Today was devoted to fun with geometry (as was some time late last night). I came up with a simpler proof of the proposition about the inscribed equilateral triangle, which I’m pleased about; the first one was a bit gnarly. I also worked on the lemmas to accompany it. It needs most of the same ones, but not the one about parallelograms.
Here are before and after shots showing the working figure for my first proof and that for my second. One proof required four new lines and two new named points. The other involved just one one of each.
(I’m looking forward to finishing this notebook so that I can move to an unruled one.)