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File: 1448814436390-0.png (10.46 KB, 316x547, 316:547, Calculator_22_7_Pi.png)

File: 1448814436399-1.png (11.98 KB, 336x547, 336:547, calculator_Pi.png)

 No.3554

Okay, I am studying math by myself (OMG what a nerd! lol). I got to one of the problems and it told me to use (22/7) to get the value of Pi. so I did that and the first three numbers of Pi (3.14) came out perfectly, but as I continued to try and calculate by hand I started to notice something…..

the numbers seem to repeat in the 22/7 image, but when using the actual symbol of Pi, the value of pie is totally different after the what I would call the main digits (3.14). Is all that matters when it comes to Pi the main digits? As long as you have 3.14 then rest of the digits don't matter?

 No.3555

>>3554

22/7 is one of possible approximations of π, which you use to make calculations easier. Another common approximation is √10, which is actually about 3.16, but it's very useful because if you have π² you can just replace it with 10 and this simplifies everything a lot.

What you have to be aware though is how good those approximations are. √10 has error of about 0.65%, the error doubles (in first order approximation) when you square the number so replacing π² with 10 gives you an error of 1.3%. 22/7 is more accurate, error is 0.040% and this should be enough if you're doing physics because you're not likely to have more precise measurements anyway. There are other even better approximations of π with a fraction like 333/106 or 355/113, but those will only complicate your calculations. The reason those approximations are used are mostly for when you're doing calculations by hand, so the hardest part is dividing your result by 7 (multiplication by 22 is pretty simple). So yeah, I'd say as long as you have 3.14 the rest of digits don't matter for practical purposes. But if you're doing hard maths, you should never simplify π.

You have to be aware though that the number π is irrational (which means you can't get it from a simple fraction), and also transcendental (which means you can't get it by using roots, or even that it cannot be a solution of any polynomial equation). However, you can construct an infinite nested fraction that has the value of exactly π, that has an obvious pattern, for example 4/(1 + 1²/(3 + 2²/(5 + 3²/(7 + 4²/(9 + 5²(…)))))).


 No.3558

>>3555

This was actually very helpful. Thanks.




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