# Where do the numbers come from, to calculate pi?

As we all know, $\pi$ is the ratio of a circle's circumference to its diameter. When you divide the circumference by the diameter, the result is $\pi$. But, here's my question:

When you enter the numbers into a PC, main frame, or whatever, what numbers do you use? It seems to me if you do not get them PRECISELY correct, the calculated value of $\pi$ will be incorrect?

• Since $\pi$ is a transcendental number, it can never be stored 'precisely' in any machine. If there were to exist integers $m,n$ such that $m=n\pi$ then this would be a different story – jameselmore Mar 19 '15 at 17:05
• @jameselmore: It really depends on what you mean by "precisely". – tomasz Mar 19 '15 at 17:07
• @jameselmore: What do you mean by without error? – tomasz Mar 19 '15 at 17:09
• @jameselmore An algorithm for computing the digits is precisely stored, for example. There are real numbers for which there is no precise storage, but $\pi$ isn't one of them. – Thomas Andrews Mar 19 '15 at 17:10
• With negligible error (say to $10$ decimal places) may be good enough for all practical purposes. – André Nicolas Mar 19 '15 at 17:10

I think the thought behind the question might be the notion that if $\pi$ is the ratio of circumference to diameter, then why can't I measure the circumference of a circular object and its diameter, throw these numbers into a computer, and get $\pi$? If we could somehow precisely measure these two attributes, then perhaps we could get precisely $\pi$.