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.

Note by Bob Krueger
7 years, 3 months ago

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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 12\frac {1}{2} the way around the middle, then 23\frac {2}{3} of the way around it, then 35\frac {3}{5} of the way around it and so forth.

Sharky Kesa - 7 years, 3 months ago

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

Bob Krueger - 7 years, 3 months ago

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

Sharky Kesa - 7 years, 3 months ago

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Looking forward to it. :)

A Former Brilliant Member - 7 years, 3 months ago

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

Josh Petrin - 7 years, 3 months ago

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WOW

Bob Krueger - 7 years, 3 months ago

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

Daniel Liu - 7 years, 3 months ago

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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, 3 months ago

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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, 3 months ago

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