Math is Beautiful and Fun

Feb 11, 2016 | Sharyland

Tangrams!

 

 

In celebration of Chinese New Year, here's an ancient Chinese geometric puzzle that's fun and challenging... and will give your spatial recognition skills a boost! A tangramconsists of seven moveable shapes called tans, which are all cut from one square. To get started, click here to download your very own set of Mathnasium tangrams and cut out each shape!

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 solve the puzzle, simply arrange all the pieces to form a figure in such a way that all pieces touch without overlapping. Trust us... there are definitely enough possible solutions to keep you occupied for quite a while! The image above shows six possible solutions. Now that you have a general idea of how tangrams work, can you create the following figures using all seven pieces in your set... or even better, use your creativity to come up with figures of your own?

House

Teacup

Chair

Christmas Tree

Boat

Rocket

Candle

A person walking