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!

[sdi]

Thank you! I'm having a lot of fun with these—it's really difficult to think in circles rather than lines, since you sorta have to come at every problem sideways. I'm slowly gaining some intuition for the problem.

I think the biggest trick to following along on paper is to work out, arithmetically, the radius of each circle drawn. Shapes always have a characteristic number associated with them, and once you've managed to work out the numbers involved, it gets a lot easier to follow: √3's make hexagons, √2's make squares, ϕ's or 1/ϕ's make pentagons...

And thank you also for the well wishes! I'm still sick, but I've at least been learning a lot...