# Mathematics applications with the Tangram puzzle

 Manipulatives TangraMagic GeoTemplet Ostomachion puzzle Mosaic patterns Circular pavings Magic Hen Links of interest Randy's Tangram Tangram Wikipedia Le Tangram Tangram Box Math Tangram Ten million of Tangrams

Pages: | 1 || 2 || 3 || 4 || 5 |

Math relations between the 5 shapes
which form the Tangram puzzle

by G. A. Sarcone & M. J. Waeber

The math relations between the 5 basic shapes of the Tangram puzzle shown below will allow you to create and/or solve new interesting geometric puzzles. The small isosceles triangle B, the square C and the rhomboid D of the Tangram all have the same area, but their surfaces are different. Actually, the square C has the smallest perimeter (4a < 2(a+b)). The large isosceles triangle E is 4 times the size of the small isosceles triangle A, but curiously its perimeter is only 2 times as big!

A small difference...

The geometrical shapes in fig. a) and b) seem to be identical... It's obvious that they are made with the same 4 Tangram pieces, but thanks to the table above, we can calculate the perimeter of each geometric figure and find that the perimeter of second diagram is approx. 1.03 times larger than the first one. The math expression is:

Pb / Pa = 2(4a+b)/2(a+3b)

By substituting the value "b" with "a2", we obtain: 1.0327...