# Does the meter link a circumference to c?

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When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length.

However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters.

The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter.

It is the relationship of the speed of light to the circumference of a circle and therefore the length of a sine-wave (2π) that I am interested in confirming my understanding is correct as I am trying to verify that there is a link between wavelength and relativistic effects.

Thanks.

Edited by TakenItSeriously

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16 minutes ago, TakenItSeriously said:

When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length.

However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters.

No, it wasn't. The distance was to be 10,000 km, which is 10^7 meters (ten million). But it was not used, since the earth isn't a perfect sphere.

Quote

The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter.

c is 299 792 458 m /s. So the former uncertainty was past the decimal.

By making c a defined number, we push uncertainty off to other constants.

Quote

It is the relationship of the speed of light to the circumference of a circle and therefore the length of a sine-wave (2π) that I am interested in confirming my understanding is correct as I am trying to verify that there is a link between wavelength and relativistic effects.

Thanks.

I don't see where you think the connection is.

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54 minutes ago, TakenItSeriously said:

length of a sine-wave (2π)

That is not the length of a sine wave, that is the length of its projection on the translational axis.

It's projection on the transverse axis is 2

The length of a sine curve is an not an elementary function and has to be evaluated by numerical methods. It is approximately 7.64.

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2 hours ago, TakenItSeriously said:

When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length.

However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters.

The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter.

It is the relationship of the speed of light to the circumference of a circle and therefore the length of a sine-wave (2π) that I am interested in confirming my understanding is correct as I am trying to verify that there is a link between wavelength and relativistic effects.

Thanks.

1 hour ago, swansont said:

1] No, it wasn't. The distance was to be 10,000 km, which is 10^7 meters (ten million). But it was not used, since the earth isn't a perfect sphere.

2] c is not an integer value in m/s. 299 792 458 m / s

By making c a defined number, we push uncertainty off to other constants.

3] I don't see where you think the connection is.

1. You’re right about the values, thanks for correcting me.

I also agree that using the Earth was an invalid example. It’s certainly not a perfect circle especially in the verticle plane since it buldges at the equator, which I assume is why it was changed to be defined based on c.

Don’t get me wrong, I think it’s an ingenious way to put uncertainty in its proper place, since it is our perception of the nature of reality that is what we must be uncertain and not reality itself. For example, uncertainty of a meter should never have any impact on the human domain since nothing can be made to a greater accuracy than we can theoreticaly measure it.

2. I’m sorry to disagree, there are only 2 variables and 1 constant in defininging the speed of light through a vacuum, the value of c and the definition of either a meter or a second. Since it is the the meter that is being defined then it must be that c is the absolute number and the meter is the uncertain unit of measure.

3. The link is the relativistic effect of time dilation and length contraction due to the constancy of c also effects frequency (inverse time) and 1/2 wavelength as the smallest unit of length for a wave in an inverse manor.

Since time and distance are always equivalent in terms of EM radiation or electronic signals that propagate at the speed of light (not to be confused with the relatively slow drift speed of electrons). Then c becomes the fixed datum for measuring  frequency and wavelength that are absolute variables in a way. as frequency increases, then wavelength must decrease in an absolutely proportionate way:

f = 1/λ

So at the beginning of the paradigm shift  in the late eighties, in high speed (in terms of frequency) digital design, I thought of the shift as an effect of frequency expansion and wavelength contraction, that we don’t think of as being strange because we always thought of the speed of light as being constant and distance and time being equivalent, at least in that field of study which is the application of electromagnetic field theory.

However, if we think of it from a srinking waves point of view, then the world seems to be growing.

There is much more to it than that but that is my general thinking.

I also applied the conservation of information from quantum field theory in terms of Special Relativity. BTW, just because concepts may come from a different field of study, it doesn't mean they can’t be properly applied in other fields as long as its applied in a valid manor.

Hawking applied it in terms of black holes which was what led to the concept of a firewall on the EH.

I proposed it as a matter/antimatter annihilation at the EH which is the same thing but includes the causality for the released energy.

BTW, apparantly someone else has made similar proposals as their is a new reference in Wikipedia for frequency in terms of wave guides including the Lorentz Factor.

correction: I should have called it relativistic impedance of a wave in terms of frequency

BTW, I forgot to mention that their was also what I initially thought must be a strange coincidence in that the paradigm shift seemed to begin having an impact at around 30 MHz or 30 million cycles/sec.

