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One of the many great things about Pi is that it's algorithmically compressible. You can express the idea of Pi using far fewer characters than are actually contained in its numerical expression (which would be an infinite number). #PiDay 1/
Between 0 and 10 (say), there are an infinite number of rational numbers: those expressible as p/q, where both p and q are integers. The rationals are "dense" - given any number between 0 and 10, there is a rational number arbitrarily close to it. 2/
But there are infinitely more irrational numbers, those that can't be expressed as p/q. It's a bigger infinity than the number of rationals. The rationals are "countable," the irrationals are "uncountable." There are a lot of irrational numbers out there. 3/
In comparison, there are very few numbers that can be expressed in a compact form. In any computer language, there are a finite number of numbers that can be calculated by an algorithm less than some fixed length, since there are only a finite number of such algorithms. 4/
Pi equals four times (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...). Easy to code up. Takes infinitely long to run, but that's okay. 5/
So Pi is special. (As are e, the square root of 2, and some others.) It's one out of a very big infinity of irrational numbers, but one that is somehow accessible to our finite minds. 6/
Kind of like the universe. An infinite number of things happen, but they are related by very simple laws of physics. Reality, like Pi, is a special point in an unending vastness of possibility. fin/
