The Golden Ratio: A Preface

Shortly here on Brilliant, I will be making a series of posts that delve into the wonders of the Golden Ratio. I'm not exactly sure how long this will go on for, but I plan to post articles every one or two days. I will try to make them short, but bear with me, I can get carried away sometimes. The articles will start out at the level of the Cosines Group, but will eventually elevate to the Torque group. I may also be posting about background information necessary to understand the golden ratio, so keep an eye out for those too. Other than that, I hope that you're all looking forward to this as much as I am.

Here's a bit of a teaser: Why do the seeds of the sunflower pictured above spiral in the way they do?

Click here for the first post about the Golden Ratio.

#CosinesGroup #TorqueGroup #TheBeautyOfMath #GoldenRatio

Easy Math Editor

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Comments

Dag nabbit. You beat me to it. I was going to do Fibonacci numbers but I see that sooner or later you'll cover them.

Well good luck on your endeavor.

Daniel Liu - 7 years, 5 months ago

Haha! The secrets are to be revealed. :) Thanks for waiting. I do plan to cover Fibonacci numbers and other sequences like them.

Bob Krueger - 7 years, 5 months ago

I would highly suggest this video: http://vimeo.com/9953368

Josh Petrin - 7 years, 5 months ago

Oh yes. I discovered that video in a page on AoPS, and it has never failed to amaze me.

Daniel Liu - 7 years, 5 months ago

WOW

Bob Krueger - 7 years, 5 months ago

Looking forward to it. :)

A Former Brilliant Member - 7 years, 5 months ago

They do this so the petals on the top don't cover the petals on the bottom. They do this by following the Fibonacci sequence like this: one petal blooms and the second petal goes $\frac {1}{2}$ the way around the middle, then $\frac {2}{3}$ of the way around it, then $\frac {3}{5}$ of the way around it and so forth.

Sharky Kesa - 7 years, 5 months ago

You've solved the problem of the petals, but what about the seeds?

Bob Krueger - 7 years, 5 months ago

I don't know but I think it may be to do with calculus.

Sharky Kesa - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$