# Has any experiment actually measured PI to many places?

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• squirrlmcduckles
In summary, the conversation discusses the concept of pi and whether it can be measured physically in a laboratory setting. It is determined that pi is a mathematical constant and can be calculated to high degrees of precision using mathematical methods. The idea of pi being affected by the expansion of the universe or the curvature of spacetime is also explored, but ultimately it is concluded that pi is a constant and not dependent on these factors. The conversation also touches on the concept of measuring the accuracy of Euclidian geometry in our universe, which is related to the value of pi.

#### 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!

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

squirrlmcduckles said:
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!
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

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.

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?

Delta2
squirrlmcduckles said:
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?
This is nonsense.

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

squirrlmcduckles said:
but has there been any 'serious' attempt to measure Pi PHYSICALLY

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

squirrlmcduckles said:
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?

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.

squirrlmcduckles said:
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?
A circumference to radius ratio of 3.0 would indicate positive curvature. A ratio of PI indicates zero curvature.

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.

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squirrlmcduckles said:
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!

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.

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.

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squirrlmcduckles said:
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?

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?

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squirrlmcduckles said:
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!
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.

gmax137 and Delta2
A.T. said:
A circumference to radius ratio of 3.0 would indicate positive curvature. A ratio of PI indicates zero curvature.
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.

Drakkith
Nugatory said:
... 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.

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.

Delta2

## 1. What is PI and why is it important in scientific experiments?

PI, or π, is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is important in scientific experiments because it is a fundamental constant that appears in many mathematical equations and is used to calculate various properties of circles and other geometric shapes.

## 2. Has PI been measured accurately in experiments?

Yes, PI has been measured accurately in experiments, but not to an infinite number of decimal places. The most accurate measurement of PI to date is 31.4 trillion digits, achieved using a supercomputer in 2019. However, for practical purposes, PI is typically rounded to 3.14 or 3.14159.

## 3. How is PI measured in experiments?

PI can be measured experimentally in a few different ways. One method is using a circular object and measuring its circumference and diameter, then dividing the circumference by the diameter to get an approximation of PI. Another method is using a series of polygons to estimate the value of PI. Additionally, there are mathematical formulas, such as the Leibniz formula, that can be used to calculate PI.

## 4. Are there any real-world applications for measuring PI to many places?

While measuring PI to many places may seem like a purely theoretical exercise, there are actually several real-world applications for highly accurate measurements of PI. For example, in fields such as physics and engineering, PI is used in calculations for things like the orbits of planets and the design of bridges and buildings. In the financial sector, PI is used in risk management and option pricing models.

## 5. Can the value of PI change in different experiments?

No, the value of PI does not change in different experiments. It is a constant value that is the same regardless of the method used to measure it. However, due to the limitations of measurement technology, the value of PI may vary slightly in different experiments, but these variations are negligible and do not affect the overall value of PI.