Comment Re:Can someone elaborate on... (Score 2, Interesting) 441
Definition of optimal: At least as good as EVERY other possible configuration of (in this case infinitely many) oranges in 3-space.
If by "see" you mean "conjecture" then, yes, it is easy to see. If by "see" you mean "prove", and thereby catch a glimpse into the fundemental reasons WHY this is the best possible stacking, then it is exceedingly difficult.
How would you go about designing a proof that would take into account every single one of the infinitely many configurations of oranges? Could you even list them? Indeed, I read somewhere that Hales said that the hardest part was reducing all the infinitely many configurations into something like 5,000 cases.
Focus on the infinite part of this problem: we're looking for an arrangement of infinitely many oranges in space such that we maximize the density of the oranges. Now, is it obvious to you that an (infinite) pyramid is denser than packing them somehow into a sphere-ish shape (with infinite radius of course)? It certainly isn't to me...
I'm not sure is this is very convincing, but it's the best I can do without really researching the problem.
If by "see" you mean "conjecture" then, yes, it is easy to see. If by "see" you mean "prove", and thereby catch a glimpse into the fundemental reasons WHY this is the best possible stacking, then it is exceedingly difficult.
How would you go about designing a proof that would take into account every single one of the infinitely many configurations of oranges? Could you even list them? Indeed, I read somewhere that Hales said that the hardest part was reducing all the infinitely many configurations into something like 5,000 cases.
Focus on the infinite part of this problem: we're looking for an arrangement of infinitely many oranges in space such that we maximize the density of the oranges. Now, is it obvious to you that an (infinite) pyramid is denser than packing them somehow into a sphere-ish shape (with infinite radius of course)? It certainly isn't to me...
I'm not sure is this is very convincing, but it's the best I can do without really researching the problem.
