Ham sandwich theorem

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

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

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

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

 Name 
The theorem is called the ham sandwich theorem because a sandwich with bread, cheese, and ham consists of three ingredients and lies in three-dimensional space. Thanks to the ham sandwich theorem it is possible to make one cut with a knife to divide the bread, the cheese, and the ham fairly between both sides.

Category:Theorems in geometry