The relativistic effect begins to be significant at about 0.1c or roughly 30 million m/s.

So, like I said, I thought it had to be a coincidence because I thought the definition of a meter was arbitrary relative to light. But thats one hell of a coincidence because 30 million is a very large number.  Then once I discovered a meter wasnt so arbitrary after all, I started to try and understand the concepts involved.

The result implies a link to how a meter is defined and what we know about a cycle which could be thought of as a wavelength (or period). the one thing we know is the fact that a wave stops behaving like a wave at geometries smaller than 1/2 λ. and that harmonically speaking, they must always be in hole units of 1/2λ

Also note that if you plot the inverse of the Lorentz factor vs speed from 0-c it is 1/4 of a circle.

Edited by TakenItSeriously

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Sorry to keep adding more, but I should say that I also expect uncertainty to be linked to irrational numbers. so in the case of a circumference (2πr) or a wavelength (2π) then the uncertainty of a meter is expressed as the uncertainty of π.

For cartessian coordinates, uncertainty carries over via the uncertainty of square roots through pythagoreans theorem.

It was an epiphany that hit me in the result of my solution for the millenium problem in the TSP problem.

Edited by TakenItSeriously

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Since you chose to ignore my last post, I will tell you straight out that the length of a metre is nothing to do with pi.

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3 hours ago, studiot said:

That is not the length of a sine wave, that is the length of its projection on the translational axis.

It's projection on the transverse axis is 2

The length of a sine curve is an not an elementary function and has to be evaluated by numerical methods. It is approximately 7.64.

48 minutes ago, studiot said:

Since you chose to ignore my last post, I will tell you straight out that the length of a metre is nothing to do with pi.

I didn’t choose to not reply, I was just too focused on a long reply to Swansots post, so I missed it.

I apologize.

Regarding your first reply, your right, in that I should have said the “wavelength of a sine-wave is 2π”

not the “length of a sine wave is 2π”. Although in terms of time or wave propagation distance wavelength is the correct application.

Regarding the connection of pi to the definition of a meter, I covered it in the reply to swansot but it is a very confusing concept so I will take some extra time to try and clarify my reasoning before replying.

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c takes on an exact value in metric only because of how the meter is defined in terms of it.

1 m = 299,792,458 m/s * 1s/299,792,458

In other systems it only has an approximate value.

Edited by Endy0816

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7 hours ago, Endy0816 said:

c takes on an exact value in metric only because of how the meter is defined in terms of it.

1 m = 299,792,458 m/s * 1s/299,792,458

In other systems it only has an approximate value.

10 hours ago, studiot said:

Since you chose to ignore my last post, I will tell you straight out that the length of a metre is nothing to do with pi.

Connecting the definition of the meter to pi if taken from the origional definition is more direct an explanation, but defining the meter based on the speed of light accomplishes the same thing, I think.

Ignoring the fact that the Earth is a flawed ecample of a circle. Lets assume for arguements sake that the Earth is a perfect sphere so It’s easier to explain.

We know that the definition of the circumference of a circle is 2πr which for a unit circle is just 2π.
We know that π is an irrational number.
Therefore the circumference of a circle should always be an irational number, that is, unless we define a metric unit in terms of the circumference of a circle.

For example:
If we try to measure the verticle circumference of the Earth based on a yard which is defined based on some kings shoe-size or something to that effect, then we would expect the circumference to be:
43,744,531.934  yards with never ending decimal places due to being an irrational number tied to pi being an irrational number.

Why this is inconvenient is the concept of harmonics which involve waves that are perfect whole multiples of 1/2λ of the fundamental wave which is tied to the circumference of a unit circle. But if the wavelength i.e. circumference of the unit circle was always an irrational number, then It requires finding a perfect whole multiple of an irrational number, wich you can never perfectly calculate.

By defining a meter to be 1/10 millionth of the distance from equater to N Pole, then the circumference of the earth is an integer of 40 million meters.

What’s more all circles regardless of their size can be expressed as a rational number when using the metric system, all because of how the meter is defined. Therefore we can always calculate the whole multiples of harmonics waves because the fundamental wave is always a rational number.

By defining the speed of light as an integer in meters we actually accomplish the exact same thing. it just requires more steps to explain why.

