In his book [b][i]Mathematical Discovery[/i][/b] George Polya defines a parameter[br]space for triangles.[br][br]Imagine a triangle whose longest side has length 1, the length of the [br]shortest side is x and the length of the third side is y.[br][br]The region in the left hand panel bounded by the lines x<=y, y<=1 and x+y>1[br]encloses all the points corresponding to the sides of such triangles.[br][br]Clearly, a point at 1,1 represents an equilateral triangle.[br]Suitably chosen points will represent isosceles triangles and right triangles.[br][br]Can any shape triangle be formed by placing the large GOLD point [br]somewhere in the region or on its boundary?[br][br][color=#ff0000][b][i]What problem(s) could/would you set for your students based on this applet?[/i][/b][/color]