How do people calculate pi?

Question

I know pi is an infinite irrational number with no definite pattern. So how do we know what numbers are in pi? In what order? Is there any way to know for sure what pi is?

If so then couldn't people find a pattern, memorize it, and recite pi to an infinite amount of digits?

I think it's weird how we can just "pull" pi from nowhere...

...

22/7 isn't pi...

22/7 ~ 3.1428

pi ~ 3.1415

Different!

Answer 1

Hit the pi button on a calculator and then equals.

Answer 2

There are several series that converge to Pi, in 1672 James Gregory foud that

Arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 ...

If one takes x=1, then the formula converges to Pi/4, so in essence, 4 - 4/3 + 4/5 - 4/7 + 4/9 ... will converge to Pi.

The problem is that this serie converge very slowly. There are other, more recent series that converge much faster, the attached links will give you some of them.

And, no, as other have pointed out, there is no repeating pattern in the decimals of Pi, which has been computer to over 200 billion digits. Which means that the average personnal computer hard disk could be filled with those and nothing else.

Answer 3

Pi is calculated via series expansion. There are a number of infinite sums that evaluate to π. That means, even though the number never repeats and can never be exactly calculated, it can be determined to any precision you wish. The oldest known series for calculating π is Gregory's series from 1671:

π = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ....)

This series converges very slowly, taking thousands of terms to get even a few digits right.

The calculation of π involves finding series expansions that converge more quickly. For example, in 1706, John Mahin devised the series:

π = 16(1/5 - 1/(3*5^2) + 1/(5*5^5) - 1/(5*5^7) + .... ) - 4(1/239 - 1/(3*239^3) + 1/(5*239^5) - ...)

This converges so fast that in 1706 it was used to get π to 100 places. When the first computers wer invented in the 50's, the same formula was used to calculate π to 2000 places.

Using similar series and today's computers there is no real limit to the number of places that can be calculated.

Answer 4

What makes you think pi comes from nowhere?

Pi is actually an amazing number...

Think about this...

Take ANY circle with ANY radius...

The circumference of that circle divided by it's diameter (or its radius x 2) = pi, or the area of a circle divided by it's radius squared will of course also give you pi.

I believe pi has been calculated to around 50,000 digit places.

So far no pattern has been found.

It would be very difficult for anyone to recite anything to an infinite amount...infinity is like two mirrors facing one another... when you see yourself in the mirror... your reflection goes on and on and on... there is no defined end to it as we know of...

Cheers,
ALK

Answer 5

A little calculus can do the trick. Think about a circle circumscribed about a hexagon- with geometry, you can calculate the perimeter of the hexagon with respect to the 'radius.' The perimeter is an approximation of the circumference of the circumscribed circle. Now what about a decagon (10-gon)? The approximation will be a little bit closer to the "true pi." A 100-gon will appear to be identical to a circle and the approximation will be closer.

This repeated smoothing-out of the circle boils down to summing a large number of terms which follow a clear pattern. Depending on how many terms you sum determines the accuracy of pi.

Answer 6

If you take the circumference of any circle and divide it by its diameter (both of which can be measured by a string and a ruler), you get pi.

If you want more digits of pi, you need to make more accurate measurements.

Also there is absolutely no pattern to pi. It has been proved not only to be irrational, but also transcendental (see link below), meaning in its decimal form it has absolutely no inner structure.

Answer 7

Well, I just use a calculator. My math teacher has a paper with pi up to maybe 10000 digits. Pi doesn't have a pattern. If it did it wouldn't be as remarkable of a #. Most people just memorize the first few digits of pi like 3.14. My dad has memorized it up to maybe 20 digits at most. I don't know where people came up with pi. No idea at all. Then again that's why I'm not planning on being a mathematician.

Answer 8

22//7 is close, but it won't come out right.
If you take the circumference of a circle and divide it by the diameter you will have pi.

You could also use the Archimedes method, the Gregory and Leibniz's Method, or the Newton method. To see these methods, go to http://people.bath.ac.uk/ma3mju/calc.html

But it is normally done with computers these days. If you want an aplet to do this on your computer, go to http://www.apfloat.org/apfloat_java/applet/pi.html

For more fun with pi, go to http://www.science.howstuffworks.com/pi.htm

Also check out Eve Andersson's homage to pi, featuring trivia, notes on calculating its value using Machin's Formula and the Monte Carlo Method, poems, photos etc. at http://www.eveander.com/pi

Answer 9

Pi definitely isn't "pulled from nowhere". We have formulas to calculate it. And no, there is no pattern to its digits - it is irrational, after all.

Look up http://mathworld.wolfram.com/Pi.html and other such links.

Answer 10

pi=22/7=3.1428