Are there situations where pi is not equal to 3.14blahblahblah?

[originalpckelly]

If you place a circle halfway in and out of the gravity well of a planet, shouldn't the circle be distorted in such a way that pi is no longer equal to 3.14blahblahblah, but rather some other ratio? Gravity is really the distortion of space/time so it should do this shouldn't it?

:withstupid:

Einstein appears to have assumed that the face of a theoretical clock would be uniformly distorted, but indeed, if placed any way in the area of space distorted by a large mass, the clock's face shouldn't be completely circular. The distortion is not uniform. I'm attempting to mathify some ideas I've had lately about the interrelationship between probability and gravity, in an effort to possibly explain why planets don't do all the weird junk electrons and other small particles do. I think explaining/proving it in terms of pi and distortion of pi is the best way to go.

Of course, that is reliant upon my basic assumption that pi can indeed be distorted being true. So, doc, why does my watch slow down at 6 and speed up at 12?

 

[unussapiens]

No.

If it's distorted it's not a circle.

 

[originalpckelly]

Can there ever be circles then?

No.

If it's distorted it's not a circle.

Shouldn't every single circle in the universe be distorted, even minutely, by the distortion of matter in some other part of the universe?

 

[Artlav]

Um.
If we look at mathematics, the pi have a defined value, so it can't change whereever the mathematician will go to.

Now, if we look at the reality, how are you going to measure a ratio? Diameter by circumference is PI in a normal circle. In distorted circle the circumference stays, but the diameter is no longer uniformly defined - it is different depending on which axis you will take. So, the definition breaks down if you look at it in reality from outside the universe, not unlike a circle painted on the stretched piece of rubber.

Can we look from outside of the universe? No for now and probably for ever, which raises a third possibility - how is the world perceived from inside the space, bent by something, like gravity? If you lived on the piece of rubber from above example, you would have been stretched too, along with light and everything else, so there will be no way to tell if the circle have a stretched shape, so the ratio will appear the same.


You really asking a somewhat philosophical question, so there is no general-case answer, only slices of the spectrum.


.

 

[originalpckelly]

Um.
If we look at mathematics, the pi have a defined value, so it can't change whereever the mathematician will go to.

Now, if we look at the reality, how are you going to measure a ratio? Diameter by circumference is PI in a normal circle. In distorted circle the circumference stays, but the diameter is no longer uniformly defined - it is different depending on which axis you will take. So, the definition breaks down if you look at it in reality from outside the universe, not unlike a circle painted on the stretched piece of rubber.

Can we look from outside of the universe? No for now and probably for ever, which raises a third possibility - how is the world perceived from inside the space, bent by something, like gravity? If you lived on the piece of rubber from above example, you would have been stretched too, along with light and everything else, so there will be no way to tell if the circle have a stretched shape, so the ratio will appear the same.


You really asking a somewhat philosophical question, so there is no general-case answer, only slices of the spectrum.


.

No it's a dumb question, as a circle is defined as having equal distance between all of it's points. I'm suggesting something that sounds like an ellipse, but I'm an idiot so an ellipse is a circle to me.

 

[Belisarius]

Mathematics is mathematics; reality is reality. Pi is always Pi.

 

[Urwumpe]

And beware of the new Pie.

 

[Belisarius]

The circumference of any pie is directly proportional to the content of steak and kidney expressed in grammes.

 

[bujin]

Mmmmmmmmmm................. pie................................

I think pi is a constant with value 3.14(etc...) in Euclidian geometry only. But then I've never got my head around non-Euclidian geometry, so I've no idea what happens when you put that circle into curved space.

 

[tblaxland]

'Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it's simpler, you see,
Than 3 point 1 4 1 5 9.

("The Lure of the Limerick" by W.S. Baring-Gould, p.5. Attributed to
Harvey L. Carter).

 

[Hielor]

I recall in a Piers Anthony novel (one of the Proton ones) there was pointed out a method by which the sum of a triangle's angles can be greater than 180 degrees. If the triangle is drawn about a strong gravitational point, the angles can be greater than 90 degrees, but the lines will be straight (while following curved space).

 

[tblaxland]

I recall in a Piers Anthony novel (one of the Proton ones) there was pointed out a method by which the sum of a triangle's angles can be greater than 180 degrees. If the triangle is drawn about a strong gravitational point, the angles can be greater than 90 degrees, but the lines will be straight (while following curved space).

Like this:

 

[Urwumpe]

Actually not. What changes is not even the circumference of a circle with the diameter 1, but is the circumference of the projection of a circle into a non-euclidean space.

 

[JamesG]

How about this after only half a cup of coffee this morning:

You can think of an eliptical orbit as a manifestation of the distortion of gravity on space time (and your circle). Were the primary mass perfectly centered on the orbit or if gravity were a uniform force then the orbit will be perfectly symetcrical. But because it drops to the square of distance, an orbit is stretched towards and away from the gravitational center.

So pi becomes defined by the same math as that describes an elliptical orbit.

?

 

[n122vu]

No it's a dumb question, as a circle is defined as having equal distance between all of it's points. I'm suggesting something that sounds like an ellipse, but I'm an idiot so an ellipse is a circle to me.

