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Circle Measurement Problem & Experiment Ideas

experimentalist

Plastic
Joined
Jan 5, 2024
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:

1705102708856.png
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:
1705101354522.png
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:
  • To understand the STEP file, I must first touch upon the system I propose we use to measure the part.
  • We would use a Renishaw SP25M scanning Probe, which will drag itself along and around the outer rim of your circular part (depending on the roughness of the surface) Click the BLUE link to see a sample video
    • While the probe drags itself along the circumference of your part, it collects points along the arc, in a pre-determined resolution. This point density can be set before measurement (ex each point can be 1mm apart, or as tight as 0.1mm, although that would add a lot of time to the scan)
    • The complete scan STEP file can be imported into a CAD software, and when looked at as a whole it may resemble an unbroken line, but when zoomed in, it is apparent that the circle is made up of points closely together
    • This same STEP file is what is used to calculate the max circumscribed and min inscribed size
    • We can measure a straight line between each point and determine the circumference in this fashion, and this would be the most accurate we can get with our measurement
      • Please note that, although the measurements themselves will be within about 4 microns of reality, we would not be measuring the circumference per se, but rather the sum of straight line lengths between each point (point resolution to be determined, but I believe the limit for our system is 0.1mm apart)
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:
we would not be measuring the circumference per se
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!
 
Borrow a VTL. Turn a 100" diameter cylinder. Take a 30' or longer fiberglass tape measure of decent quality, wrap it around the circumference and read off the number. It will be within the accuracy of the tape measure 314.16". It will be noticeably and unquestionably measure less than 314.46". That discrepancy is well within the accuracy of a decent surveyor's tape to verify.

Experimentalist, do you realize B's argument, if valid, would equally invalidate all calculus performed with limits? Do you realize how contrary to centuries of experience that is? Do you still put forward B's argument as valid? Have we learned anything since Zeno? It's only been 2500 years, after all.
 
So pi does not equal what we thought pi to be up to 4th significant digit or 2*pi*r does not equal circumference (which is hard being that is taken from the definition of pi).
 
Before we dig into this, we need to know your opinions on Moore Jig Borer #3?
It weighs several thousands of pounds & is engineered to very accurately spot & size holes.
As far as its relevance to circle measurement... I apologize it's not immediately obvious to me.
and..

Have you ever tried to design and/or build a motor-generator perpetual motion machine?
No (having no need to), but if 3.14159... is inaccurate as B claims, it's correction is a step closer to one.

Concerning efficiency: any n-sided polygon rolling on a flat plane surface will have its center oscillating between a min. and a max.
and is therefore less efficient than a circle whose center remains a fixed proximity to the plane. This is what isoperimetric equality implies:
the center of (only) a perfect circle remains a constant proximity to the plane it rolls on. Polygons do not do this even as n → ∞
as they are always losing motion (ie. kinetic energy) to the y-axis (orthogonal to x-) due to the vertices of the polygon lifting the origin.

B instead argues for n = 4 with side length π/4 (a perfect square). Even if/as this rolls over its own vertices... it still rolls π.
Actually, the perpetual-motion machine only works using an alternator-motor, which has an efficiency equal to the reciprocal of a motor-generator.
This is interesting because according to B, for Φ = R + r = √5/2 - 1/2, any one length π/4 = 1/√Φ (multiplicative reciprocal of √Φ).
If π = 4/√Φ, this means √Φ = 4/π = 1.272... Interestingly, 4/3.14159... is 1.273... what we expect if the circle is slightly too small.
Borrow a VTL. Turn a 100" diameter cylinder. Take a 30' or longer fiberglass tape measure of decent quality, wrap it around the circumference and read off the number.
Thanks for the suggestion, I'll check my local area.
It will be within the accuracy of the tape measure 314.16". It will be noticeably and unquestionably measure less than 314.46".
That's okay if true but we need an experiment which removes any & all doubt for either party.
I only care about the experiment & its control, not the arguments being made anymore.
If anything, it is an exercise in conducting an experiment to test an hypothesis
instead of blindly assuming things like humanity can't be so out-of-touch with reality.
That discrepancy is well within the accuracy of a decent surveyor's tape to verify.

Experimentalist, do you realize B's argument, if valid, would equally invalidate all calculus performed with limits?
It's not something I think about because I would have to see an experiment(s) for something so important as this.
I understand both sides of the argument & I don't care to hear anymore because only a real-world experiment settles it.
I find anyone assuming it is or is not true without having even looked is not being honest with themselves and/or others.
Do you realize how contrary to centuries of experience that is?
Archimedes' "assumption of entrapment" (to trap pi between two polygons) is well over 2000 years old.
It is by far the oldest & most enduring basic underlying assumption modern science has operated on.

