Vsauce

# How Many Sides Does A Circle Have?

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You probably think you know a circle. Maybe you’ve even thought a little bit about what a circle is and what a circle isn’t. But do you know how many sides a circle has? Australia didn’t, 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 there’s 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 it’s inside/outside or left and right. And the one thing we know is that sides are relative to something greater.

So, what’s 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 Mandelbrot’s 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

Editing by John Swan

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