Some random thoughts for #PiDay.
I usually mark occasions like this with flags, but I don’t have a particularly good mathematics flag or a Pi flag. I’ll have to work on that for next year.
I’ll start off with a brain check. How much Pi is in there? Let’s see.
3.14159265358979323846. That’s 20 places past the decimal point. Is that right? Wolfram Alpha says yes.
Learning the digits of Pi was kinda fun and every few years I’d get it in my head to learn a few more digits, usually in clumps of three. Still, I never understood why someone would memorize Pi to 100 or 1000 decimal places.
This begs a question then. Are 21 significant figures enough? I thought about this last year, inspired by an article called “How Much Pi Do You Really Need.” The website asked me to sign up for a membership so I didn’t read it. Thinking about it was more fun anyway. So let’s go!
The radius of the Milky Way Galaxy is about 52,850 light years. That’s kinda-sorta the distance from Trantor to Terminus for my #Foundation friends if we assume that Trantor was in the middle of that big black hole in the center of the galaxy.
Fifty-two thousand, eight hundred and fifty light years is about: 3.1 x 1017 miles or 1.97 x 1022 inches. We’d need 18 significant figures to measure the circumference of the galaxy to the nearest mile or 23 to get to the nearest inch. So, assuming we could measure everything else as accurately (which, of course, we can’t) we’d need Pi accurate to 17 or 22 digits respectively. Thus π = 3.1415926535897932384626 is all the Pi you need for even the most impractical purposes. My 20 digits are more than enough.
For practical purposes? The serious answer can’t be more than four or five.
Featured Image: Some art done by mathematics students at Elmira College on Pi Day, 2019. The pictures were built out of graphs of functions in Cartesian and polar coordinates.