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July 1st, 2017, 01:40 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 154 Thanks: 21  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. 
July 1st, 2017, 06:30 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,706 Thanks: 1356 
What do you mean by "more accurate", given that $\pi$ is exactly the semiperimeter of a unit circle?

July 3rd, 2017, 10:40 AM  #3 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 370 Thanks: 68 
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. 
July 3rd, 2017, 10:55 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 740 Thanks: 299  Quote:
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 $\pi \approx 3.14.$  
July 3rd, 2017, 11:52 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra 
$\frac{355}{113}=3.1415929$ is good for detailed work. $\frac{22}7=3.143$ for every day. 
July 3rd, 2017, 01:19 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra  
July 3rd, 2017, 01:43 PM  #7 
Senior Member Joined: Aug 2012 Posts: 1,427 Thanks: 351  
August 1st, 2017, 12:23 PM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,573 Thanks: 667  

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