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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 ...
A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate the area of a shape, the sheet is overlaid on the shape and the dots within the shape are counted.
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 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.
The conventional method of finding a watershed boundary is to draw it by hand on a paper topographic map, or on a transparent overlay.The watershed area can then be estimated using a planimeter, by overlaying graph paper and counting grid cells, or the result can be digitized for use with mapping software.
One could instead find the largest centrally symmetric convex subset , and then apply Minkowski's theorem to , or equivalently apply Blichfeldt's theorem to . However, in many cases a given non-convex set X {\displaystyle X} has a subset Y ⊂ X {\displaystyle Y\subset X} that is larger than 1 2 K {\displaystyle {\tfrac {1}{2}}K} , whose ...
A planimeter, which mechanically computes polar integrals. This result can be found as follows. First, the interval [a, b] is divided into n subintervals, where n is some positive integer. Thus Δφ, the angle measure of each subinterval, is equal to b − a (the total angle measure of the interval), divided by n, the number of subintervals.
Action describes energy summed up over the time a process lasts (time integral over energy). Its dimension is the same as that of an angular momentum.. A phototube provides a voltage measurement which permits the calculation of the quantized action (Planck constant) of light.