I totally disagree.
Saying that "pi isn't really about circles" is totally wrong and removes it from any properties people can easily grasp.
He argues that pi should be defined as a property of a differential equation. This is obviously stupid, because it makes mathematics impossible to teach.
For me it gets the worst when he claims that Euler's equation has no relation to circles. Which is, really, really stupid.
The complex exponential represents rotations in space. This connectiom can only arise when you understand first that pi is in fact about circles.
The circle is the underlying principle of pi.
Its a nicely written post, but I think its a bit misleading.
This type of exposition preys on peoples feeling that there must be something deeper going on, but ultimately just kicks a real grasp of math down the road. On the bright side maybe a few more people know of the complex exponential though?
The truth is that there is no royal road. No perfect explanation. Nobody can tell you what a mathematical concept really is. The only surefire route is through experience doing and using math.
If you want to know what these numbers "are"... then simply do more math. I encourage you to squeeze some philosophy in as well. Reading Wittgenstein's lectures on mathematics, after taking my first model theory course, really messed me up for awhile!
Yes, there is no royal road.
But there is a very harsh one. There you ignore that pi is about circles and instead think of it as the period of some solution to a differential equation.
I like this tour of pi, however 2pii being a period of the exp() function seems quite related to circles to me. Either way, that last bit about the gaussian distribution minimizing entropy and convolving with itself was really amazing. Someone should do a similar post on just the normal distribution and why its so ubiquitous
He argues that pi should be defined as a property of a differential equation. This is obviously stupid, because it makes mathematics impossible to teach.
For me it gets the worst when he claims that Euler's equation has no relation to circles. Which is, really, really stupid. The complex exponential represents rotations in space. This connectiom can only arise when you understand first that pi is in fact about circles. The circle is the underlying principle of pi.