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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:
SarahAndQuack · 30/05/2019 23:40

As I said, I'd have thought the issue is we've not defined what small means here.

I'm not disagreeing with you.

mineofuselessinformation · 30/05/2019 23:43

'Sides' are straight lines.
As PP have mentioned, the more sides a polygon has the more 'circle like' the 2d shapes becomes.
Therefore, the number of sides has to be infinite.

DadDadDad · 31/05/2019 00:25

mine - but if there are an infinite number of these straight sides on a circle can you point to a single one? Unfortunately, mathematicians have discovered that making that "therefore" leap with infinite processes can hide some logical twists. For example:

In Heaven, there are an infinite number of silver coins labelled 1, 2, 3, ... and an infinitely expanding chest in which they can be placed.

Every morning, Angel A puts ten coins in the chest: on the first day coins 1,2, .. 10; on the second day 11, 12, ... 20; and so on.

Every evening, Angel B removes one coin from the chest: on the first day coin 1; on the second day coin 2; and so on.

It seems obvious that eventually B will remove every number from the chest, so surely after infinite days the chest will be empty. (Name a coin that would be left in the chest).

Elsewhere, Angel C has her own chest and infinite gold coins labelled 1, 2, 3, .... C does the same as Angel A, putting 1-10 in on the first morning; 11-20 in on the second morning; and so on.

Angel D each evening removes one coin from C's chest: coin 10 on the first day; coin 20 on the second day; and so on.

It seems obvious that C will only ever remove the multiples of 10, so after infinite time, the chest will contain an infinity of coins.

But someone watching from a distance will simply see two chests where every morning ten coins are put in and every evening one coin is taken out. How can one chest end up empty and one end up infinitely full after infinite days have passed?

JAPAB · 31/05/2019 00:56

It seems obvious that eventually B will remove every number from the chest, so surely after infinite days the chest will be empty. (Name a coin that would be left in the chest).

Does it? At the end of each day there will be nine new coinds, and no matter what number coin B gets up to, there will be 9x that number left in the chest. Or maybe I am misunderstanding due to the hour. But surely B would only remove every coin if A stopped.

SoupDragon · 31/05/2019 07:45

so it can't be infinitesimally small if I can find something smaller.

So, the same as infinity then.

It seems obvious that eventually B will remove every number from the chest

No it doesn't. 10 go in, one goes out, 9 remain. [comfused]

DadDadDad · 31/05/2019 08:02

Tell me the number of a coin that gets left in A’s chest.

NoineNoine · 31/05/2019 08:18

An infinite sides

Piglet89 · 31/05/2019 08:24

A circle has but one circumference.

CornishMaid1 · 31/05/2019 08:38

The answer is a circle has 0, 1 or infinity sides depending on how you interpret sides and the construction of a circle.

SoupDragon · 31/05/2019 09:23

Tell me the number of a coin that gets left in A’s chest.

Why? 10 go in, 1 goes out, tell me why there are none left?

Foxmuffin · 31/05/2019 09:24

One!

Original poster
Ravingstarfish · 31/05/2019 13:16

The answer is 1 side according to the tutor although it’s nice to see all of the answers!

OP posts:
M3lon · 31/05/2019 13:48

DadDadDad

The thieving angel has taken out an infinite number of coins (lets call is infinityT (for thieving)...but the coins infinityT+1, infinityT+2 ....etc. are still in there....such that there are 9 times as many coins in the chest than the thieving angel has taken.

It doesn't matter that the numbers are both infinite...one is still allowed to be 9 times bigger than the other.

M3lon · 31/05/2019 13:54

Circles certainly have 1 edge by the way....the word 'side' is not perhaps well defined!

careerchange456 · 31/05/2019 13:56

Year 2 teacher

We've been told that key stage 1 should be taught that a circle has no sides with a side being a line between two vertices. We've been told to teach that a circle has 1 curve.

But all the teaching resources tend to have a circle with 1 side...

DadDadDad · 31/05/2019 14:20

M3lon - infinity is not a number so you can't make arithmetic statements like infinity+1 or infinity x 9.

FudgeBrownie2019 · 31/05/2019 14:23

Reception teacher and I always teach that a circle has one side. I've no idea if that's correct, but it's what I answer when they ask.

MatchSetPoint · 31/05/2019 14:24

I’m sure it is just one, two sides inside and out would make it a ring and not a circle would it not?

JAPAB · 31/05/2019 14:26

But all the teaching resources tend to have a circle with 1 side...

Some things arelike that. I remember being taught that the square root of 4 is plus or minus 2. Outside of school the convention has been that the square root of 4 is 2, and only 2.

As for the angel, there is no number that will never get removed. So I suppose that if you could see time all at once, the whole infinity of it, you couldn't name a coin that B hasn't taken.

So you would have a situation where there is no coin B hasn't taken at some point on the infinite time line, yet there are always going to be coins in the chest.

But this paradox is probably more due to human conceptions of infinity. I mean, how could you see infinite time and appraise it all at once.

DadDadDad · 31/05/2019 14:35

JAPAB - I think that's why mathematicians are careful about how they use infinity. We are trying to imagine a point in time (and our human brains envisage it as a point a long, long time in the future). when the process is complete and we assess which coins are in the chest. But the process never completes - that's what infinite means.

Mathematicians might talk about infinite sets (and they have a technical way of defining that), but that's not the same as an infinite number. en.wikipedia.org/wiki/Cardinality

SoupDragon · 31/05/2019 16:30

you couldn't name a coin that B hasn't taken.

I'm going to take a punt on him being unable to find coin 999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 under all the other remaining coins that are on top of it.

M3lon · 31/05/2019 18:31

daddaddad what you really cannot do is assert that someone has to name an infinitely high number than say those numbers don't have names!

There is no paradox in your 'puzzle' its perfectly possible to remove an infinite number of coins and still have an infinite number left.

Also I can have nine times a many coins as you even if we both have infinitely many...you just count how many I have for each of yours. simple.

StealthPolarBear · 31/05/2019 18:39

OK I'm going to throw in another one. If a circle has an infinite number of sides do we agree an oval does too, but fewer?

Gth1234 · 31/05/2019 18:39

seriously it depends how you define a circle.

en.wikipedia.org/wiki/Circle

given this part of the article near the top, it would sort of imply there is an interior and an exterior, and in those terms 2 sides.

A circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.

FiddlesticksAkimbo · 31/05/2019 18:40

Tell me the number of a coin that gets left in A’s chest

On any given numbered day the coin which is that number plus 1 will still be in the chest. You don't need to dabble in infinity. Or have I missed something?