Quadrature of the Triangle
- Judah L Schwartz
The quadrature of a triangle is the construction of a square having the same area as the triangle using only a ruler and compass - sometimes referred to as "squaring the triangle". This applet allows the construction of a rectangle with the same area as the triangle. The applet "Quadrature of the Rectangle" has already shown how to constructed a square with same area as that of the rectangle. This applet, taken together with "Quadrature of the Rectangle" allows for the construction of a square with the same area as that of the triangle.
Can you now devise an argument that shows that the quadrature of any polygon is possible? Does this imply the one can "square the circle"? Why or why not?