A radius-5 circle overlaid with a grid of dots in the pattern of a dot planimeter. When counting dots near the boundary of the shape as 1/2, there are 69 interior dots and 20 boundary dots for an estimated area of 79, close to the actual area of 25π ≈ 78.54.
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. The estimate of area is the number of dots counted multiplied by the area of a single grid square. In some variations, dots that land on or near the boundary of the shape are counted as half of a unit. The dots may also be grouped into larger square groups by lines drawn onto the transparency, allowing groups that are entirely within the shape to be added to the count rather than requiring their dots to be counted one by one.[1]
The estimation of area by means of a dot grid has also been called the dot grid method or (particularly when the alignment of the grid with the shape is random) systematic sampling.[2] Perhaps because of its simplicity, it has been repeatedly reinvented.[3][4][5]
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A dotplanimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots...
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