Pi

 

In celebration of Pi Day of the Century, 3-14-15.

Pi is an infinite series of non-repeating digits that seemingly go on forever and apparently never show a pattern. Although no one has ever gotten to the end of Pi’s digits, it is proved that the digits are both infinite and non-repeating by the many proofs that Pi is an irrational number — one that cannot be expressed by a ratio of two integers (a fraction).

Here is an excerpt from the New Yorker article, “Why Pi Matters” by Steven Strogatz (see Sources).

So it’s fair to ask: Why do mathematicians care so much about pi? Is it some kind of weird circle fixation? Hardly. The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. They go on forever, seemingly at random—except that they can’t possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi.

Pi touches infinity in other ways. For example, there are astonishing formulas in which an endless procession of smaller and smaller numbers adds up to pi. One of the earliest such infinite series to be discovered says that pi equals four times the sum 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + ⋯. The appearance of this formula alone is cause for celebration. It connects all odd numbers to pi, thereby also linking number theory to circles and geometry. In this way, pi joins two seemingly separate mathematical universes, like a cosmic wormhole.

http://www.newyorker.com/tech/elements/pi-day-why-pi-matters