Mathematicians just assume the outscribed n-gon must always have a greater perimeter as its n → ∞.
According to B, this is not always true because at n = 59 the circle rolls further for the same reason
explained to Donkey Hotey (loss of efficiency to y-axis due to having vertices).
Do you still put forward B's argument as valid?
I don't & neither does B - the Pythagorean theorem is making the argument for me.
B could get hit by a train but I'd still be taking the argument seriously.

It is because the Pythagorean theorem predicts 3.1446... B makes the argument. Otherwise, B is irrelevant.
To argue against it would require arguing against the validity of the theorem itself or how it is used... not B.
Have we learned anything since Zeno? It's only been 2500 years, after all.
When a metrologist (ie. a scientist of measurement) admits they don't actually measure the circumference... no, not really.
One would expect a metrologist to have a passion for the science of measurement... except today's don't measure curves.
So pi does not equal what we thought pi to be up to 4th significant digit or 2*pi*r does not equal circumference (which is hard being that is taken from the definition of pi).
If the Pythagorean theorem calculation is true, 3.14159... is numerically wrong from the thousandth. The product 2πr = π is still true regardless.
In order to test what B is arguing, we need to test it in the actual physical universe. The problem is one metrologists admit they introduce.

Here is a bare-bones example of one approach which tries to actualize B's argument:

1705153053014.png

Wheel can be a precision engineered wireframe made out of invar (to combat heat expansion) with right-angled spokes.
It can have very fine axial line(s) (~0.3mm) etched directly into it to serve as zero points for alignment purposes.
It can house a two-way digital level (& two singles on the y-axis if necessary) to indicate the angles of the circle's axes.
Any modern prof. real-time digital tape measurer with min. +/- 1/16" accuracy at 3.5 m (pref. 1/32") can tolerate this scale.
Flat plane surface can be made out of a flat ceramic to any width. Same zero point etch & reference to a straight edge.

I like this kind of approach because it tries to 1:1 B's argument therefore be in a position to more clearly falsify it.
If any one planar point of a d ≤ 1 diameter circle fails to travel further than 3.1416 m... (ie. realistically 3.142 to be clear)
B has a reality-check problem. If we get into c > 3.143 territory... B can argue if d ≤ 1, π ≠ 3.14159...

If anyone has or comes up with any experimental approaches to this problem, please feel free to share public or pm & thanks again.
 
... mathematicians dropped the ball ...
which left a flat on one side and explains everything that's wrong with the universe.

I can't escape a feeling that this discussion will end up in the same place as the discussion of how many angels can dance on the point of a pin. According to an on-line Scientific American article "The approximation 3.14 is about ½ percent off from the true value, and the fairly well known 3.14159 is within 0.000084 percent. If you were building a fence around a giant circular swimming pool with a radius of 100 meters and used that approximation to estimate the amount of fencing you would need, you would be half a millimeter short. Half a millimeter is tiny compared with the total fence length, 628.3185 meters. Being within half a millimeter is surely sufficient, and the tools you are using to make the fence probably introduce more uncertainty into your structure than your approximation of pi."

The measurement methods being suggested here seem positively agricultural compared with the requirements of the job, and I detect a certain lack of understanding of basic science.

"Concerning efficiency: any n-sided polygon rolling on a flat plane surface will have its center oscillating between a min. and a max.
and is therefore less efficient than a circle whose center remains a fixed proximity to the plane. This is what isoperimetric equality implies:
the center of (only) a perfect circle remains a constant proximity to the plane it rolls on. Polygons do not do this even as n → ∞
as they are always losing motion (ie. kinetic energy) to the y-axis (orthogonal to x-) due to the vertices of the polygon lifting the origin."


The polygon as it rolls does lose motion (velocity would be a better word) as its centre of mass rises, but it does not lose energy - the reduction in kinetic energy is converted into increased gravitational potential energy. As the polygon rolls over the vertex, the centre of mass falls again and the increase in potential energy is transformed back into kinetic energy. Assuming, as physicists do, that everything is infinitely rigid and so on, there is no loss of energy, so there is no loss of efficiency, whatever that means in this context.

B instead argues for n = 4 with side length π/4 (a perfect square). Even if/as this rolls over its own vertices... it still rolls π.

