Yes, I see that. Cool. On Fri, Jan 12, 2018 at 2:21 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
By tangency contact I guess you mean contact with negligible mating surface.
If we don't permit that and we want a minimum mating surface, it's easy to change it to a solution requiring only twice the number of pieces.
On Fri, Jan 12, 2018 at 11:17 AM, Allan Wechsler <acwacw@gmail.com> wrote:
Oh. If we are permitting tangency contact, then I see the solution Tom has in mind :)
On Fri, Jan 12, 2018 at 2:16 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Well, you've stumped me!
On Fri, Jan 12, 2018 at 2:15 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
There's a much simpler and cleaner solution to the 2D case.
On Fri, Jan 12, 2018 at 11:13 AM, Allan Wechsler <acwacw@gmail.com> wrote:
I was an idiot not to look at the the 2D case first. I don't have a detailed solution, but the sketch is, a roughly square section in the middle cut into planks, which get reassembled end-to-end to make the outside of the square, and then the four remaining sections of the circle get chopped up fine enough to fill in the middle. I would guess it can be done in about 20 pieces at most.
On Fri, Jan 12, 2018 at 1:37 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
... I didn't see the solution for 2D immediately ... but suddenly I did.
Neat puzzle.
On Fri, Jan 12, 2018 at 10:07 AM, Allan Wechsler < acwacw@gmail.com> wrote:
> It's obviously possible to dissect a sphere into pieces that could be > reassembled into something that looks like a cube from the outside. Inside, > it would be hollow, possibly with a bunch of spare pieces rattling around > inside. > > Feasibility sketch: build thin polyhedral planks from the inner part of the > sphere, with 45-degree bevels where necessary to let them form the cube's > edges and vertices. All the extra material could be chopped up into > manageable chunks and hidden in the interior. If there's too much extra > material, redesign with thinner planks to make the outer cube bigger. > > Intuitively, it feels like we could get away with just a few dozen pieces > or so: maybe 4 to 6 per face, and then an approximately equal number to > pack inside ... but I don't know. Can anybody provide an explicit > construction, or make lower-bound arguments about the number of pieces? > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >
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