November

It could have been—a bird out of season, dropping bright-feathered on my shoulder. … It could have been a tongueless dwarf standing by the road to point the way. …

That's a fragment from Rosencrantz & Guildenstern Are Dead that's been on my mind recently. I try to be aware of such omens.

In January, after two years of work, I finished writing about continued fractions and the pattern.

At the time, I was excited to read the book Markov's Theorem and 100 Years of the Uniqueness Conjecture, but I was also excited to get in touch with the author Martin Aigner and share all the fun things I'd found, even though none of them were really new. So, I was staggered to learn that he had passed away in October, just three months earlier. He was 81 years old. I hope he had a good life.

Since then, I've done some reading and learned some amazing things. And I'll tell you about them! I have plans for two and a half essays, but only one is finished.

The True Pattern

I also have plans for two essays of reference material, but only one is finished.

Bibliography

The main reason the other essays aren't finished is that I got sidetracked into creating some essays to represent ideas that I'd already written about. The motivations were all slightly different.

• For How to Compute Inverses in U_n, I needed to refer to it (from an essay that isn't finished yet), and also I had a shiny new algorithm to present.
• For How to Solve Simultaneous Congruences, I was just dissatisfied with my previous explanations.
• For Numbers as Polynomials, I needed to refer to it, but then my plans changed. I'm still happy to have it as a counterpart to Negative Digits, though.

That's all for now.