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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]].

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 probably 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.

[[Category:mathematics]]

[[Category:mathematics]]

[[Category:topology]]

[[Category:topology]]