Math Is Beautiful (and Fun): Tangrams!

By Damaris | Added Feb 19, 2016

As we continue to celebrate math in all its beauty, here's an ancient Chinese geometric puzzle that's fun and challenging... and will give your spatial recognition skills a boost! A tangram consists of seven moveable shapes called tans, which are all cut from one square.

All tangrams are made up of tans with the following shapes and proportions relative to the square they're cut from. Each side of the main square equals 1 unit, and its area equals 1 square unit (source):

  • 5 right triangles—2 small (hypotenuse of 1/2, sides of √2/4, and area of 1/16), 1 medium (hypotenuse of √2/2, sides of 1/2, and area of 1/8), and 2 large (hypotenuse of 1, sides of √2/2, and area of 1/4);
  • 1 square (sides of √2/4 and area of 1/8); and
  • 1 parallelogram (sides of 1/2 and √2/4, and area of 1/8).

To get started, click here to download your very own tangram activity packet, including a set of tangrams you can cut out, as well as some tangram puzzles for you to solve! To solve each puzzle, simply arrange all the pieces to form the silhouetted figure in such a way that all pieces touch without overlapping. When you're done, flex your spatial recognition muscles a little more and see if you can create the following figures using all seven pieces in your set:






A person walking

Then, using your imagination, what other figures can you make? Get those creative juices flowing and have fun!