In essence we have taken the uncertainty of our measurements of circles and thransered it to be uncertainty of the length of a meter. But thats not a problem because we cannot create things any more accuratly then we can measure them. so the meter being uncertain is never an issue for us in the human domain

I hope that makes sense, because I only just now worked out the details of that confusing but ingenious definition for the meter.

Correction:
A unit circle would still have an irational circumference because the radius is defined as 1 so the circumference must be 2π.
However the concept still applies to any wavelength that has some length that is not based on a unit circle. I appologize if my getting that backwards cused some confusion.
Edited by TakenItSeriously
correction for a unit circle

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43 minutes ago, TakenItSeriously said:

For example:
If we try to measure the verticle circumference of the Earth based on a yard which is defined based on some kings shoe-size or something to that effect, then we would expect the circumference to be:
43,744,531.934  yards with never ending decimal places due to being an irrational number tied to pi being an irrational number.

That isn't true. The circumference of a circle, in some arbitrary  unit, could easily be an integer multiple of those units. (What that tells us about the radius of that circle is then something else).

Just take (for example) a piece of string exactly 43,744,532 yards long. Make a circle of it.

Or a piece of string exactly 40 inches long. Make a circle of it.

Edited by pzkpfw

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1 minute ago, pzkpfw said:

That isn't true. The circumference of a circle, in some arbitrary  unit, could easily be an integer multiple of those units. (What that tells us about the radius of that circle is then something else).

Just take a piece of string exactly 43,744,532 yards long. Make a circle of it.

But that requires rounding which would create error in calculating the wavelength of harmonic waves.

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Rounding what?

Your implication was that no circle could have a circumference of an  integer number of units. That's wrong.

That the speed of light can be expressed in metres per some unit of time, and metres were previously (inaccurately) linked to something that was part of almost a circle, does not produce the relationship you seem to be seeing.

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34 minutes ago, pzkpfw said:

Rounding what?

Your implication was that no circle could have a circumference of an  integer number of units. That's wrong.

That the speed of light can be expressed in metres per some unit of time, and metres were previously (inaccurately) linked to something that was part of almost a circle, does not produce the relationship you seem to be seeing.

I think you may have misread the post.

1 hour ago, TakenItSeriously said:

Therefore the circumference of a circle should always be an irational number, that is, unless we define a metric unit in terms of the circumference of a circle.

ie, by defining the metric unit to a circumference of a circle it causes all circumferences expressed in metric units to be a rational number.

I could be wrong about that as I didnt have a chance to check my work. but this is something that I seem to recall as being understood, so I would prefer to search for a corresponding explanation.

I think I misunderstood what you were suggesting in that we could define a circle to having a definitive circumference. That’s true but I don't know how useful that would be since we usually measure distances that lie on a circumference. Therefore we could always assume that measurements in metric would have some definitive value.

I also think the value of any wavelength should have a definitive value at least in theory, even if there will always be some error in our measurements.

Edited by TakenItSeriously

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22 minutes ago, TakenItSeriously said:

I think you may have misread the post.

ie, by defining the metric unit to a circumference of a circle it causes all circumferences expressed in metric units to be a rational number.

I could be wrong about that as I didnt have a chance to check my work. but this is something that I seem to recall as being understood, so I would prefer to search for a corresponding explanation.

Will it isn't, so...

We changed the meter's length and got c to be an exact value in the bargain.

Not too shabby.

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13 hours ago, TakenItSeriously said:

3. The link is the relativistic effect of time dilation and length contraction due to the constancy of c also effects frequency (inverse time) and 1/2 wavelength as the smallest unit of length for a wave in an inverse manor.

Since time and distance are always equivalent in terms of EM radiation or electronic signals that propagate at the speed of light (not to be confused with the relatively slow drift speed of electrons). Then c becomes the fixed datum for measuring  frequency and wavelength that are absolute variables in a way. as frequency increases, then wavelength must decrease in an absolutely proportionate way:

f = 1/λ

So at the beginning of the paradigm shift  in the late eighties, in high speed (in terms of frequency) digital design, I thought of the shift as an effect of frequency expansion and wavelength contraction, that we don’t think of as being strange because we always thought of the speed of light as being constant and distance and time being equivalent, at least in that field of study which is the application of electromagnetic field theory.

Nothing to do with a circle

13 hours ago, TakenItSeriously said:

BTW, I forgot to mention that their was also what I initially thought must be a strange coincidence in that the paradigm shift seemed to begin having an impact at around 30 MHz or 30 million cycles/sec.

