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Circle Measurement Problem & Experiment Ideas

Your questions have zero practical value here.
The opposite is true: it deals directly with circle measurement & the metrology of a real object.
If it has no practical value to you... why are you wasting your own & others' time? Just leave.
Given your initial response, you never had an intention of being on-topic in the first place.
See that title at the top? PRACTICAL Machinist?
Yes. Both experiments & measurements of real precision-machined objects are all practical.
If Pi calculations
The topic is NOT about pi "calculations".
It is about circle measurement & experimental ideas.
Do you have either? No? This topic doesn't concern you.
 
When's Rajhlinux going to jump in with a post on how people have been doing this to sub micron level in their garages with Moore jig grinders converted to surface grinders.
 
Hello,

To help convey what is an otherwise deeply embedded problem, person A & B are having a discussion
about a hypothetical 1 m diameter circular object rolling straight on a flat plane surface. Person C is present & listening.

Person A believes the object will roll no further than 3.1416...m because its circumference is π m according to c = πd for d = 1.
Person B claims according to the Pythagorean theorem, the same object will actually roll no less than than 3.1446...m.

A reminds B of Archimedes' upper- and lower-bounds 223/71 < π < 22/7 with 22/7 < 3.1446... therefore the latter can't be correct.
B reminds A of a property of plane geometry called isoperimetric inequality & its proof finally coming only as recently as the 19th C:

View attachment 422847
source

with it always having applied not only to Archimedes' non-circular approach to circle measurement,
but to any & all similarly exhaustive approaches which neglect to establish isoperimetric equality
between line & curve from the onset.

A does not believe anything B says & instead asks A for the math predicting such a number.
B produces:
View attachment 422841
and suggests any & all carefully designed & controlled real-world experiments
will reliably & reproducibly reflect 3.1446... instead of 3.14159... as per Pythagoras.

Person A still doesn't believe this & orders a simple flat 1m diameter circular disk from a precision engineer
& takes it to a metrology lab to have its diameter & circumference measured. However, when asking how
the circumference would be measured & how accurately, the metrologist responded concerning the use of a STEP file:

emphasis added

Person A asks B whether or not this measurement approach is affected by isoperimetric inequality.
Person B states it is & metrologists don't actually measure the circumference... as the one above admits:

because the probed points are afterwards being treated as the vertices of a non-circular polygon whose perimeter is taken instead.

B goes on: in fairness to metrologists, mathematicians dropped the ball on failing to retroactively apply isoperimetric inequality to Archimedes' pi.
Upon proving it, they forgot they've always used polygons to arrive at 3.14159... itself, which is meant to be a perfect circle (it is not).
It is impossible to surround any real unit diameter circlular object with a length of only 3.14159... it will never fully surround.

The isoperimetrically equivalent polygon of sides n is n = 4, not n → ∞ because each c/4 of c reflects one of four discrete convex sides.
For a circle, its side is convex (ie. curved) but nonetheless discrete: it is contained by two right-angled radii of length 1/2 each.
As it rolls, the convex side translates itself as a linear line onto the flat plane directly. This implies isoperimetric equaltity at n = 4.

Person A notices C has been silent & asks what they think.

C states they don't believe either until they see the results of a properly conducted experiment
involving taking a direct measurement of the circumference of a sufficiently circular object
in a way which eliminates any & all possible introductions of isoperimetric inequality.

This means no point probes or connect-the-dots, no use n-gons which diverge away from n = 4.
Accuracy min. req. is nearest circ. mm per diametric m:

If 3.1416... is closer to reality, we expect a roll distance of ~3141.6 mm per full rot.
If 3.1446... is closer to reality, we expect a roll distance of ~3144.6 mm per full rot.
The raw numerical difference we need to capture is 3 mm on the circumference.

If you were (or are) a metrologist or engineer... how would you design & conduct a measurement experiment
which circumvents the problem of isoperimetric inequality while/as being accurate enough to the nearest mm?
You can use any circular object, precision engineer any parts & use any digital technology you want.

I am in the position of C and will be performing the experiment myself and am happy to share when completed.
Thanks for reading & looking forward to different ideas & approaches!
Lets see if this is AI,
The above cannot factually come to proof for either of the 3 parties.

Each separate entity (A,B,C) existing in its own subjective reality and has a totally separate reality to the other, each's perception of an objective reality, does not make one exist as an absolution.
Therefore the perceived outcome to each would be different in some way unmeasurable to the others.

If the test was performed by a 3rd party (C) to ensure an unbiased result to the two, neither subject A nor B could be absolutely sure a bias was not added to sway the proof in the others favor.
The only way each subject A and subject B could rely on factual unbiased proof in the test would be do do it themselves,
but then the outcome for each could not be used by the other for proof as each could have applied bias for their own results.

Due to spacetime, with each entity residing in different locations, each's entities perception to any outcome can be skewed slightly.
without the parameter of time added to the equation we have no idea if the proof for each is happening at the same time with the same parameters with difference space time warp.

Also we are missing the parameters of the subject to assimilate the outcome or proof of the test.
Each subject has a limitation to interact with its existence with only one sensory input, sight, touch, taste, sound are all factually touch sensors, or better energy sensors.

If the subjects are missing one of their touch or energy sensors(missing parameter), such as the eyes, they will have no way of seeing the tests proof, or outcome.
A blind subject could be audibly told that the test was confirmed or denied in their favor,
but there would be no way for each entity to factually know the test was done without bias by the 3rd party who conducted the test.

This list can go on and on, in the end their is no factual way to objectively prove eithers paradoxical hypothesis to an absolute, or even as mentioned to a mm.

haha :D
 
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I have no idea what this thread is really about. The question that most of us have contemplated since the year of our Lord 1975 is and always will be "What is the airspeed velocity of an unladen swallow?" Apparently, the correct answer may be dependent on whether it is an African swallow or a European swallow.
 








 
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