Sorry to be late. We discovered baby fish in a tank that we had thought was empty, and that needed some quick attention. The water seems nearly all right and we’re taking measures to get the nitrate back in line. Fish-keeping is a great hobby for someone with tendency towards obsessions and who likes numbers because there is no end of tests you can start running and charts you can start to keep.
So I’ve seen two baby fish, one about the width of a fingernail and one about half that. We’re figuring to keep them inside until they’re large enough not to be accidentally eaten by the bigger goldfish, which means they might just be in there until we move fish inside for the winter. We’ll see.
Back to my archives, though. The hypersphere is a piece from the first A-to-Z I ever did. I could probably write a more complicated essay today. But the hypersphere is a good example of taking a concept familiar, as circles and as spheres, and generalizing it. Looking at what’s particularly interesting in a concept and how it might apply in different contexts. So it’s a good introduction to a useful bit of geometry, yes, but also to a kind of thinking mathematicians do all the time.