The relativistic effect begins to be significant at about 0.1c or roughly 30 million m/s.

So, like I said, I thought it had to be a coincidence because I thought the definition of a meter was arbitrary relative to light. But thats one hell of a coincidence because 30 million is a very large number.  Then once I discovered a meter wasnt so arbitrary after all, I started to try and understand the concepts involved.

Since the speed of light is given in m/s, it's going to be connected to the meter, and the second.

13 hours ago, TakenItSeriously said:

The result implies a link to how a meter is defined and what we know about a cycle which could be thought of as a wavelength (or period). the one thing we know is the fact that a wave stops behaving like a wave at geometries smaller than 1/2 λ. and that harmonically speaking, they must always be in hole units of 1/2λ

No connection to c here.

13 hours ago, TakenItSeriously said:

Also note that if you plot the inverse of the Lorentz factor vs speed from 0-c it is 1/4 of a circle.

No, it's not.

12 hours ago, TakenItSeriously said:

Sorry to keep adding more, but I should say that I also expect uncertainty to be linked to irrational numbers. so in the case of a circumference (2πr) or a wavelength (2π) then the uncertainty of a meter is expressed as the uncertainty of π.

No. The uncertainty in realizing the length of a meter is going to be based on experimental biases and errors. π is known to many more digits than the precision of any measurement.

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36 minutes ago, TakenItSeriously said:

I think you may have misread the post.

Non, au contraire, it is you who has it wrong.

It is not necessary for for the circumference to be a whole number. All that is necessary is that it be a non trancendental one like pi. although +1 to pzkpfw for clarity of comment.

Then it is the radius which becomes trancendental not the circumference.

In 1790 they could not have guaranteed that the length of the Paris meridian was not such a number times the unit circumference.

Nor could we today.

In any case the French got it wrong so the metre, was only ever the distance, under specific climatic conditions, between two marks on first an iron, then a platinum/iridium bar.

Later it was tied to the distance between successive peaks of certain light waves.

You do not need pi to identify this distance.

Edited by studiot

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41 minutes ago, TakenItSeriously said:

I think you may have misread the post.

ie, by defining the metric unit to a circumference of a circle it causes all circumferences expressed in metric units to be a rational number.

I could be wrong about that as I didnt have a chance to check my work. but this is something that I seem to recall as being understood, so I would prefer to search for a corresponding explanation.

I think I misunderstood what you were suggesting in that we could define a circle to having a definitive circumference. That’s true but I don't know how useful that would be since we usually measure distances that lie on a circumference. Therefore we could always assume that measurements in metric would have some definitive value.

I also think the value of any wavelength should have a definitive value at least in theory, even if there will always be some error in our measurements.

I edited my reply to pzkpfw. when I missed the point he was making.

I was confused by his rounding the value of the example I gave and missed his point that defining a circle would only change the radius to be irrational.

I acknowledged my mistake and made a counter point but a couple of corss-posts didnt see it and replied based on my origional error.

I’m reposting to clarify where our thinking is currently at so as not to create future confusion.

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If it's any consolation, there are some interesting formulae involving pi and trig functions.

First there is Euler's Identity

${e^{i\pi }} + 1 = 0$

Then there is the series for th inverse tangent

${\tan ^{ - 1}}\left( x \right) = x - \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \frac{{{x^7}}}{7}...........$

Now if we put x = 1 then the series becomes

${\tan ^{ - 1}}\left( 1 \right) = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7}...........$

and remembering that the angle whose tangent is 1 is $\frac{\pi }{4}$

$\frac{\pi }{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7}...........$

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1 hour ago, studiot said:

If it's any consolation, there are some interesting formulae involving pi and trig functions.

First there is Euler's Identity

${e^{i\pi }} + 1 = 0$

Then there is the series for th inverse tangent

${\tan ^{ - 1}}\left( x \right) = x - \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \frac{{{x^7}}}{7}...........$

Now if we put x = 1 then the series becomes

${\tan ^{ - 1}}\left( 1 \right) = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7}...........$

and remembering that the angle whose tangent is 1 is $\frac{\pi }{4}$

$\frac{\pi }{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7}...........$

Thanks,

it seems like the math formatting didnt take at least on my browser making it difficult for me to distinguish symbolism from syntax.