Nobody could fault B's logic, but we are still faced with how to measure pi. How many of the 62,831,853,071,796 digits reported in 2022 should we use with our "modern prof. real-time digital tape measurer with min. +/- 1/16" accuracy at 3.5 m"?
 
which left a flat on one side and explains everything that's wrong with the universe.
Nothing is wrong with the universe, it is working just fine.

One actual problem is human beings not challenging basic underlying assumptions (ie. doing "science") and/or performing experiments.
I can't escape a feeling that this discussion will end up in the same place as the discussion of how many angels can dance on the point of a pin.
It's the opposite of this because there aren't any real angels to count.
For a unit diameter circle, it surrounds the "real element" square s² = 1/2.
According to an on-line Scientific American article "The approximation 3.14 is about ½ percent off from the true value, and the fairly well known 3.14159 is within 0.000084 percent. If you were building a fence around a giant circular swimming pool with a radius of 100 meters and used that approximation to estimate the amount of fencing you would need, you would be half a millimeter short. Half a millimeter is tiny compared with the total fence length, 628.3185 meters. Being within half a millimeter is surely sufficient, and the tools you are using to make the fence probably introduce more uncertainty into your structure than your approximation of pi."
If the fence were circular, you would be over half a meter short... not half a mm.
If you made it a surrounding polygon instead, you would be fine but capture less area for more fence.
They are not taking into account isoperimetric inequality shaving 0.003 per 1 diametric unit.
The measurement methods being suggested here seem positively agricultural compared with the requirements of the job, and I detect a certain lack of understanding of basic science.
The requirements are to capture a circumferential 3mm discrepancy per unit diameter.

Indeed there is a basic lack of understanding of science somewhere:
science is an ongoing process of incessantly & unreservedly
challenging basic underlying assumptions, beliefs & conclusions.

If one is not doing this... one is not doing science.
"Concerning efficiency: any n-sided polygon rolling on a flat plane surface will have its center oscillating between a min. and a max.
and is therefore less efficient than a circle whose center remains a fixed proximity to the plane. This is what isoperimetric equality implies:
the center of (only) a perfect circle remains a constant proximity to the plane it rolls on. Polygons do not do this even as n → ∞
as they are always losing motion (ie. kinetic energy) to the y-axis (orthogonal to x-) due to the vertices of the polygon lifting the origin."
This is true.
The polygon as it rolls does lose motion (velocity would be a better word) as its centre of mass rises, but it does not lose energy
It loses energy to the y-axis which would otherwise be focused solely towards the x-.
The total energy does not go down.. just how much of that is vector y instead of vector x.
- the reduction in kinetic energy is converted into increased gravitational potential energy.
No reduction in total energy, only reduction in translational motion focused along x-axis.
Because of this, the circle overtakes the polygon at n = 59 for losing nothing.
As the polygon rolls over the vertex, the centre of mass falls again and the increase in potential energy is transformed back into kinetic energy.
No, it lost it to the y-axis. Once the radius is no longer 1/2, the kinetic energy is spread over two axis.
so there is no loss of efficiency, whatever that means in this context.
There is certainly a loss of efficiency along the x-axis.
There is also a loss of efficiency of the unit itself.

If person A is given 4 000 000 unit squares & they make 3 141 590 circles out of them, whereas
person B is given the same & makes as much as 3 144 605... who is more efficient with their material?
Person B would be cutting the circle out with circular motion whereas A would be cutting a larger non-circle out.

If all kinetic energy is not expended along the x-axis... it's losing it elsewhere.
In the case of any/all non-circlular n-gons whose n > 59, it loses up-to 0.001% per rot. to the y-axis.
B instead argues for n = 4 with side length π/4 (a perfect square). Even if/as this rolls over its own vertices... it still rolls π.

Nobody could fault B's logic, but we are still faced with how to measure pi.
Yes... C would agree & that's what C wants before assuming or believing anything.
How many of the 62,831,853,071,796 digits reported in 2022 should we use with our "modern prof. real-time digital tape measurer with min. +/- 1/16" accuracy at 3.5 m"?
According to B, everything beyond the thousandth is wrong so we can ignore 62,831,853,071,793 of those.

If B's argument is correct, the only correct digits humanity has are the first three (3.14...) & it is not followed by a 1.
I'm sorry if this was/is not clear but we only need to the nearest mm if the circular object is as small as 1m diameter.

If A is correct... the object will roll no further than 3.1416 m.
If B is correct... the object will roll no less than 3.1446 m.
 
