Moss's Egg

[sdi]

The highlighted curve is called Moss's Egg, though I'm not certain who Moss is. (The link cites Dixon's Mathographics—I ordered a copy, perhaps it'll tell me.) I was surprised to find a way to construct it using only 8 circles! This is because circles naturally want to generate √3's, so usually it'd take extra effort to generate the √2 proportions the egg demands, but it turned out to only require going a single circle out of my way.

Comments

[violetcabra]

If I may, I applaud these proofs you are doing. They are well beyond my capacities to follow along, and I am deeply impressed! Also, I hope you are feeling better!

[boccaderlupo]

Agreed with violetcabra. These posts are beyond my grasp, but they are captivating images and the process itself seems interesting.

Maybe you've addressed already, but wondering if you are "tracing" this back to the "shape" of the soul, according to the ancients, as a kind of ritual meditative technique...?

Axé

[sdi]

It is worth noting that this construction of Moss's Egg implies another nice, simple construction of a square (e.g. Napoleon's problem):