Vsauce! Kevin here.
You may know May 10th, 2020 as Children’s Day in the Maldives or Mother’s Day in Mexico. Or
Bono’s 60th birthday, or the anniversary of serial killer John Wayne Gacy’s death.
But on May 10th, 2020, Australia had a very serious question -- as a nation,
it collectively needed to know how many sides a circle has.
The answer is... a little more nuanced than it may seem. There’s the easy math answer,
the real life answer, and the answer that’s part hard math and part real life.
Listen, the answer can be pretty straightforward. If you’re LAZY, or if you want to stick to the
most basic math. A polygon is a two-dimensional shape on a plane that has a defined number of
sides -- or actually, angles. It’s right in the name, the Greek “poluganon” means
“many-angled.” Triangle is a trigon, three angles. Tridecagon, 13 angles. And 13 sides.
But how many angles does a circle have? Well… none, really. Is that a… none-agon? Naught-agon?
Zilch-agon? There aren’t any points at which two lines make a vertex. That can make it a
monogon, which Euclidean geometry categorizes as a degenerate polygon because its endpoints overlap.
But if you’re just looking at a circle, you aren’t seeing any angles -- you’re really just seeing one
continuous side. There’s the first answer, a circle has one side. The end? Right? WRONG!
WHAT IS A SIDE? This is where it gets tricky.
In math, a side is really an edge or a face depending on whether we’re working in 2
or 3 dimensions. But in real life, a side is… a side. You refer to the left side of your body or
the side of a ship, or the outside and inside of your house. “Side” in Olde English pretty much
set the tone for how we think of the word: it meant the left or right flank of a person.
But when we think about what a side is, it’s always relative to the whole.
Humans have bilateral symmetry, so the left of your body is a mirror image of the right,
for the most part. That whole unit -- your body -- means we can break it down into relative sides and
have it make sense. A side is about position relative to something greater. Like, a side dish
of your meal is relative to the main dish of the meal. The steak or whatever. Spaghetti? Hot Dogs?
You know what I mean! You can’t have the port side of a ship without drawing a mental line
of symmetry lengthwise in its center. You can’t talk about how the inside of your thigh
hurts without silently differentiating it from the obvious outside of your leg.
Or let’s talk about starfish! Look at a starfish because that’s
radial symmetry coming from the center outward. It’s got 10 faces with two on each arm,
but we’d say it has five sides -- and each of those sides has a left side and a right side. So
it’s got 5 sides or 10 sides depending on how we’re breaking it down.
It’s positional. It’s directional. It’s relative. But...
we’re supposed to be talking about circles! Circles! Okay, Alright, alright.
Well, now we’ve got at least one more answer -- a circle’s got
an inside and an outside, 2 totally legitimate sides. But
that’s probably wrong. Because... WHAT ABOUT WHEELS? WHEELS.
You’ve got a circle and it’s rolling on a flat surface. Between gravity and friction,
eventually it stops. Let’s imagine a wheel as a perfect circle. Because it’s a perfect
circle and the surface is perfectly flat, the actual point of contact between the two is
infinitesimal in size. Does that make the point of contact a side? Probably -- and how many are
there? I could roll a circle 10,000 times and it’s never gonna stop in exactly the
same place. That suggests there are infinite sides -- just like
the coast of the continent that feverishly wished for an answer to this very question.
The coast of Australia is infinitely long. Don’t believe me? You should!
Imagine measuring the coastline of Australia using a measuring stick 20 kilometers long.
Then you go back and measure it with a 1 kilometer measuring stick -- the measurement would actually
be significantly longer because you’re able to capture more detail in the twists and turns of the
coastline. If you did it by the meter? Even more. Centimeter, Millimeter, nanometer, femtometer… the
smaller your unit of measurement, the more you reduce the uncertainty
and increase that coastline. And if your unit of measurement can become
infinitely small, then how does the coastline NOT become infinitely large?!
It’s the same exact concept with ‘sides’ of a circle. We’ve got an infinite number
of points at which a circle can come to rest as it’s rolling on a plane,
and the only limitation we have is in our ability to measure it. So
how many sides would it have if we could count the atoms, or the electrons, or the quarks?
Sorry, Australia, but how many sides does a circle have just
doesn’t have a definitive answer -- depending on how you look at the problem, a circle can have
no sides, one side, two sides, or… infinite sides.
So what side are YOU on? How many sides do you think a circle has?
Let me know down BELOW in the bottom side of this video.
And as always -- thanks for watching.