B Has any experiment actually measured PI to many places?

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1. May 31, 2016

squirrlmcduckles

Ok,
This probably seems a silly question, but has there been any 'serious' attempt to measure Pi PHYSICALLY, like in a lab, using say a light fiber in a circle and one down the radius?
If so, where can I find the results/paper?
Thanks!

2. May 31, 2016

Drakkith

Staff Emeritus
Pi is a mathematical constant. It is determined through mathematical means, not through experimental means.

3. May 31, 2016

SteamKing

Staff Emeritus
What would be the point? Any physical measurement would be limited to a handful of decimal places only, and π has been calculated to more than 13 trillion decimal places as of 2015.

https://en.wikipedia.org/wiki/Pi

4. May 31, 2016

pixel

squirrlmcduckles: Maybe you are thinking along the following lines: π is defined as the ratio of the circumference of a circle to its diameter. In order to know what that value is, we need to draw a circle and measure the circumference and the diameter, i.e. a physical measurement. But π turns up in many mathematical expressions that can be calculated by computer to high degrees of precision. So we are not dependent on a physical measurement.

5. Jun 1, 2016

squirrlmcduckles

Well, the reason for the seemingly weird question is this.
Pi represents a measurement of 2d to 1d ratio, if we were in a curved spacetime, say on an apple surface, the value of Pi would be different.

So my real thought is, is Pi actually 3.0, and the .14159 just an effect of the expansion of the universe? i.e local/global spacetime curvature?

6. Jun 1, 2016

SteamKing

Staff Emeritus
This is nonsense.

The circumference of a circle is a length, a one-dimensional quantity. Pi is not a 2d to 1d ratio.

7. Jun 1, 2016

A.T.

You shouldn't have put "serious" in scare quotes.

8. Jun 1, 2016

Drakkith

Staff Emeritus
No. Pi really is 3.14159...
You can mathematically construct a circle in a flat geometry and the ratio of the circumference of the circle to its diameter is exactly pi. Just about any graphing utility on the web will let you do this.

9. Jun 1, 2016

A.T.

A circumference to radius ratio of 3.0 would indicate positive curvature. A ratio of PI indicates zero curvature.

10. Jun 1, 2016

Delta²

Your thought is very interesting at least to me. However what is being said here by other members that you can calculate the value of pi much better using mathematical methods rather than physical ones, especially nowdays that computer hardware has evolved alot.

For example it is

$\pi\approx 4 \sum\limits_{n=0}^{k} \frac{(-1)^n}{(2n+1)}$

the higher k you put the better approximation of pi you get.

Last edited: Jun 1, 2016
11. Jun 1, 2016

ZapperZ

Staff Emeritus
pi is a mathematical constant, not a physical constant. It is similar to e, the number 42, etc... You do not "verify" them via experiments. You verify/derive them via logical mathematical arguments.

Zz.

12. Jun 1, 2016

Staff: Mentor

Might be interesting to know how many drops N of Buffon's needle on average one has to make to achieve n correct decimals of π with say .95 certainty.

Last edited: Jun 1, 2016
13. Jun 1, 2016

DocZaius

Or wait, maybe pi is actually 100 and the -96.858 is just an effect of the expansion of the universe? Or maybe pi is 10,000 and etc... Let me guess, my suggestions for pi seem silly but 3 seems reasonable to you?

Last edited: Jun 1, 2016
14. Jun 1, 2016

A.T.

15. Jun 1, 2016

Staff: Mentor

Pi is by definition the ratio of the radius of a circle to its diameter in Euclidian space, and its value has been calculated to many decimal places (and can always be calculated to more). Thus, the measurement that you're describing is not a measurement of the value of pi - we already know that. It is a measurement of how accurately Euclidian geometry describes the universe we live in; any discrepancy between calculated value of pi and the measured ratio (that cannot be attributed to the inaccuracy of the measurement) indicates that we do not live in a perfectly Euclidian universe.

16. Jun 1, 2016

jbriggs444

Note that such a ratio would not be a constant. It would depend on the radius of the circle. The smaller the circle, the smaller the effect of the region's curvature on the ratio of circumference to diameter. In the limit of increasingly small circles, the ratio is still pi, regardless of whether curvature is positive, negative or zero -- as long as it is not infinite.

Edit: Consider, for instance, circles scribed on the surface of the earth. The length of the equator (circumference) is twice the distance from equator to pole and back (diameter). But a crop circle will have a circumference to diameter ratio pretty close to pi.

17. Jun 1, 2016

gmax137

I think this was the OP's point?

Seems to me, the deviation from Euclidean in any small circle is so small that it would be lost in the measurement errors. So, you'd need to measure a really big circle. Unless you're caught in the grip of a black hole, isn't "our universe" pretty flat? Then a really big circle would be Euclidean so you wouldn't see any deviation.