Polya's Triangle Space
- Judah L Schwartz
In his book Mathematical Discovery George Polya defines a parameter space for triangles. Imagine a triangle whose longest side has length 1, the length of the shortest side is x and the length of the third side is y. The region in the left hand panel bounded by the lines x<=y, y<=1 and x+y>1 encloses all the points corresponding to the sides of such triangles. Clearly, a point at 1,1 represents an equilateral triangle. Suitably chosen points will represent isosceles triangles and right triangles. Can any shape triangle be formed by placing the large GOLD point somewhere in the region or on its boundary? What problem(s) could/would you set for your students based on this applet?