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…. Congratulations! You now know the Fibonacci Sequence! If you want to be technical, the nth number in the sequence F(n)=F(n-1)+F(n-2).

So if you’re still with me throughout this mathematical jargon, you’re probably wondering where the golden ratio comes into all of this. Φ is the ratio of the longest side over the shortest side, or more specifically F(n)/F(n-1). There’s a quick chart below to show you how the ratio approaches 1.618.

Let’s switch for a minute and use a and b for the dimensions of the rectangle. This rectangle fits the golden ratio if (a+b)/a=a/b=Φ. Well (a+b)/a=1+(b/a), and 1+(b/a)=1+(1/Φ). From this, we see Φ=1+(1/Φ).

fibonacciphi




 

Alright, enough of this “education” nonsense. Let’s get to the fun stuff! The golden ratio can be seen in so many things in our daily lives. While we don’t consciously recognize it, our subconscious perceives it as beauty. The spacing of facial features, the perfect spiral of a seashell, or even the petals on a blossoming flower all have aspects fitting the golden ratio. More on this here.

This is the spiral created by the golden ratio and the Fibonacci sequence explained above.

spiral

It can be seen in a variety of places.

Most recently, I found it in a picture of my own and had a gleefully geeky moment of pure joy. I know it’s not perfect, but the main features of the photo fall near the curve.

20161015_131326.png

I am hoping I continue to find this curve in various places and I challenge you to do the same. A simple google search shows me that some people already have!

And I had to save the best for last. “Best” being relative…I guess funniest is a better word choice. Here’s Mr. Trump and his strange, golden ratio hair.

trump

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