Difference between revisions of "Ham Sandwich Theorem"
Jump to navigation
Jump to search
(Here 'tis. Bon appetit!) |
m |
||
| Line 1: | Line 1: | ||
| − | The '''Ham Sandwich Theorem''' is a theorem in [[ | + | The '''Ham Sandwich Theorem''' is a theorem in [[Topology|topology]] stating that the volume of any three 3-dimensional objects of any shape (imagined as a slice of bread, some ham, and another slice of bread) can all be perfectly bisected with one plane. That is, one straight slice of a knife will create two half-sandwiches, with exactly equal amounts of bread on top, equal amounts of ham, and equal amounts of bread on the bottom. It is the three-dimensional version of the two-dimensional [[Two-Pancake Problem]]. |
| − | Visualizing this at an intuitive level is | + | Visualizing this at an intuitive level is no easier if one replaces bread, ham, and bread with Earth, Mars, and Jupiter. |
[[Category:mathematics]] | [[Category:mathematics]] | ||
[[Category:topology]] | [[Category:topology]] | ||
Revision as of 02:12, July 9, 2011
The Ham Sandwich Theorem is a theorem in topology stating that the volume of any three 3-dimensional objects of any shape (imagined as a slice of bread, some ham, and another slice of bread) can all be perfectly bisected with one plane. That is, one straight slice of a knife will create two half-sandwiches, with exactly equal amounts of bread on top, equal amounts of ham, and equal amounts of bread on the bottom. It is the three-dimensional version of the two-dimensional Two-Pancake Problem.
Visualizing this at an intuitive level is no easier if one replaces bread, ham, and bread with Earth, Mars, and Jupiter.