The probability that two values a and b chosen at random between 0 and 1 will yield an [b]obtuse triangle[/b] with side lengths 1, a, and b is [math]\frac{\pi}{4}-\frac{1}{2}[/math]. Geometrically, being an obtuse triangle corresponds to the point (a,b) being inside the unit circle [math]x^2+y^2=1[/math] but above the line [math]x+y=1[/math]. [br][br]Another way of stating at this: randomly generate N triangles with side lengths 1, a, and b (with a and b between 0 and 1). If T of them are obtuse, then [math]\frac{4T}{N}+2[/math] is approximately π.[br](Source: [i]Ingenuity in Mathematics [/i]by Ross Honsberger.)