feels like there's a theorem
only surfaces that satisfy a certain condition are planes and spheres.

like “the two principal curvatures are equal and constant”.

“curvature” is way too difficult for me to understand at this point.

a cylinder 🥫 is

if the radius is infinite, it's a plane.

if the radius is finite, and the height is infinite, it's an infinite surface.
its “curvature” is constant—but zero, it seems.

1)
a paraboloid of revolution 🥣 comes to mind first.
food sits at the bottom, but the rim is infinitely far.

but 🥣 doesn't have a constant “curviness”.

(if it were, it'd be a sphere 🌐—finite)

been using five AIs, ChatGPT, Gemini, Grok, Perplexity, and Claude, in five windows on my macbook. still figuring them out.

2) Yes, a sphere with an infinite radius is a plane.

a circle with an infinite radius is a line—called a generalized circle, cline, or circline.
https://en.wikipedia.org/wiki/Generalised_circle

a plane is infinite, but a sphere is finite.
(the area of a sphere is 4πr²)

1) are there any infinite curved surfaces?
2) can a sphere have an infinite radius? (would it become a plane...??)

took a stimulant

woke up (2am)

sry for so many genshin posts.
setting up the world's first institute for the study of low level genshin gameplay.

4-1
idk if we can win under lvl 20.
lisa, d traveler, lynette, barbara/noelle
hyperbloom team (?)
3 enemies left.
time's up.

Spiral Abyss
2-1 2* https://youtu.be/1bN2FQl1UNI
2-2 3*
2-3 1*

3-1 3* https://youtu.be/Tb5fu3Q02T8
3-2 2* https://youtu.be/ucP5r0q97xo
3-3 1*
see description for details.