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The images show the principles of a linear and a polar planimeter. The pointer M at one end of the planimeter follows the contour C of the surface S to be measured. For the linear planimeter the movement of the "elbow" E is restricted to the y-axis. For the polar planimeter the "elbow" is connected to an arm with its other endpoint O at a fixed ...
To measure planimetrics a planimeter or dot planimeter is used. This rather advanced analog technology is being taken over by simple image measurement software tools like, ImageJ, Adobe Acrobat, Google Earth Pro, Gimp, Photoshop and KLONK Image Measurement which can help do this kind of work from digitalized images.
The dot planimeter differs from other types of planimeter, which measure the area of a shape by passing a device around its boundary. [ 5 ] The Steinhaus longimeter is a similar transparency-based device for estimating the length of curves by counting crossings.
Dot planimeter, a similar transparency-based device for estimating area, ... From MathWorld — A Wolfram Web Resource. Information about patent (DRGM 1241513)
The company's showroom and office building at 127 Fulton Street in the Financial District of Manhattan K&E manufacturing complex in Hoboken, New Jersey. The Keuffel and Esser Co., also known as K&E, was an American drafting instrument and supplies company founded in 1867 by German immigrants Wilhelm J. D. Keuffel and Hermann Esser.
The dot planimeter is physical device for estimating the area of shapes based on the same principle. It consists of a square grid of dots, printed on a transparent sheet; the area of a shape can be estimated as the product of the number of dots in the shape with the area of a grid square.
In application areas, the dot planimeter is a transparency-based device for estimating the area of a shape by counting the grid points that it contains. [26] The Farey sequence is an ordered sequence of rational numbers with bounded denominators whose analysis involves Pick's theorem. [27]
Source: Dolph 1977: "the dot planimeter yielded the best estimate of the population mean leaf area for the majority of species" Reviewed: 2008 Beijing Wushu Tournament; Created by David Eppstein . Self-nominated at 21:44, 22 April 2021 (UTC). The article is new enough and long enough. It is neutral and cites many reliable sources.