Last edited:
1705175609328.png
This one. The others do not apply as we are on a flat plane surface.

This length L is the same as in L² ≥ 4πA and demonstrates how the distance travelled by the origin is identical to the length of the curve.
All one would do to square π is square L by constructing the square whose side is L. The area contained will be L².

This is identical to what was shown earlier with L/4 / C/4 = L/C = 1. As the video correctly states: the origin travels the same distance
as the numerical circumference of the circle rolling. This is precisely the property the Pythagorean approach is using & avoids inequality entirely.

1705176198797.png

This property is what B is arguing Archimedes missed (by no fault of his own because the inequality was not proven until very recently).
However, since the inequality was finally proven in the 19th C... all mathematicians since have 0 excuses.

The moment they proved it, they should have retroactively applied it to anything & everything which came before it... but they didn't.
Because they didn't, they were/are never in a position to inform metrologists their point-probe approach is producing a numerical error.

Hopefully this clarifies why the Roll Method was/is suggested as an opening idea:
it will travel a distance equiv. to the numerical circumference. Thanks for posting &
feel free to continue to brainstorm ideas on what experiment(s) could most resolutely
settle A & B's argument. Whichever it is, it needs a good experiment for closure.
 
Whataya' guys think? AI fishing for it's own answers to give to other people? I was wrong about the perpetual motion person. She turned out to be real. Still not sure about Moore Jig Borer #3.
 
Whataya' guys think? AI fishing for it's own answers to give to other people? I was wrong about the perpetual motion person. She turned out to be real. Still not sure about Moore Jig Borer #3.
In all honesty I just need to take in as many real-world experiment ideas as I can, find the best possible (yet financially practical) one, do it for them & settle the debate.
This debate is based on real groups of people & I am arbitrating between them by stating nobody knows for sure until the hypothesis is actually tested.

Even more honestly: people here are falling into the same back-and-forth trap A and B are & it's noise.
I am done with A & B, I am C and don't care about anything but a well-designed and well-conducted real-world experiment.

B is making an argument which has implications about reality (itself) & can therefore in reality be tested. This follows as a matter of principle.
If B were postulating values for virtual pi's which we can't see or measure... I would suggest they virtually stand in front of a train at night wearing a garbage bag.
I've already heard both sides & I understand the arguments & where each side is at. There is no more going back & forth... it's a simple matter of... the matter itself.

In reality, either a 1m diameter circular anything rolls according to Archimedes' 3.14159... or B's 3.1446... per rot. Reality has the final say.
The scale doesn't matter, I just use 1m as a reference because it is generally easy for people to understand on-the-fly: it's the unit denominator of π.
If there are no ideas beyond the Roll Method, are there any thoughts on how to improve the Roll Method?
 
In a planar space there's no question that the circumference of a circle is pi times the diameter. In your mind, there is apparently some question. But this is not a question that needs answering. The answer is known. The discrepancy you suggest might exist is so large that it would have been well-known for centuries. If you want, in your heart of hearts, to confirm this for yourself, more power to you. But it's completely unnecessary.
I am arbitrating between them by stating nobody knows for sure until the hypothesis is actually tested.
It's not a f**king hypothesis. It's a physical property of the Universe. The answer is definitely and unquestionably known. And generations of people working with precision measuring gear in multiple trades have never had any evidence that the answer might be anything else.

You know what a surveyor's wheel is? Why have surveyors not detected a 0.1% discrepancy between the distances reported by surveyor's wheels and the distances reported by direct linear measurement by tape, chain, or laser interferometry? It's because there is no such discrepancy!
 
You know what a surveyor's wheel is? Why have surveyors not detected a 0.1% discrepancy between the distances reported by surveyor's wheels and the distances reported by direct linear measurement by tape, chain, or laser interferometry? It's because there is no such discrepancy!
If the property traveled has small bumps will not such be off?
Why does it not agree with a tape?
Been into the nasty argument with the nasty neighbor over 3-6 inches of property line?
 
In a planar space there's no question that the circumference of a circle is pi times the diameter.
Correct.
In your mind, there is apparently some question.
Incorrect.

At no point did I suggest the circumference of a circle is somehow not equal to πd for diameter d.
In fact, the Pythagorean proof provided identifies the diameter as 1... meaning the circumference must be π.