I can just google the identity/series to read them so its not a big deal.

I just thought Id mention it to double check that it wasnt a compatiblility problem with my browser. (safari on iPad) that had always lacked the math syntax feature for writing math, though it always read the syntax fine in the old forum format.

much bettr, thanks.

How diid you get the quoteed portion in my reply to update? Is that a new forum option that I’m not aware of?

1 hour ago, studiot said:

If it's any consolation, there are some interesting formulae involving pi and trig functions.

First there is Euler's Identity

eiπ+1=0

Then there is the series for th inverse tangent

tan1(x)=xx33+x55x77...........

Now if we put x = 1 then the series becomes

tan1(1)=113+1517...........

and remembering that the angle whose tangent is 1 is π4

π4=113+1517...........

so is the point of that result being that pi is constructed from a series of rational fractions which is an irrational result due to the series being infinite?

Curiouser and curiouser, now the two quotes are showing series that are the inverse opposites of each other lol.

Edited by TakenItSeriously

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17 hours ago, TakenItSeriously said:

the uncertainty of a meter is expressed as the uncertainty of π.

There is no uncertainty in pi.

5 hours ago, TakenItSeriously said:

ie, by defining the metric unit to a circumference of a circle it causes all circumferences expressed in metric units to be a rational number.

Nonsense. If the radius is, for example, 1 metre then the circumference will be an irrational number. (And vice versa)

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4 hours ago, TakenItSeriously said:

it seems like the math formatting didnt take at least on my browser making it difficult for me to distinguish symbolism from syntax

Yes lots of us have this trouble and we find that you need to resolve it by clicking on the page refresh button (and waiting up to 2 minutes) whilst the 'improved' SF site goes off to Mathjax and finds the relevant symbols.

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Just to confuse the issue, there is at least one unit of measurement whose definition makes it an irrational ratio to another widely accepted unit.
https://en.wikipedia.org/wiki/Parsec

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On 11/15/2017 at 9:11 AM, studiot said:

Yes lots of us have this trouble and we find that you need to resolve it by clicking on the page refresh button (and waiting up to 2 minutes) whilst the 'improved' SF site goes off to Mathjax and finds the relevant symbols.

Ahh, thanks for the tip.

On 11/15/2017 at 11:19 AM, John Cuthber said:

Just to confuse the issue, there is at least one unit of measurement whose definition makes it an irrational ratio to another widely accepted unit.
https://en.wikipedia.org/wiki/Parsec

I’ve often wondered why Cosmology chose the Parsec over the Lightyear. since the light year makes it so much easier to use c = 1 ly/yr.

I guess its because when c =1, then the unit circle makes the wavelength of light an irrational number again?

On 11/15/2017 at 8:07 AM, Strange said:

There is no uncertainty in pi.

Nonsense. If the radius is, for example, 1 metre then the circumference will be an irrational number. (And vice versa)

The precise value of pi is uncertain to me.

Re:the second issue:

But again:

While circles can be defined to have either a rational value for the circumference or radius, but not both, by defining a meter the way they did, it makes it so that measuring the circumference of circles that occur in nature when using metric always be a rational result.

Edited by TakenItSeriously

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2 hours ago, TakenItSeriously said:

I guess its because when c =1, then the unit circle makes the wavelength of light an irrational number again?

The wavelength of light has nothing to do with light years or parsecs:

• All light travels at the same speed.
• Light can have any wavelength (rational or irrational)
• c is not equal to 1
• The wavelength of light has nothing to do with the unit circle.
2 hours ago, TakenItSeriously said:

The precise value of pi is uncertain to me.

Well, I guess that is a problem you need to fix by understanding how it is defined.

2 hours ago, TakenItSeriously said:

by defining a meter the way they did, it makes it so that measuring the circumference of circles that occur in nature when using metric always be a rational result.

Obviously not. The circumference of a circle can have any value it is not constrained to be rational. If the radius is one metre, the circumference will be irrational, when measured in metres.

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3 hours ago, TakenItSeriously said:

While circles can be defined to have either a rational value for the circumference or radius, but not both, by defining a meter the way they did, it makes it so that measuring the circumference of circles that occur in nature when using metric always be a rational result.

24 minutes ago, Strange said:

.Obviously not. The circumference of a circle can have any value it is not constrained to be rational. If the radius is one metre, the circumference will be irrational, when measured in metres.

Your quoting my post out of context.