On Monday the prof brought a planimeter to class. (A planimeter is a device which, when moved along a closed curve, displays its signed area.) It has a switch for square inches or square centimeters. I pulled out a sheet of graph paper on which he marked a 25 mm square. He set it to square inches and traced out the square. It displayed a number with seven or more digits after the point. I flipped it to square centimeters and traced a 30 mm square. It displayed a simple 8.9.
I don't know the details of the design, but this planimeter has two wheels connected by an axle, a hinge, and a third wheel. The formula for area consists of multiplying the rotation of the two wheels by the sine of the hinge and integrating the result. Since a sine is involved, there's no way it could be computing simple rational numbers. It looks like it accumulates the area as an overly precise number, rounds it to the nearest 0.1 cm², and then converts it to square inches. Pierre
