▲ | dole 5 hours ago | |||||||||||||||||||||||||||||||||||||||||||
Even though onions aren't perfectly symmetrical, they still optimally grow or radiate out from one axis/line through the middle. Stick a toothpick through a sphere as this line, and slice the sphere through perpendicular to the axis, you'll get circles from a sphere, or half-disks from a half onion if you keep slicing perpendicular. I'm lazy and cut my onions perpendicularly through halves, and don't try a radial cut for uniformity. | ||||||||||||||||||||||||||||||||||||||||||||
▲ | yunwal 5 hours ago | parent [-] | |||||||||||||||||||||||||||||||||||||||||||
> Even though onions aren't perfectly symmetrical The question I have is not about modeling an imperfect object as a perfect abstraction, it's about modeling a 3D object as a 2d object, and assuming that the optimization still holds. I think it's pretty plainly clear that it doesn't. Think about some cross-section of the onion that's closer to you and smaller than the center cross-section. Let's say it's of radius 0.25 instead of 1. The slices you take of it will be much more vertical than the center slice. This changes things. My intuition tells me it means the optimal solution is shallower than the solution found here, since you'd want the "average" cross-section to follow this constant. | ||||||||||||||||||||||||||||||||||||||||||||
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