IN PURSUIT OF COAT-HANGERS 161 This is analogous to dividing a shape into rectangles, as we did for the linear planimeter. Interestingly, our argument shows that the radius OA of the circle on which A is constrained to move does not enter into the equations which give us the area of the shape. Hence, we could (on very shaky ground indeed) connect the theory of the polar and linear planimeters by suggesting that a linear planimeter is nothing more than a polar planimeter in which the arm OA is infinitely long. Of course, this requires a huge leap of faith but does provide a conceptual link between the two, seemingly different, devices. 8.6 The Hatchet Planimeter of Prytz So at last we come to the planimeter that was examined at the beginning of the chapter. This is known as the hatchet plan- imeter and was invented in 1875 by the Danish cavalry officer and mathematician Holgar Prytz, whose biography is given in Pedersen (1987). The device itself is disarmingly simple, really