Pi Day Rant 2018! (Patreon)

It's 3/14/1...8, and we're just going to roll with it. Why not have Pi be 3.1418...?

As I explain, it ends up being the worst Pi Day ever. And that was before we got the news of Stephen Hawking's passing, so if Pi Day 2018 wasn't the worst before, it certainly is now!

My favourite part of making this video was probably putting more sport in Sport Arena Stadium. In a different video we could have gone deep down the path of the curvature of space, but for Pi Day I'm happy to just plant the idea and incite curiosity. Also note the connection to Triple Piano.

But if one wants to get all space science on it, one could mention how part of what seems to make gravity work and the earth stay in orbit (or one way to think about it) is that space already does curve to the right alternative amount. Changing it just won't do! Also curved space is a little more complicated than just switching to one consistent alternative Pi. Hopefully those curious will go look into it.

I like how it came together, with relevant political undertones twisted and focused toward a ridiculous but interesting extreme, because that's what Pi Day is all about, right? 

My other favourite part of making this video was when I looked up ellipse perimeter equations, not knowing how complicated they are beforehand. The mathematical truth couldn't have worked out better for the video and that part basically wrote itself. How interesting that it's so tricky to calculate!

The "alternative ellipse" perimeter equation I propose, (a+b)π, also worked out nicely and is actually not a super terrible approximation (or at least, I challenge you to create a better one that's as simple). It's an average of what the perimeter would be for an a-radius circle and a b-radius circle, which works because (2πa + 2πb)/2 has all the 2s dance off together. 

The apparent simplicity of the reduced fraction hides the fact that it's an average. You couldn't do this with Tau! Which is just one more example of how while Pi might SEEM simpler and better in this case, reducing it actually obscures the mathematical truth. (τa + τb)/2 looks like what it is: an average perimeter for circles of two different radiuses. While πa + πb takes a second to understand, and π(a+b) yet another.

Still, I had fun creating that particular recreational obscurational approximational alternative equation :D

One argument for Tau is that many equations end up simpler with that extra 2 taken out (like τr instead of 2πr), but there's also examples where the Tau version is more complicated in a way that reveals the nature of the thing. Like how τr²/2 is more complicated than πr², but says more about the nature of what it means to take the area of a circle, that it's more triangly feeling and less squarey feeling.

One of the many things I find fascinating within mathematics, and ontologically, is how different ways of notating things that are mathematically equivalent can read with such different meaning, reveal different properties, and just "feel" so different. A topic I hint at sometimes in videos but someday would like to dive deeper into.

Anyway, happy Pi Day! I hope you find interesting things to think about and share today!

Vi Hart