A circle is in fact an ellipse that has both of the focii located in the exact same position. A circle is always an ellipse, but an ellipse is only a circle if the focii are together. So, if we distort the circle in three-dimensional space, from above it might appear that the focii are together from an x/y perspective, but they will be apart on the z axis, thereby removing the possibility of the ellipse being a true circle.

This is in fact what actually happens to an orbit over a planet and why an orbit can never truly be circular and eccentricity can never truly equal zero around an uneven body. Because the surface of the planet is uneven and not completly spherical, the uneven distribution of the planet's mass pulls on the orbiting body such that it distorts the orbit a tiny bit each time around and the result is an elliptical orbit, not a completely circular one, which is kind of the same thing JamesG was getting at...

 

[n72.75]

3.1415926535897932384626433823795028841979393993
all from memory

 

[astrosammy]

3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4 4 0 6 5 6 6 4 3 0 8 6 0 2 1 3 9 4 9 4 6 3 9 5 2 2 4 7 3 7 1 9 0 7 0 2 1 7 9 8 6 0 9 4 3 7 0 2 7 7 0 5 3 9 2 1 7 1 7 6 2 9 3 1 7 6 7 5 2 3 8 4 6 7 4 8 1 8 4 6 7 6 6 9 4 0 5 1 3 2 0 0 0 5 6 8 1 2 7 1 4 5 2 6 3 5 6 0 8 2 7 7 8 5 7 7 1 3 4 2 7 5 7 7 8 9 6 0 9 1 7 3 6 3 7 1 7 8 7 2 1 4 6 8 4 4 0 9 0 1 2 2 4 9 5 3 4 3 0 1 4 6 5 4 9 5 8 5 3 7 1 0 5 0 7 9 2 2 7 9 6 8 9 2 5 8 9 2 3 5 4 2 0 1 9 9 5 6 1 1 2 1 2 9 0 2 1 9 6 0 8 6 4 0 3 4 4 1 8 1 5 9 8 1 3 6 2 9 7 7 4 7 7 1 3 0 9 9 6 0 5 1 8 7 0 7 2 1 1 3 4 9 9 9 9 9 9 8 3 7 2 9 7 8 0 4 9 9 5 1 0 5 9 7 3 1 7 3 2 8 1 6 0 9 6 3 1 8 5 9 5 0 2 4 4 5 9 4 5

Even more exactly: http://www.aip.de/~wasi/PI/Pibel/pibel_10mio.pdf

Maybe it would change to 9999999999999999999999999 near a black hole :lol:.

 

[cjp]

No, Pi comes from mathematics, not from physics. When the physics becomes different (close to a black hole or whatever), it doesn't change pi, because the value of pi is not a matter of physics. When things that used to be circles no longer are true circles (e.g. when 'space-time' is bent, and you're no longer in an 'euclidean space'), then it simply means that those things are no longer properly described by the mathematics of circles. The value of pi still holds for circles, but circles can no longer be used in your physics.

There are mathematical methods for calculating (approximating) the value of pi. From the definition of pi, you can prove these methods to be correct. Always correct. So you might as well re-define pi to be the result of such a calculation.

In that sense, saying that pi could have a different value than 3.1415...etc. is not much different from saying that 1+1 could have a different value than 2.

 

[Rixile]

Pi is a Irrational Number, so it would go on a everlasting trip. Kind of like space.

 

[martins]

3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4 4 0 6 5 6 6 4 3 0 8 6 0 2 1 3 9 4 9 4 6 3 9 5 2 2 4 7 3 7 1 9 0 7 0 2 1 7 9 8 6 0 9 4 3 7 0 2 7 7 0 5 3 9 2 1 7 1 7 6 2 9 3 1 7 6 7 5 2 3 8 4 6 7 4 8 1 8 4 6 7 6 6 9 4 0 5 1 3 2 0 0 0 5 6 8 1 2 7 1 4 5 2 6 3 5 6 0 8 2 7 7 8 5 7 7 1 3 4 2 7 5 7 7 8 9 6 0 9 1 7 3 6 3 7 1 7 8 7 2 1 4 6 8 4 4 0 9 0 1 2 2 4 9 5 3 4 3 0 1 4 6 5 4 9 5 8 5 3 7 1 0 5 0 7 9 2 2 7 9 6 8 9 2 5 8 9 2 3 5 4 2 0 1 9 9 5 6 1 1 2 1 2 9 0 2 1 9 6 0 8 6 4 0 3 4 4 1 8 1 5 9 8 1 3 6 2 9 7 7 4 7 7 1 3 0 9 9 6 0 5 1 8 7 0 7 2 1 1 3 4 9 9 9 9 9 9 8 3 7 2 9 7 8 0 4 9 9 5 1 0 5 9 7 3 1 7 3 2 8 1 6 0 9 6 3 1 8 5 9 5 0 2 4 4 5 9 4 5

I once wrote a program to compute pi to arbitrary precision that used some superconvergent series approximation (fun in a sad geeky sort of way ). I stopped after about half a million digits, because I ran out of paper. The only useful thing about it was the arbitrary-precision floating point system I implemented for it.