Difference between revisions of "Ham Sandwich Theorem"

Latest revision as of 00:40, September 22, 2018

The Ham Sandwich Theorem is a theorem in mathematical analysis 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.

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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 [[analysis|mathematical analysis]] 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|England]], where ham sandwiches have two slices of bread and one of ham, with no lettuce, tomato or pickles.
+[[Category:Topology]]
-[[Category:mathematics]]
-[[Category:topology]]