In nobodies mind is there question about this.
But this is not a question that needs answering.
Correct... it was never called into question by anyone.
You are either under misapprehension or derailing.
The answer is known.
There was never a question.
The discrepancy you suggest might exist is so large that it would have been well-known for centuries.
I don't suggest it, B does... and I don't assume human beings aren't capable of such egregious mistakes.
I place more trust in the actual physics of the universe than I do any human beings in it.
I've never had a math equation lie to me unless there was/is a mistake in it somewhere.
If you see a mistake in the mathematical argument somewhere, that I'd like to hear about.
If you want, in your heart of hearts, to confirm this for yourself, more power to you. But it's completely unnecessary.
It's not unnecessary if there is an ongoing dispute which can be solved with an experiment.
It's not a f**king hypothesis.
Yes it is & is a scientific one... because it can be tested & confirmed, as you previously implied.
One can't scientifically test an hypothesis unless it is falsifiable.
A & B can not both be correct, thus at least one of their arguments is falsifiable according to the outcome of a real-world experiment.
It's a physical property of the Universe.
The curvature constant is... yes. Therefore, it is crucial one not have it wrong.
The answer is definitely and unquestionably known.
We know the diameter is 1. This was never in question.
And generations of people working with precision measuring gear in multiple trades have never had any evidence that the answer might be anything else.
Why would they? They anyways have the correct radius... just the wrong number associated with it if B is correct.
The only thing that happens is 3.14159... is standing in place of 3.1446... reality stays the same as it always was.

The assumption(s):
i. Humanity can't be so ignorant,
ii. Someone would have realized it by now,
iii. Nothing would work,
etc.

weigh nothing against a real-world experiment.
You know what a surveyor's wheel is?
Yes & I also know how they calibrate them.
Why have surveyors not detected a 0.1% discrepancy between the distances reported by surveyor's wheels and the distances reported by direct linear measurement by tape, chain, or laser interferometry?
Ask them how they calibrate them.
Similar to the metrologist visited by A,
A inquired about measuring wheels.

We can compare answers after.
But only after you look (for yourself).
It's because there is no such discrepancy!
But there is such assumption.
Please stay on-topic from now on.

The topic is circle measurement & experiment... not the circle constant itself.
I'm not here to pick any one side, only represent their positions as they did.
 
Most discussions on here are supposed to have a purpose or a question. What is your question and why did you pick a manufacturing forum? It would be different if you were a long-time member and happened to contemplate the lint in your navel one morning. It's entirely different that you signed up here and immediately began questioning established mathematics. What's next, how many different ways to hard boil an egg?
 
Sorry I'm not contributing, I gave up on things like this a long time ago.
My friends get mad who are into it.
I call it useless knowledge.
Yes its interesting, and intellectual, but it does nothing for you in life by gathering it.

 
Most discussions on here are supposed to have a purpose or a question.
Quoting myself:
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?
That's the question.
What is your question and why did you pick a manufacturing forum?
Because the experiment requires both precision engineering & metrological analysis.

I am posting in the metrology section because this relates to circle measurement of a precision-engineered circular object.
It would be different if you were a long-time member and happened to contemplate the lint in your navel one morning.
No, it wouldn't.
It's entirely different that you signed up here and immediately began questioning established mathematics.
As earlier implied, you apparently can not read. I am not questioning anything, B is.
You are trying to attack something that isn't even real & I don't even care about.
You as an '07 should know better than to be spamming with off-topic.

The topic is circle measurement & experimentation. You are off-topic.
If you have any suggestions as to how to improve Roll Method, feel free.
If you have your own suggestions, feel free.
What's next, how many different ways to hard boil an egg?
A report for being off-topic.
 
Because the experiment requires both precision engineering & metrological analysis.

I am posting in the metrology section because this relates to circle measurement of a precision-engineered circular object.
Your questions have zero practical value here. See that title at the top? PRACTICAL Machinist? If Pi calculations built and got the Webb telescope out to the L2 point and stable, it's good enough for anything here on earth.
 
Quoting myself:

That's the question.

Because the experiment requires both precision engineering & metrological analysis.

I am posting in the metrology section because this relates to circle measurement of a precision-engineered circular object.

No, it wouldn't.

As earlier implied, you apparently can not read. I am not questioning anything, B is.
You are trying to attack something that isn't even real & I don't even care about.
You as an '07 should know better than to be spamming with off-topic.

The topic is circle measurement & experimentation. You are off-topic.
If you have any suggestions as to how to improve Roll Method, feel free.
If you have your own suggestions, feel free.

A report for being off-topic.
Haha, I see the truth in subject now, and its relative use, NICE! Good one!
I hope this post adds.
 








 
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