AdministratorDecember 10, 2021 at 7:10 am
I like your claim here! While that feels good initially, I’m freshly thinking about another message from the forum I just responded to about similar triangles. We can explore all of the side lengths of a set of similar triangles via a composed unit – which is continuous as well as explore the sides in a single triangle via multiplicative comparison which is also continuous. I wonder if an argument could be made to say “often” or “most often” for your claim? We’d have to think more on this though.