Tito Gonnella's Planimeter

Planimeters are area measuring tools: actually they are precision instruments used to trace around a closed loop of an object to find its area. Planimeters are used by engineers, surveyors, contractors, designers, medical professionals, and more. There are many kinds of planimeters, but principally roller and polar planimeters were introduced and used. Roller planimeters are attached to wheels that allow unlimited horizontal travel and vertical travel within the limits of the arm movement. Polar planimeters are attached to a weighed base by an arm that allows movement with a circular area. Roller units offer more versatility since they are not "pinned" down to the work area. The tracer arm should be moved in a clockwise direction and returned to the original starting point. The area could then be read directly on the dials. Moving the arm counterclockwise will give a negative reading. This can be used to subtract smaller areas contained in larger ones. Better planimeters have adjustments to allow the device to read in various units and scales. Other units simply read in a fixed scale such as square centimeters and require the results to be scaled to the units required. The Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, the concept having been pioneered by Johann Martin Hermann in 1814. This paper first delineates the mathematical principles on which the planimeter works, and then summarizes the principal types of planimeters.