Difference between revisions of "Ham Sandwich Theorem"
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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]]. | 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 no easier if one replaces bread, ham, and bread with Earth, Mars, and Jupiter. | + | Visualizing this at an intuitive level is no easier if one replaces bread, ham, and bread with Earth, Mars, and Jupiter. It is probably easier if you're from [[England|England]], where ham sandwiches have two slices of bread and one of ham, with no lettuce, tomato or pickles. |
[[Category:mathematics]] | [[Category:mathematics]] | ||
[[Category:topology]] | [[Category:topology]] | ||
Revision as of 02:24, 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. It is probably easier if you're from England, where ham sandwiches have two slices of bread and one of ham, with no lettuce, tomato or pickles.