planimeter

pla·nim·e·ter

P0350500 (plə-nĭm′ĭ-tər, plā-)n. An instrument that measures the area of a plane figure as a mechanically coupled pointer traverses the perimeter of the figure.

pla′ni·met′ric (plā′nə-mĕt′rĭk), pla′ni·met′ri·cal (-rĭ-kəl) adj.pla·nim′e·try n.

planimeter

(plæˈnɪmɪtə) n (Mathematics) a mechanical integrating instrument for measuring the area of an irregular plane figure, such as the area under a curve, by moving a point attached to an arm around the perimeter of the figure

pla•nim•e•ter

(pləˈnɪm ɪ tər)

n. an instrument for measuring the area of plane figures. [1855–60] pla•ni•met•ric (ˌpleɪ nəˈmɛt rɪc) adj.

Thesaurus

Noun

planimeter - a measuring instrument for measuring the area of an irregular plane figureintegratormeasuring device, measuring instrument, measuring system - instrument that shows the extent or amount or quantity or degree of something

Translations

planimetro

Planimeter

planimeter

[plə′nim·əd·ər] (engineering) A device used for measuring the area of any plane surface by tracing the boundary of the area.

Planimeter

a mathematical instrument for measuring the areas of plane figures of arbitrary shape. The most widespread type is the polar planimeter, which was invented by the Swiss mathematician J. Amsler in 1854.

Figure 1

The principle of operation of such a planimeter is shown in Figure 1. When the oriented line segment AB moves in the plane, the area of the figure swept out by it is equal to the product of the length of AB and the length of the arc described by the segment’s midpoint. The quantity σ is equal to the length of the arc of rotation of the integrating wheel if the wheel is placed at the midpoint of AB and its axis coincides with the segment. The polar planimeter (Figure 2) has a polar arm and a tracing arm, which are pivoted at the point B. The polar arm can be rotated about the pole pivot O. The integrating wheel and the counting mechanism are located on a special carriage that can slide along the tracing arm, thereby changing the length of the arm.

Figure 2. Polar planimeter: (O) pole, (OB) polar arm, (A) tracing pointer, (AB) tracing arm, (C) carriage, (W) integrating wheel, (M) counting mechanism

In every planimeter the function of the sweeping line segment is performed by the tracing arm, at one end of which is fastened a pointer for tracing out the figure’s outline and the other end of which moves along a “directrix.” The directrix is a straight line in a linear planimeter, a circle in a polar planimeter, and a point in a radial planimeter. Linear and polar planimeters are used to compute areas bounded by curves given graphically and to calculate integrals of the form

Radial planimeters permit integrals of the form

to be found if the curve r = f (ϕ) is drawn in polar coordinates.

planimeter

A mechanical integrator for measuring the area of a plane surface usually within a given perimeter on a map.

planimeter

pla·nim·e·ter

(plă-nim'ĕ-tĕr), An instrument formed of jointed levers with a recording index, used for measuring the area of any surface, by tracing its boundaries. [L. planum, plane, + G. metron, measure]

planimeter

(plā-nĭm′ĕ-tĕr) [″ + Gr. metron, measure] An apparatus used to measure the area of a plane figure by passing a tracer around the boundaries.

pla·nim·e·ter

(plă-nim'ĕ-tĕr) An instrument formed of jointed levers with a recording index used for measuring the area of any surface, by tracing its boundaries. [L. planum, plane, + G. metron, measure]

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Synonyms for planimeter

noun a measuring instrument for measuring the area of an irregular plane figure

Synonyms

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