For geeks, there are some great holidays on the calendar. Of course, there is also Mole Day (October 23rd), which commemorates Avogadro’s number, but the number is huge (on the order of 10)twenty three) and very important in physics. Euler’s ubiquitous number (e = 2.718…) has e days (2/7). But the best thing about him is Pi Day, which is held on March 14th. Because the infinitely long decimal approximation of pi starts at 3.14. There’s a lot to be said about Pi. I have been writing Pi Day articles for his 14 years. (this is a partial list).
What is pi (or π as the Greeks called it)? By definition, it is the ratio of the circumference of a circle to its diameter. It’s not clear why it’s so special, but Pi appears in a lot of cool places that don’t seem to have anything to do with circles. But one of the strangest things about pi is that it is an irrational number. This means that the value cannot be expressed as a decimal of two integers. yes. The number 22/7 (22 ÷ 7) is a good approximation, but it is not pi.
But wait a minute. When we say that Pi is an irrational number, all we really mean is that Pi is an irrational number in the number system we use, that is, the decimal or base-10 number system. is. But there is nothing inevitable about that system. As you probably know, computers use a base-2, or binary, number system. Base-10 was probably chosen during the analog era. Because we can count on his ten fingers. (Fun fact: the Latin origin of digit teeth finger, means “finger”. )
So, is there a number system in which pi is rational? The answer is “yes.”
Wait a minute, what is a numbering system?
Let’s see how the number system works. Imagine you are in a bean counter in the time of Neanderthals. For each successive bean, write down a different symbol on the cave wall. For 200 beans, you need 200 symbols. I call it “numbers” because it’s mind-boggling.
One day, he meets a wise Homo sapiens who says, “You’re trying too hard!” They have a new system with just 10 symbols written from 0 to 9 that can represent any amount of beans. Once you get to 9, move one place to the left and start again, so each digit is a multiple of 10. After that, it becomes a multiple of 100, increasing successively to powers of 10.
Consider the number 214. There are two 100s, one 10, and four 1s. What this actually means can be written as:
Illustration: Rhett Alleyne