[evan_au]

A circle is a closed line drawn in the plane, using a device (calipers)

Greek mathematicians were very suspicious of physical devices, because they can never be perfect (unlike the purity of geometry).

But they accepted the compass because it was an imperfect, physical implementation that delivered an approximation to the pure, perfect circle that existed only in their minds.

If the value of pi can vary over a narrow range (eg 3.14 to 3.16), then I think that you have been stung by the imperfect physical implementation.

By the way, they did not accept measurement marks on rulers or tape measures, because the physical imperfections are too great - so how did you measure 3.16?

Archimedes, the Greek geometer, measured pi to several decimal places without using primitive physical rulers. He did it by surrounding a circle with polygons. He narrowed it down to 3¹⁰/₇₁ < π < 3¹/₇, or 3.1408< π <3.1429.

So clearly, if you have measured 3.16, you have made an error, due to cheating! (The Greek geometers were quite strict about not cheating!)

See: https://en.wikipedia.org/wiki/Approximations_of_%CF%80#Polygon_approximation_to_a_circle

Can pi Change?
Yes, it can change from π (miniscule) to Π (majuscule).
But they both mean the same to a Greek.

[aetzbar (OP)]

You're right that physical measurements are not perfect.
Therefore, measurement can not determine perfect equality.
But, measurement can certainly determine, inequality.
The measurement I propose is not of length, but of ratio numbers
The measurement uses two circuits, and it should determine.
Large diameter / small diameter > Large circumference / small circumference
The inequality is tiny, but the conclusions are dramatic
A detailed description of the measurement can be found in the attached article

[Bored chemist]

But, measurement can certainly determine, inequality.

No, not really.
Not if the inequallity is small enough.
However you are talking about really big changes " 3.1416 to 3.164"
And the experiment which you keep trying to ignore shows that any change is much much smaller than that.

[Bored chemist]

if this interests you, this is an experiment that a scientific institution should do.

Thanks

THEY ALREADY DID

[aetzbar (OP)]

The experiment I propose to do is a multidisciplinary experiment
Physical measurement, which affects geometry and mathematics.
The experiment brings new geometry after Euclid, in which pi changes.
And mathematics should admit an embarrassing mistake when it provided proof that Pi is a fixed number.

[Bored chemist]

The experiment I propose to do is a multidisciplinary experiment
Physical measurement, which affects geometry and mathematics.
The experiment brings new geometry after Euclid, in which pi changes.
And mathematics should admit an embarrassing mistake when it provided proof that Pi is a fixed number.

Why would anyone divert funds to look at this when they already know that the answer is the same as it has been for 2000 years. ( they know that from things like the experiment I told you about.)
Especially when they see that you can't explain how a ring casts a circular shadow.

[aetzbar (OP)]

Good for you for the great interest in Pi's fascinating subject
Maybe you should write a short article on the subject.

[Bored chemist]

Good for you for the great interest in Pi's fascinating subject
Maybe you should write a short article on the subject.

OK
here's a very short article
Pi=Pi.