Math CentralQuandaries & Queries


Question from Tracy, a parent:

A square with a side of 4 ft needs to be cut into four shapes with the same area. can you find six different was to cut the square?


I'll give you one infinite set of ways. and two challenges. Find the center of the square, and cut right across it with two cuts at right angles to each other. Depending on your choice of slopes this gives infinitely many solutions.

First challenge: find more solutions, with pieces that are not quadrilaterals, based on the idea of rotational symmetry used in my solutions.

Second challenge: find solutions that are not based on fourfold rotational symmetry.

Good Hunting!


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