Triangulation Puzzles


1.

Cut a unit square into 5 triangles, all of which have area less than .21.

2.

Cut a square into 5 triangles whose areas are in geometric progression.

3.

Cut a square into 5 isoceles triangles, no two of which are similar.
(solution by Evan Whitney)

4.

Cut a square into 7 isoceles right triangles, no two of which are congruent.
(second solution by Bob Wainwright)

5.

Cut a square into 8 right triangles, all having one leg twice
as long as the other, no two of which are congruent.

6.

Cut a square into 8 acute triangles.
(solution by David Epstein)

7.

Cut a unit square into 8 triangles with sides no larger than 5/8.

8.

Pack 7 equilateral triangles with side 1/2 into a unit square.


Back to