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Original poster

How many sides does a circle have?

166 replies

Ravingstarfish · 30/05/2019 12:16

Just that really. My sons tutor has taught him this and several people have said she’s wrong.... so how many sides does a circle have?

OP posts:
StealthPolarBear · 30/05/2019 19:41

I say infinite

StealthPolarBear · 30/05/2019 19:42

The more sides you add to a shape the more circle y they get. So a dodecahedron looks similar to a circle in a way a hexagon doesn't. As the number of sides approaches infinity, the shape becomes a circle.

CapybarasLoveCake · 30/05/2019 19:45

Just had this for yr6 SATs. One side.

user1480880826 · 30/05/2019 19:47

How are so many people concluding that a circle has 2 sides?! “An inside and an outside”?!

Either you’re all taking the piss or you’ve had too much to drink.

StealthPolarBear · 30/05/2019 19:47

But it's really not one!
The inside and outside thing originated as a joke. Not sure if sone people think it's serious.

bridgetreilly · 30/05/2019 19:48

An infinite number of straight sides.

User10fuckingmillion · 30/05/2019 19:49

I was taught 1 at school

User10fuckingmillion · 30/05/2019 19:50

Or infinite (depending on the teacher!) I think that’s right

bridgetreilly · 30/05/2019 19:50

One is just plain wrong. In geometry a 'side' implies a straight side. It is patently obvious that a circle does not have one straight side. It has one edge, which is the correct term for the boundary constraining it.

DadDadDad · 30/05/2019 20:00

If it has an infinite number of sides, how long is each side?

bridgetreilly · 30/05/2019 20:00

DadDadDad

Infinitesimally small.

DadDadDad · 30/05/2019 20:01

I'm with others who think a side has to be straight line segment. Give me your definition of side and I'll answer your question.

StealthPolarBear · 30/05/2019 20:02

Yes as a pp said infinitesimal

DadDadDad · 30/05/2019 20:32

A length has to be real number greater than or equal to zero. Infinitesimally small is no such number and so can't be assigned to a length.

SoupDragon · 30/05/2019 22:40

A length has to be real number greater than or equal to zero. Infinitesimally small is no such number and so can't be assigned to a length.

If a length can be zero it can be a very very very tiny amount bigger than zero and hence infinitesimally small.

DadDadDad · 30/05/2019 22:54

Nope, any number greater than zero is not infinitesimally small. If the number you have in mind is x, then x/2 is even smaller, so it can't be infinitesimally small if I can find something smaller.

goodwinter · 30/05/2019 22:59

The more sides you add to a shape the more circle y they get. So a dodecahedron looks similar to a circle in a way a hexagon doesn't. As the number of sides approaches infinity, the shape becomes a circle.

This is how I understand it too.

vinhotinto · 30/05/2019 23:02

I order parts with an inner dimension and an outer dimension, Id & od

fraumaximoo · 30/05/2019 23:05

1

vinhotinto · 30/05/2019 23:06

Sorry diameter not dimension

SarahAndQuack · 30/05/2019 23:07

Nope, any number greater than zero is not infinitesimally small. If the number you have in mind is x, then x/2 is even smaller, so it can't be infinitesimally small if I can find something smaller.

But you can have smaller and larger infinities, so what's the issue?

(NB, I know nothing much about maths, but my brother and his wife are mathematicians who work on, amongst other things, infinities of different sizes. I'm currently on holiday with them, so am aware of this!)

I would have thought the issue is that we haven't defined what 'small' means here.

DadDadDad · 30/05/2019 23:08

@goodwinter - mathematicians have learned to be careful about how they use and talk about infinity. If you have a process where you add more and more sides, that process never gets to a circle - it gets closer and closer, arbitrarily close, so we can say the limit of the process is a circle, but that's not saying that the end of the process is a circle (because the process is endless, hence infinite).

DadDadDad · 30/05/2019 23:15

But you can have smaller and larger infinities, so what's the issue?

That's a different concept, where we are talking about the sizes of sets and some sets are infinite. There, we can have an infinite set that is bigger than another infinite set, in that however you pair up the two sets, one will have members left over.

Even there, intuition can lead you astray. The set of whole numbers {1, 2, 3, ... } is obviously infinite, as is the set of even numbers {2, 4, 6, ...}. You might think the first set is bigger than the second but it's not because you can pair the sets up:
1 2
2 4
3 6
4 8

But the set of fractions {1/2, 2/3, ... 54/7, ... 962 / 329... } is not bigger than the set of whole numbers.

SarahAndQuack · 30/05/2019 23:27

Yes, I understand the reasoning for why there are smaller and larger infinities. I don't follow why that means you can't have something infinitesimally small if something else is smaller, but I don't doubt it's the case if you say so! Grin

DadDadDad · 30/05/2019 23:35

Because it's possible to give a rigorous definition of what is meant by an infinitely large set (eg it has a subset that can be paired up with the natural numbers), and what is meant by one infinite set being larger than another.

If you can give a rigorous definition of an infinitely small quantity and what it means for one such quantity to be smaller than another, then we can decide if such a thing exists.