Why is Pi wrong?

[ludwig]

It should be exactly 3 but it's slightly out. How did that happen?
Could there be somewhere else in the universe where it is 3?

[squarebear]

I think "lop" there is used to describe the state of their ears rather than a particular breed. :-)

[ChuckFickens]

This has to be one of the most diverse threads I've ever seen!

[ludwig]

I like your idea notafish, but I don't think it would be a circle - just a curved line.

Maybe that's the answer though - if you took that curved line and looked at it from a certain angle, you could make the ends join up and pi would be three.

[jomifl]

Notafish...nearly a circle, you could draw a straight line between the ends, no one would notice.

[ChuckFickens]

Notafish...

It would be a magic circle.... just like the ones that magicians use when they do the joining the rings trick.

[squarebear]

Yes, you could try explaining that there is three times as much paper on three fivers than a twenty and so it must be worth more. That should convince them ;-)

[squarebear]

pi iz rong coz dere's no E on tha end lololol

[anneasquith]

doc, how did you fall away down to science ? did you fall out of bed. maybe a nice aber will give you a leg up.

[jake-the-peg]

Got a headache Doc? don't read this then.

Pi is the ratio between a circle's circumference and it's diameter. This is the case in Euclidean space - a flat plane.

Now imagine a circle drawn on a bendy sheet of rubber that is stretched in the middle. Now the diameter is much larger Pi has become smaller.

From General relativity we know that large gravitational masses bend space - the value of Pi around a black hole would depend on how you draw your circle and how you measure it.

This is why Pi is normally defined only in Euclidean space.

See here for more on non-euclidean geometries
http://knol.google.co...try/13vv5m9radaus/17#

[squarebear]

Ah but once you start bending circles, you have ellipses and so the ratio of pi is no longer relevent.

If you stretch a circle and keep it a circle, the diameter also increases and the pi ratio still applies.

[vascop]

Obviously what's needed here is a definition of a circle that we can all agree on. Here's one possible definition:
Get a piece of paper and a compass (the one with a pencil attached to one arm and a sharply pointed piece of metal to the other). Stick the pointy thing into the paper and rotate the compass, holding it near the top where the two arms are joined, while keeping the pencil point in contact with the paper. Keep going until the curve drawn by the pencil joins up.
Let's agree to call this kind of curve is a circle.
Now measure the diameter and the circumference and divide the circumference by the diameter. Write down what you get.
Now draw some more circles in the same way but for different distances between the metal point and the pencil point and every time calculate the value of the circumference divided by the diameter.Write it down again.
You will find that you always get a value around 3.1.
Interesting that you always get what appears to be the same number - it isn't obvious.
So let's call this pi.

[jomifl]

Jake has just demonstrated that space is curved, if we were in some other part of the universe where space isn't curved then Pi might be equal to 3.

[jake-the-peg]

No a circle in non euclidean space is still a circle.

the idea of bending the sheet isn't a good analogy when you measure it the distance is still the same from all points to the centre because the radii appear to be warped similarly from our outside perspective.

This is why nobody really came up with non-Euclidean geometry unil the 19th Century - it's pretty difficult to get your head around.

Turns out though that it's just the ticket for solve Einsteins field equations that describe the universe

[Count-A-Strong]

(Count enters stage left in in a Military uniform sporting a handlebar moustach, cane under arm)

Now look here, this is SILLY. It statred of a s a nice sensible debate about pi and now rabbits and allsorts have become invilved. Stop that....It's SILLY!

[Ellipsis]

I think ludwig is taking the Pis.

[Marijn]

Or If you want it so badly to be 3; draw your dividing line slightly off centre, and it'll be short enough to be a third of the circumference. It won't technically be a diameter though, it'll be a magic diameter ;-)