## 18 July 2024

### Proof that pi equals 4

Available at multiple places on the internet, where you can find discussions of varying quality.  It's basically a reminder that interesting things happen at infinity.

1. This circle also has infinitely many corners.

2. Similarly, you can "prove" that the square root of 2 = 2 by starting with a square of sides = 1 and reducing two adjacent sides ad infinitum to create a hypotenuse of length 2, along with the Pythagorean Theorem.

1. That would logically follow. Absolutely.

3. Simple conflation. The area inside the jagged lines approach the area of the circle. But the infinite peaks and valleys still keep the length of its lines at 4.

4. The sum of all the natural numbers equal to -1/12 https://www.youtube.com/watch?v=w-I6XTVZXww (Numberphile, a great math channel!)

5. The good news is that, FINALLY, I will be able to memorize pi to the one millionth place!

6. The point of science is to take things that are counter-intuitive and study them, figure out what's going on and make them intuitive.

The funny thing is that people who make up these things never follow through and start driving on squared of wheels.

7. Not never... https://external-content.duckduckgo.com/iu/?u=http%3A%2F%2Fnetstorage.discovery.com%2Ffeeds%2Fbrightcove%2Fasset-stills%2Fdsc%2F136734381737214045601501197_SQUARE_WHEELS.jpg&f=1&nofb=1&ipt=869a5f7d0876306ec8859ac5e2296f4a72c7de7391c298c58524a27f3e75b0c2&ipo=images

8. Not never... [I tried to add an image URL of a vehicle with square wheels - seemed to get swallowed up without trace]

1. Every comment on every post is "swallowed up" briefly. All 67,000 comments on TYWKIWDBI pass through me first, to weed out spam and idiots.

9. The infinity that surprised me most when I first encountered it. There are different sizes of infinity.
For instance, there are an infinite number of integers, but there are also an infinite number of even integers. An infinity 1/2 the size of the first

1. And yet they're both the same infinity.

10. Limits in mathematics are interesting, discombobulating things. There is a figure that one meets in calculus called a Gabriel's horn (also called Torricelli's trumpet). It is a simple rotation in 3D that can be filled with paint (finite volume) but its surface cannot be panted (infinite area).
https://en.wikipedia.org/wiki/Gabriel%27s_horn