The number pi goes on forever because it is an “infinite decimal.” That is, it has an infinite amount of numbers to the right of the decimal points. Unlike some finite numbers, like .3333333… and .123456789123456789, pi does not have a pattern to it, and therefore all its digits can never be known—the numbers are infinite, and without any pattern to distinguish them, we will never know what exactly pi is. In general mathematics, for convenience’s sake, many people accept 3.14159 as an equivalent to pi.
At this point in time Pi has been calculated up to 5 trillion digits. That’s 5 trillion digits with no apparent pattern. If a pattern is ever found (the debate on this topic is a fiery one) then Pi will be considered as “terminating.” However, it should be noted that for a number to be infinite it must be larger than any other number, and Pi = 3.1415 < 3.1416. So although the decimals used to represent Pi appear infinite, the number itself is not.
Check out this fascinating account of Alexander J. Yee and Shigeru Kondo’s 5 trillion digit computation of Pi.
Pi goes on forever simply because it represents a fraction that does not divide evenly. Pi itself is a constant that comes from the ratio between any given circle’s circumference to its diameter; no matter the size of the circle, its circumference divided by its diameter will be 3.14159…
Interestingly, pi is also the ratio of a circle’s area to its radius squared. It can also be defined as the area of the Unit Circle (the circle used in Trigonometry with its center at (0,0) with a radius of 1). Pi pops up in a lot of places in our geometric system, which is why it is so enigmatic.
Pi might not go on forever – we’re not sure yet. Presently, there are mathematicians following the progress of pi and its seemingly infinite sequence in an effort to determine if it does, in fact, have an end. So we can never really be sure if pi goes on forever or not UNLESS we find the end of it!
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