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|  ukrainian | Mar 3, 2006 6:27pm | I was just bored here and got to thinking something. Pi is ratio of a circles circumference to its diameter(pi=c/d). So if you have a circle with a diameter of 1 meter the circumference will be pi, an endless number. So can not have an exact find the exact circumference. But then I quickly relized the circle doesnt need to have diameter of one becouse the unit of measure doesnt matter. A unit of measure is your choice to choose. So If you take what ever the diameter is of whatever circle you look at and make it 1(custom unit). That would circumference exactly pi(custum units) and would make the circumference unending. Then to get will always be a ratio wich will compare your custom unit with a more standard one like a meter. So there would be a conversion factor. And you cant convert an endless number. So when looked at this way the mesurement of all circumferences is approximate. And even with the most advanced equipment a circumfrence could never be found. This would affect all area measurements and etc. Then I quickly realized the same could be said for a 60-60 right traingle, since the hypotensue will be the square root of 2 another never ending number. I guess if you take a step back you will say of course all those measurements are approximate you can all ways measure to a sharper point. Forgot where I was going with this but I would love to see people smarter then a alabama high school student elaborate on this.
But I said I had a question, so here's one isn't pi(to the fartherst place known) just really a long measurement of things unmeasureable? |
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|  jgweissman | Mar 4, 2006 12:00am | The math answer: Pi is exactly Pi, don't worry about the decimal representation.
The physics answer: Compute Pi to greater accuracy than the relevant physical measurements, and there will be insignificant impact on the accuracy of the final result. That is, if you know the radius to 1% accuracy, compute Pi to within .01%, and you can find the circumference to within 1.0101%, close enough to 1%. |
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| | | vecours | Mar 4, 2006 10:59am | | stand up and face the far wall then walk half way there,then half again, and again, you will never reach the wall |
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Sponsor |  Morosoph | Mar 5, 2006 6:52am | 3, 4: Xeno necessitated calculus.
Answer to the riddle: each stage takes half the time, so the time taken to complete those infinite stages is (time for first step times) 1 + ½ + ¼ +... = Sigma(n=0,inf){1/n} = 2. Ie., after twice the time that it took to do your first step, you'll have completed all of them, and so reached the end-point. |
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Sponsor | | Vortexfugue | Mar 5, 2006 9:08am | | Yes, this I know, I love calculus. :) |
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| | broessel | Mar 13, 2006 5:26am | " So there would be a conversion factor. And you cant convert an endless number."
Sure you can, why not? For example, if your conversion factor is 1/3, then your circumference is pi/3 - still irrational, but still correct.
If you're going to say that pi/3 can never be written completely as a decimal because it would take forever to compute, the same is true of pi or any other irrational number.
Ultimately, though, if you want to discuss objects in reality, we work under an atomic theory, in which matter is in discrete pieces rather than being continuous. Any circle that you make is going to have a rational representation, because it will be made up of a finite number of pieces with non-zero size. |
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| | ajinx999 | Aug 12, 2007 8:41am | We calculate perimeter of a polygon by measuring its each side. A circle is the limit of a polygon with 'n' side where n tends to infinity. Now, how one is going to measure the perimeter or the circumference of a circle? I thought about this and got a simple explanation. You can calculate the exact circumference in this way; consider a circular ring, cut it at a point and spread it linearly. Then, measure the length of the ring (It becomes a line segment when cut). That is the circumference of the circle. In this way, circumference can be measured accurately. This is foolproof. Now, measure the diameter of the circular ring. The ratio of the circumference (or length) to the diameter is pi. And now, the question arises: how to convert an irrational number like pi using a conversion factor in calculation of circle parameters? The most important aspect of pi is that it is a RATIO. It has no unit. It doesn't need a conversion factor.
If you take diameter of an arbitrary circle as a custom unit, then the circumference will be multiplied by the required conversion factor. Pi will remain as it is. For example, if you consider a diameter of 0.5 m as 1 unit, then the circumference will be pi custom units. Circumference in meters will be 0.5*pi m. Therefore, here 0.5 m per custom unit is the conversion factor. For any unit you consider, the ratio remains the same that is pi. |
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