If you're asking "do you have a purpose in all these?" the answer is "no, I'm just playing." :) Life has been harsh and having the capacity for play is rare and precious: you know my opinions on She-Who-Delights-In-Play, so I take it as a sacred act and try to enjoy myself! The way with these things is that playing tends to lead one to deeper insight, so maybe I'll have something deeper to say about it sometime. (Or maybe not! The play is enough.)
If you're asking "why circles?" the answer is that I was really surprised to discover the Mohr-Mascheroni Theorem—anything you can do with compasses and straightedge, you can do with compasses alone—and wanted to develop an intuition for why. But in playing around with it, I've found that compass-only constructions have a very different feel to them; normal construction feel like you're using a set of tools in known ways; but compass-only constructions are much more mysterious, more like a puzzle. I suppose the mystery of it fascinates me.
Also, I like how the space is less explored. People far smarter than I have been doing "normal" geometry for millennia: it's very well understood, and there's 40 constructions for anything. If you search around for compass-only constructions, though, it's hard to find much of anything. So if you want to know how to draw something, the only way is to sort it out yourself!
also like any straight male I like round things more than straight things
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Date: 2022-11-26 01:04 pm (UTC)If you're asking "why circles?" the answer is that I was really surprised to discover the Mohr-Mascheroni Theorem—anything you can do with compasses and straightedge, you can do with compasses alone—and wanted to develop an intuition for why. But in playing around with it, I've found that compass-only constructions have a very different feel to them; normal construction feel like you're using a set of tools in known ways; but compass-only constructions are much more mysterious, more like a puzzle. I suppose the mystery of it fascinates me.
Also, I like how the space is less explored. People far smarter than I have been doing "normal" geometry for millennia: it's very well understood, and there's 40 constructions for anything. If you search around for compass-only constructions, though, it's hard to find much of anything. So if you want to know how to draw something, the only way is to sort it out yourself!
also like any straight male I like round things more than straight things