# Golden Ratio.

#### jnicholes

Hello,

So, I learned something new about math from a friend of mine that I wanted to share. Here is the rundown:

I am making a holiday present for my mother out of wood. A lot of geometry involved in that, which is what I like to do. My friend told me to, "Use the Golden ratio in the design."

Curious, I said, "What is the Golden Ratio?" He told me the number, which is approximately 1.618. He told me all about it.

After making the present, I experimented with the golden ratio and learned some cool things I wanted to share.

First, You can find the Golden ratio, (Approximately,) by using the Fibonacci Sequence. For this example, I will go a long way to a high Fibonacci number, 121393. Now, divide that by the Fibonacci number below that, which is 75025.

so, in a nutshell, 121393/75025=1.618033989........

Take the highest Fibonacci Number and divide it by the Fibonacci number below it, and you get the golden ratio. That is what I learned.

You can also get the golden ratio by 2sin(54)

After more experimenting, I found more cool stuff. The golden ratio, when used properly follows the Fibonacci sequence. Here is an example where x=the golden ratio:

10/x=6.180339887....
6.180339887..../x=3.819660113....
3.819660113..../x=2.360679775....

Notice a pattern?

2.360679775....
3.819660113....
6.180339887....
10

The first and second equal the 3rd, the second and third equals the 4th, and so on. It follows the Fibonacci Sequence!

That is what I learned. A good lesson about Mathematics.

• idontknow

#### romsek

Math Team
pro graphics designers live and breathe the golden ratio.