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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 · 31/05/2019 18:40

" Outside of school the convention has been that the square root of 4 is 2, and only 2."
That's just wrong though. I suppose in a situation where you only care about positive numbers it might be conventional but it is wrong.

Gth1234 · 31/05/2019 18:43

@StealthPolarBear

It depends how you define the circle and the ellipse, but for the same area, the ellipse will have a bigger circumference, and therefore have more sides. Alternatively, for the same circumference, the ellipse encloses a smaller area.

Gth1234 · 31/05/2019 18:49

@StealthPolarBear

and outside of academia, nobody, has seen a square root of -1.

I'll be a pie-eyed emu, as someone once said. I'll leave you to research this.

bridgetreilly · 31/05/2019 18:59

And the tutor is still wrong to say that it has 1 side. It has 1 edge. Those are definited differently and she should know better.

FiddlesticksAkimbo · 31/05/2019 19:04

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?

Why fewer? Triangles all have three sides, but they can be different shapes.

HolesinTheSoles · 31/05/2019 19:08

It depends how you define a side. If it's the number of discontinuities (i.e. corners) then it has zero. If you calculate the ratio of the area of an n-sided shape to the perimeter in terms of the distance of each corner to the centre and tend n to infinity you get the correct ratio of a circle so that would suggest that a circle can be seen as a regular infinity-gon (i.e. inifite sided shape).

Essentially the question is poorly defined and so it has no definitive answer. You first need to establish by what you mean by side before you can answer.

StealthPolarBear · 31/05/2019 19:10

Fewer because an ovals are straighter. Although the pointer ends are pointer too so maybe they balance out

Gth1234 · 31/05/2019 19:13

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?

I have already explained that an ellipse clearly has more sides/tangents than a circle, as it has a longer circumference. It's a bigger infinity.

HolesinTheSoles · 31/05/2019 19:17

Outside of school the convention has been that the square root of 4 is 2, and only 2.

ERR no not at all. The square root as a function is usually defined as positive values only as a one to many mapping can't be considered a function. The calculator uses this convention. In lots of practical applications the positive square root is the only one that makes sense and so automatically used (e.g. I have a square field of area 4m^2 how long are the sides). However there are many many technical uses of maths beyond this in which the negative square root is used.

goodwinter · 31/05/2019 19:35

@DadDadDad Help me out here please...

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).

On day 1: A adds 10 coins, B takes 1. 9 coins in chest.
On day 2: A adds 10 coins, B takes 1. 18 coins in chest.
On day 3: A adds 10 coins, B takes 1. 27 coins in chest.
On day 4: A adds 10 coins, B takes 1. 36 coins in chest.
On day 5: A adds 10 coins, B takes 1. 45 coins in chest.
...and so on.

How would the chest ever have 0 coins in it?

How is it any different than saying "Each day angel Y places 9 coins in the chest"?

I think asking to name the coins is playing a silly game, because you then say you can't name infinity. On X day, angel B will remove X coin from the chest. So it goes for X+1 day and X+1 coin, X+2 day and X+2 coin, etc etc... meanwhile the chest is filling up with 9 extra coins every day.

How will that get to zero?!

goodwinter · 31/05/2019 19:37

@FiddlesticksAkimbo Ha - should have read your post first because I've basically said the same thing but in a much more long-winded way...!

FiddlesticksAkimbo · 31/05/2019 19:41

Hi Goodwinter,

It seems a transparent nonsense to me! We must await Daddaddad to show us where we have gone wrong Grin

JAPAB · 31/05/2019 19:48

Perhaps I wasn't clear re the square root thing. I was referring to the use of "the".

In school THE square root of 4 was +/-2.

Outside of school THE square root of 4 is 2.
-2 is A square root of 4, but not THE square root.

THE is reserved for the non-negative root only.

autumneve · 31/05/2019 19:55

"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."

So then how many sides does a semicircle have?

JAPAB · 31/05/2019 19:58

How is it any different than saying "Each day angel Y places 9 coins in the chest"?

Nothing is removing the coins in that case. If you examine the chest at any discrete point of time, then of course at that point there will always be more coins left.

I think however we are meant to envisage appraising the whole situation after an infinite amount of time. With an infinite amount of time, every coin put in will have been removed. To say that there are still coins left suggests you are examining a discrete point in time, not appraising the whole of infinite time. Or something.

Fakeflowersandlemonade · 31/05/2019 19:59

Primary TA here. A circle has 1 side

autumneve · 31/05/2019 20:01

My educated brain is saying 1.

My brain that is now influenced by this thread is saying 0.

Tunnocks34 · 31/05/2019 20:03

From my experience primary school teachers and tutors always teach it was one side.

They are wrong, it has 0 sides, and 1 curved edge. It’s something that as a math teacher I often come across.

Polygons have sides. Circles don’t.

Dieu · 31/05/2019 20:03

I thought it was one.

DadDadDad · 31/05/2019 20:11

I agree, JAPAB.

Perhaps we can simplify it. Suppose I told you that Angel A didn't bother putting coins in the chest daily but actually started on day 1 with all the coins already in the chest (the infinite set of coins labelled 1, 2, 3, ...). On day 1, B comes along and removes coin 1; on day 2, B removes coin 2; ... If that continues to infinity, then B removes every coin and the chest is empty. So, what difference does it make that A puts in 10 at a time? We get counter-intuitive, contradictory answers because we can't actually have a process that happens an infinite number of times.

Tunnocks34 · 31/05/2019 20:18

I think probably at primary school level, one curved side would be classed as correct, particularly in lower primary.

HolesinTheSoles · 31/05/2019 20:18

Primary TA here. A circle has 1 side

Not to be a massive snob but it's actual a subtle question which is definitely not answered in the primary school curriculum. As asked it's a poorly defined question that has no answer - until you can define what a side is you can't tell how many sides it has. The answer could be either 0 , 1 or infinity depending on which definition you use.

HolesinTheSoles · 31/05/2019 20:23

and outside of academia, nobody, has seen a square root of -1.

Total and utter rubbish. Anyone working working in any remotely technical stem field (engineering, computer science, many areas of actuarial science, statistics, finance etc etc) uses the square root of -1 and results proved which require it's use all the time. It's certainly not an abstract concept used only in the ivory tower of academia.

HolesinTheSoles · 31/05/2019 20:27

*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).*

Complete nonsense. If A puts in 10 coins a day and B removed 1 coin a day the total numbers of coins in the chest at day 9 will be 9n. As we tend n to infinity the number of coins in the chest also tends to infinity. That's actual fairly simple to understand without hidden logical twists.

goodwinter · 31/05/2019 20:28

@DadDadDad we've mentioned in this thread that some infinities are bigger than others. An infinite number of coins are taken out of the chest, but a larger infinite number of coins are put into the chest, surely?

If you reversed it, and said: "the chest starts with one coin. Each day A takes out 1 coin and B then puts in 10 coins", would that still end up with no coins being in the chest after an infinite time?

Sorry, I just can't grasp this! Each day there are 9 more coins in the chest. As long as more coins are being added than taken away each day, no matter how this goes on for, the number of coins in the chest will still be increasing.

SURELY?! It's messing with my head!