Happy Tau Day! It’s funny. I feels like I’ve written a lot of posts about pi plus few about it’s bigger sibling, tau. Yet the reality is that I’ve only ever written one Tau Day post, and that was back in 2014. (As far as celebrating Pi Day, I’ve only written three posts in eight years: 2015, 2016, & 2019.)
What I’m probably remembering is mentioning pi a lot here (which is vaguely ironic in that I won’t eat pie — mostly I don’t like cooked fruit, but there’s always been something about pie that didn’t appeal — something about baking blackbirds in a crust or something).
It’s true that I am fascinated by the number.
Well, it’s Pi Day once again (although this date becomes more and more inaccurate as the century proceeds). So, once again, I’ll opine that Tau Day is cooler. (see: Happy Tau Day!)
Last year, for extra-special Pi Day, I wrote a post that pretty much says all I have to say about Pi. (see: Here Today; Pi Tomorrow) That post was actually published the day before. I used the actual day to kick off last Spring’s series on Special Relativity.
So what remains to be said? Not much, really, but I’ve never let that stop me before, so why start now?
It’s pi day! Be irrational!
Earlier this week I mentioned that “this coming Saturday is a doubly special date (especially this year).” One of the things that makes it special is that it is pi day — 3/14 (at least for those who put the month before the day). What makes it extra-special this year is that it’s 3/14/15— a pi day that comes around only once per century. (Super-duper extra-special pi day, which happens only once in a given calendar, happened way back on 3/14/1529.)
I’ve written before about the magical pi, and I’m not going to get into it, as such, today. I’m more of a tau-ist, anyway; pi is only half as interesting. (Unfortunately, extra-special tau day isn’t until 6/28/31, and the super-duper extra-special day isn’t until 6/28/3185!)
What I do want to talk about is a fascinating property of pi.
This might seem like another math post… but it’s not! It’s a geometry post! And geometry is fun, beautiful and easy. After all, it’s just circles and lines and angles. Well, mostly. Like anything, if you really want to get into it, then things can get complex (math pun; sorry). But considering it was invented thousands of years ago, can it really be that much harder than, say, the latest smart phone?
Even the dreaded trigonometry is fairly simple once you grasp the basic idea that the angles of a triangle are directly related to the length of its sides. (Okay, admittedly, that’s a bit of a simplification. The (other two) angles of a right-angle triangle are directly related to the ratios of the length of its sides, but still.)
However, this isn’t about trig; this is about tau!