A new year (2022)
What does one do on the first day of a new year but write a blog post, and in it clearly delineate all plans for the coming year? Well, I'm doing the first part, but not the second, as I know that any plans will not be fulfilled - something always gets in the way.
You will notice a complete absence of posts last year after April. This was due to pressures both at work and outside, and left me with little mental energy to blog. I don't know that this year will be much different.
However, a few things to note (in no particular order):
I decided to upgrade my VPS, starting with my installation of Nextcloud. I've been using Nextcloud as a replacement for Dropbox for years. But I managed to stuff-up an upgrade. While it was unavailable to me I used Syncthing to keep my various computers in sync with each other, and I must say this works extremely well. So well, in fact, that it seems hardly worth going back to Nextcloud. And it seems that there are people who are ditching Nextcloud for simpler solutions: Syncthing for syncing, and something else for backups. Rsync could be used here; I've also been recommended to look at Duplicati.
The upgrade of both Nextcloud and my VPS system (Ubuntu 18.04 to Ubuntu 20.04) both went awry, and I ended up with a non-working system. I could ssh into it, but none of the services would work. So I decided to ditch the lot, and start from scratch by re-imaging my VPS. This "scorched earth" approach meant at one stroke I got rid of years of accumulated rubbish: files and apps I'd downloaded, experimented and discarded; any number of old unused docker containers and images. (Although I had made an effort to clean up those.)
And I've been slowly building everything back up again, with much external help in particular for managing traefik, which I like very much. But it has a configuration which is tricky, at least for me.
I did manage to attach a USB drive to my home wireless router, and make that drive visible to both Linux and Windows - which took longer than it should have, as I kept misunderstanding descriptions and instructions. But it's working now. So in one sense I have at least local backups. However, I also need "off-site" backups.
In my teaching this last year I used, as for previous years, a mixture of Excel and Geogebra for my numerical methods class, and Excel with its Solver add-in for my linear programming class. These students are all pre-service teachers, and so I use the software they will be most likely to encounter in their professional lives. I have come to quite like Excel, and my students even get to do a bit of VBA programming. (Well, I write the programs, and then they edit them slightly.)
I have a love-hate relationship with Geogebra. It does many things well, but there's always an annoying limit, or things you can't change. I hope to write up about this. But here's one: Geogebra's default variable names for lists (if you don't give them names yourself) are l1, l2, l3 and so on. But Geogebra uses a sans-serif font in which a lower-case L is indistinguishable from an upper-case I. And you can't change the font. So if you're seeing "l1" for the first time, you can't distinguish the first character. This is a very poor GUI decision. And it annoys me a lot, because it would be trivial to fix: use an upper-case L instead, or allow users to change the font!
I taught for the first time a data analytics subject, based around R, which I'd never before used. Well, there's nothing like having to teach something to learn it quickly, and I learned it well enough to teach it to a beginning class, and also to enjoy it. Like all languages, R comes in for plenty of criticism, and much of its functionality can be managed now with Python, but R has been a sort of standard for a decade or more, and that alone is a very good reason for learning it. What's more, it seems to be getting a new lease of life with the tidyverse suite of packages byHadley Wickham. And these come with excellent documentation.
I finished the year looking again at bicentric polygons, which fascinate me. Some years ago, Phil Todd, the creator of the Saltire geometry application, found a bicentric pentagon whose vertices were a subset of the vertices of a regular nonagon. You can see his PDF file here.
I was wondering if there are other bicentric polygons whose vertices are subsets of a regular \(n\)-gon (other than triangles or regularly-spaced vertices), and this led me on a bit of a hunt. Using a very inefficient program (and in Python), I found no other bicentric pentagons, and the only bicentric quadrilaterals were right-angled kites; that is, whose vertices are at
\[ (\pm 1,0),\quad (\cos(x),\pm\sin(x)) \]
for \(0<x<\pi/2\). This either means there are no others, or there are others I haven't found. I don't know. It would be nice to discover a symmetric but non-regular bicentric hexagon with vertices a subset of an \(n\)-gon, for \(n>7\).
So - software and mathematics - plenty going on!