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How Many Sides Does A Circle Have?

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Channel: Vsauce2
Categories: Science
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Watch my newest video, "Could a Toothpaste Sandwich Brush Your Teeth?": https://youtu.be/OdeiWhETqQY

You probably think you know a circle. Maybe youve even thought a little bit about what a circle is and what a circle isnt. But do you know how many sides a circle has? Australia didnt, and the answer is more complicated than it seems.

You can do it the easy way with simple geometry. You can do it the common sense way, which is a little more realistic. And you can think in terms of degenerate polygons to really complicate the math.

But theres more to it than that, and it depends on what we consider a side. Not just a mathematical side, either -- a side in real life, a side of a shape, a body, an animal, or a thing. Humanity has been thinking about sides for a long time, whether its inside/outside or left and right. And the one thing we know is that sides are relative to something greater.

So, whats the side of a circle relative to? Its center? The world around it? Is it an exception to the rule in that there are no sides at all? By looking at language, math, and old-fashioned ingenuity, we employ everything from Mandelbrots coastline paradox to Old English to answer the question of How many sides does a circle have? Sort of. Almost. Maybe. Definitely.

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Hosted and Produced by Kevin Lieber
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Research and Writing by Matthew Tabor

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