You Can Count on Pi

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For geeks, location are respective awesome holidays connected nan calendar. There is of people Mole Day (10/23) to commemorate Avogadro's number, which is immense (on nan bid of 1023) and hugely important successful physics. There's e Day (2/7) for Euler's ubiquitous number (e = 2.718…). But nan champion is Pi Day, held connected March 14 because nan infinitely agelong decimal approximation of pi originates pinch 3.14. There's truthful overmuch to opportunity astir pi—I've been penning Pi Day posts for 14 years. (Here's a partial list).

What is pi (or arsenic nan Greeks would say, π)? By definition, it's nan ratio of nan circumference to nan diameter of a circle. It's not evident why that should beryllium special, but pi shows up successful a bunch of cool places that look to person thing to do pinch circles. But 1 of nan weirdest things astir pi is that it's an irrational number. That intends it's a worth that can't beryllium expressed arsenic a fraction of 2 integers. Oh, sure. The number 22/7 (22 ÷ 7) is simply a adjacent approximation, but it's not pi.

But hold a second. When we opportunity pi is irrational, each we're really saying is that it's irrational successful nan strategy of numbers we use, which is nan base-10, aliases decimal, system. But there's thing inevitable astir that system. As you astir apt know, computers usage a base-2, aliases binary, number system. Base-10 was astir apt chosen successful nan analog era because we person 10 fingers to count on. (Fun fact: The Latin guidelines of digit is digitus, which intends “finger.”)

So could location beryllium a number strategy successful which pi is rational? The reply is yes.

Wait, What’s a Number System?

Let's reappraisal really a number strategy works. Imagine you're a legume antagonistic backmost successful Neanderthal times. For each successive bean, you constitute down a different awesome connected nan wall of your cave. For 200 beans, you request 200 symbols. It's mind-numbing, and truthful you telephone them “numbers.”

One time you meet a clever Homo sapiens who says, “You're moving excessively hard!” They person a caller strategy pinch conscionable 10 symbols, written arsenic 0 to 9, which tin correspond immoderate amount of beans. Once you scope 9, you conscionable move complete 1 spot to nan near and commencement again, wherever each digit is now a aggregate of 10. After that it's multiples of 100, and truthful connected successful successively higher powers of 10.

Take nan number 214: We person 2 hundreds, 1 ten, and 4 ones. We tin constitute what this really intends arsenic nan following:

Illustration: Rhett Allain