Timeline for Math puzzles for dinner
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2010 at 18:12 | comment | added | aorq | Full-blown calculus isn't necessary. You only need Cavalieri's principle: en.wikipedia.org/wiki/… | |
| Jun 27, 2010 at 15:40 | comment | added | user5794 | Jonah, I don't think you're missing anything. To solve rigorously, I think you need calculus. Gardner's own answer basically said that, assuming you understand that the problem is well-posed, the answer must not depend upon the size of the sphere. So take the sphere with hole of diameter approaching zero (i.e. a sphere of diameter 6 units), which is just the whole sphere (i.e. 36π cubic units). | |
| Jun 26, 2010 at 14:54 | comment | added | Jonah Ostroff | It's easy to see what the answer has to be once you're told there's an answer, but I don't see how to prove it without setting up an integral. What am I missing? | |
| Jun 24, 2010 at 18:59 | comment | added | Kiochi | @Michael: Indeed! I first saw this as an exercise while I was teaching calculus and was somewhat surprised/annoyed by how long it took me to figure out. | |
| Jun 24, 2010 at 17:42 | comment | added | Michael Lugo | This is an amusing exercise for calculus courses (solids of revolution), although calculus is not necessary. | |
| Jun 24, 2010 at 17:30 | history | answered | user5794 | CC BY-SA 2.5 |