Name: 黄金比（なぜ不合理なのか） - Numberphile (The Golden Ratio (why it is so irrational) - Numberphile)
Uploaded: 2021-01-14T10:15:33.000Z
Duration: 15 min 13 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

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I want to tell you about a very famous number that you've heard about before.

I want to tell you why it is what it is, and it's the golden ratio.

A lot of people think the golden ratio is this mystical thing.

And it is, but not for the reasons they think.

But I want to do that, and I want to tell you why it's interesting.

And I want to do that through a mechanism of flowers,

and you may have heard a connection with Golden Ratio and Flowers before,

but I want to show you why that connection is there.

For the sake of this little video, I'll be the scribe

But I'd like you to imagine, Brady,  that you are a flower.

Your job as a flower is to deal with your seeds,

which is kind of the job of everything living.

and we're gonna model this flower in a mathematical way.

This is not how flowers actually grow, but there are connections.

When you grow a seed, I'm gonna represent that by putting a little blob.

Now that's a seed you've grown from the centre of your flower,

and one option you could have is you've got to decide where to put your seeds.

And I'm going to give you the option of only

how much do you turn around before  you grow your next seed?

you're going to grow seeds out like this.

If you don't turn, the next seed goes next to it,

This is a really bad arrangement for a flower,

So the obvious thing if I'm going to do this model,

of like, if a flower could grow by putting a seed and turning a bit.

What would happen if you turn an amount of a turn.

So I'm going to talk about fractions of turns.

And maybe I'm going to call these spokes,

because, just to get you in the mood,  lets do a third.

You can probably predict it pretty easily.

I mean, none of these are good flower designs,

but the consequences of choosing a number  has given you some patterns.

So if I jumped, say,  to a tenth of a turn,

would you care to predict  what you would see?

And so I don't think the the spoke behaviour is very surprising.

if I told you what would happen with 3/10.

you'll end up not repeating yourself for a bit

So there's this really nice thing in Mathematics called a conjecture.

Looks like it's the denominator of the fraction

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黄金比（なぜ不合理なのか） - Numberphile (The Golden Ratio (why it is so irrational) - Numberphile)

obvious

kinda

brilliant

familiar