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.

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TopNewestDag 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 · 3 years, 7 months ago

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– Bob Krueger · 3 years, 7 months ago

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

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 · 3 years, 7 months ago

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– Bob Krueger · 3 years, 7 months ago

You've solved the problem of the petals, but what about the seeds?Log in to reply

– Sharky Kesa · 3 years, 7 months ago

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

Looking forward to it. :) – Yash Talekar · 3 years, 7 months ago

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I would highly suggest this video: http://vimeo.com/9953368 – Josh Petrin · 3 years, 7 months ago

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– Bob Krueger · 3 years, 7 months ago

WOWLog in to reply

– Daniel Liu · 3 years, 7 months ago

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