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| Authored by: jesse on Tuesday, June 18 2013 @ 02:25 PM EDT |
There are several algorithms for computing the actual value of pi... Among
the simplest...
pi = sqrt(12) * sum(k=0,k=infinity,
(-3^(-k))/(2*k+1))
Carry that out for 21 terms and you get the value of
pi to the first 11 decimal places.
You get the exact value when carried
out to infinity...
Thus, no physical measurements involved at
all.
http://en.wikipedia.org/wiki/Approximations_of_%CF%80[ Reply to This | Parent | # ]
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| Authored by: jesse on Tuesday, June 18 2013 @ 02:28 PM EDT |
| rather than fact of nature. After all, pi is a product of mathematics... :) [ Reply to This | Parent | # ]
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| Authored by: stegu on Tuesday, June 18 2013 @ 08:17 PM EDT |
> Any number you can reach by measurement is rational.
Actually, no. Sorry, but I'm the kind of geek that knows this, and cares.
Measurements can never give you exact results, rational or otherwise. All you
get is an approximation.
Counting things can reach exact results. You can say "I have three
pigs" and be exactly right. You can even count the hairs on those pigs, and
calculate various rational numbers based on counting stuff, like the average
number of hairs per pig in your own population of three pigs. You can even look
in your records and say with absolute certainty how much you paid for your
pigs.
However, you can never "know" the weight, age or size of a pig (or any
other physical object) other than by making an approximation that is absolutely
100% certain to be either too big or too small by some amount. It's physically
impossible to make exact measurements, not just implausible.
Discussing the fine points about the distinction between rational and irrational
numbers ("countable" versus "uncountable" sets) is
completely moot when it comes to physical measurements.
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