a. cube: slice from one corner through the center of mass of the cube (to the opposite corner). b. tetrahedron: slice at midpoints (I think). I might not be describing this correctly although I know the solution. Regardless, it's pretty elegant: the two pieces are symmetrical I think the Museum Shop (Glendale Galleria has one, I think) sells this as a wooden puzzle for about $10. c. This is straight from memory, and I can't really test it because I don't have access to hollow donuts. I think you slice from the tangent of one side to the tangent of the other but I'm not exactly sure. Email doesn't describe this well so we'll go for poor ASCII graphics: O/O except the / should have a smaller slope. I think this was Gary's QOD so he might still have the book he pulled the question from.
- Of course, I have to disagree with Leslie's description of (a), where I believe the cutting plane is the plane perpendicular to a diagonal that meets at the center of the cube.
- Leslie has retracted her answer to (a) and has provided an elucidating link. I've stolen two of the images on that page:
- Leslie has retracted her answer to (a) and has provided an elucidating link. I've stolen two of the images on that page:
- Well, (b) is just hard to explain. Each piece will basically look like the blade of a hatchet, with each side being a trapezoid, and with a really fat square base.
- And I still have no idea what (c) looks like.
- Leslie managed to find the source(?) of the question, which is Martin Gardner's New Mathematical Diversions from Scientific American. Here is my rendition of his illustration:
I guess I believe this solution now, though I don't know whether I believe those ellipses are really circles...
- Leslie managed to find the source(?) of the question, which is Martin Gardner's New Mathematical Diversions from Scientific American. Here is my rendition of his illustration:
