January

The giant thread that started with Approximation Quality is finally complete! Last time I thought there was just one essay left, but in fact there were seven. I split The Discriminant in two, adding One More Discriminant, so the final thread length is 17, but after that I took my own advice and created more or less independent essays.

Properties of Rotations
Reflection Symmetry
A Nice Correspondence (and Six Operations)

An Interesting Detail

Fortunately I was able to resist the temptation to name One More Discriminant after an excellent joke from an otherwise pretty stupid photoshop contest about bad movie sequels.

Shia LaBeouf
    in
We Found Another Mohican

Looking back at the past six months, it's been an ordeal. The whole time, I thought I was nearly done, but like clockwork, every month I found another topic that needed to be split out. I kept working, though, and eventually the process came to an end.

Looking back at the past two years of constantly thinking about continued fractions, it feels like I've written a master's thesis. Too bad I didn't discover anything new!

I don't like research, too much uncertainty, so why was I doing research? I can think of three answers to that question.

First, like I said near the end of The Pattern, I wanted to see how far I could get by myself.

Second, the only goal was to see how far I could get, so when a problem became intractable, I stopped working on it, and when I ran out of ideas, I was done. That removed most of the uncertainty.

Third, I really wanted to read these two nice books.

[Aigner] Markov's Theorem and 100 Years of the Uniqueness Conjecture
[Olds] Continued Fractions

And now I can!

This episode has been brought to you by Panera Bread coffee and the numbers 1 and 2.