the form being integrated is quadratic in r, meaning that the rate at which area changes with respect to change in angle varies quadratically with the radius. For a parametric equation in polar coordinates, where both r and θ vary as a function of time, this becomes For a polar planimeter the total rotation of the wheel is proportional to as the rotation is proportional to the distance traveled, which at any point in time is proportional to radius and to change in angle, as in the circumference of a circle (). This last integrand can be recognized as the derivative of the earlier integrand (with respect to r), and shows that a polar planimeter computes the area integral in terms of the derivative, which is reflected in Green's theorem, which equates a line integral of a function on a (1-dimensional) contour to the (2-dimensional) integral of the derivative. See also Curvimeter Dot planimeter Mathematical instrument Integraph Shoelace formula References Sources External links Hatchet Planimeter P. Kunkel: Whistleralley site, The Planimeter Larry's Planimeter Platter Wuerzburg Planimeter Page Robert Foote's planimeter page Computer model of a planimeter Tanya Leise's planimeter explanations and As the Planimeter’s Wheel Turns Make a simple planimeter Photo: Geographers using planimeters (1940–1941) O. Knill and D. Winter: Green's Theorem and the Planimeter Dimensional instruments Technical drawing tools Mathematical tools Measuring instruments Area