Ham sandwich theorem

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The ham sandwich theorem is a math theorem that says that a number of objects in the same number of dimension can be cut into two equal parts with a cut that is one dimension less.

Examples[change | change source]

One dimension[change | change source]

One dimension is a line. A section of the line can be cut exactly in half with a single point.

Two dimensions[change | change source]

Two dimensions is a flat sheet. Two shapes on this sheet can be cut exactly in half with a single line.

Three dimensions[change | change source]

Three dimensions is space. Three objects in space can be cut exactly in half with a single flat sheet.

Four dimensions[change | change source]

Four dimensions is a hyperspace. Four hyper-objects can be cut exactly in half with a single space.

Name[change | change source]

The theorem is called the ham sandwich theorem because sandwiches are made of three dimensional pieces of bread that are cut in half with a flat sheet, like a slice of ham. If there were three pieces of bread, it would be possible to make one cut along a plane to divide each of bread into two equal pieces. If a piece of ham is then put between each sliced piece of bread, the result would be three ham sandwiches.