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July 1st, 2017, 01:40 AM   #1
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Constant pi

$\displaystyle \pi $ is an irrational ratio $\displaystyle \frac{P}{d}=\pi=3,14...$
Does there exist any more accurate rational ratio than $\displaystyle \pi$ ? (can it be showed)

Last edited by idontknow; July 1st, 2017 at 01:42 AM.
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July 1st, 2017, 06:30 AM   #2
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What do you mean by "more accurate", given that $\pi$ is exactly the semiperimeter of a unit circle?
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July 3rd, 2017, 10:40 AM   #3
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Skipjack, I think he/she means an exact number such as 22/7.

No, "idontknow" pi is not equal to any ratio. But there are many others that are closer to pi than 22/7.

Written as a decimal numeral, the digits of pi continue for ever without repetition. That is what is meant by an "irrational number" such as pi. The more digits, the closer you get to pi.
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July 3rd, 2017, 10:55 AM   #4
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Quote:
Originally Posted by idontknow View Post
$\displaystyle \pi $ is an irrational ratio $\displaystyle \frac{P}{d}=\pi=3,14...$
Does there exist any more accurate rational ratio than $\displaystyle \pi$ ? (can it be showed)
A "rational number" is defined to be an integer divided by another integer.

It was a great surprise to mathematicians some 2500 years ago when they discovered that there were geometric ratios that were not rational numbers. They had thought up to then that every geometric ratio would be a rational number.

So we are left with the weird linguistic fact that not all imaginable ratios are "rational" numbers.

The best that can be done is to calculate approximations to $\pi.$ That has been done to millions of decimal places. For very precise work, you can use

$\pi \approx 3.1415926$

or for less fussy work

$\pi \approx 3.1416$

or for everyday work

$\pi \approx 3.14.$
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July 3rd, 2017, 11:52 AM   #5
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$\frac{355}{113}=3.1415929$ is good for detailed work.
$\frac{22}7=3.143$ for every day.
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July 3rd, 2017, 01:19 PM   #6
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https://blogs.scientificamerican.com...ction-instead/
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July 3rd, 2017, 01:43 PM   #7
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Quote:
Originally Posted by v8archie View Post
$\frac{22}7=3.143$ for every day.
How about on pi day?
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August 1st, 2017, 12:23 PM   #8
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Quote:
Originally Posted by Maschke View Post
How about on pi day?
Then you must bow deeply and use at least one hundred digits!
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