Haberdasher Set

This classic puzzle forms a square and an equilateral triangle. It can also be used to explore the relationship between the area and the perimeter of regular polygons and more.

In addition to the basic Haberdasher Puzzle this puzzle can be used to explore a number of important ideas in geometry and other branches of mathematics. Here are some suggestions:

1) Use the set to explore congruent angles. Each of the four pieces has one right angle and three of the four pieces have a sixty degree angle. Both the sixty degree and the ninety degree angles can be proved by congruence combined with the observation that they will form a straight line.

2) Establish that any configuration of the four pieces produces the same area. Follow this by exploring the relationship between area and perimeter. Students can approximate the perimeter by actually measuring the respective configurations. Ask the students to make a conjecture about the perimeter as the number of sides (regular polygons) increases. You might ask the students what shape is approached as the number of sides becomes very large.

3) This puzzle now leads us to observe that the perimeter decreases toward a limit. The circumference of a circle of equal area establishes the lowest possible perimeter. So, we have moved from forming a square and an equilateral triangle to introducing the concept of a limit.

4) Please share with us any other applications you find for this particular puzzle!

Photo shows TWO sets for illustration purposes.

If you like this puzzle, check our resource page for books by Greg Frederickson!

The regular PENTAGON is equal in area to the Haberdasher Puzzle and is included to provide a third polygon to explore the relationship between area and perimeter!

All of the plastic sets are excellent for use on overhead projector as well as tabletop.

Haberdasher Set
Price $20.00
Includes solution and support material
(plus shipping and handling)