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Topic: Planimeter

In the News (Tue 21 May 13)

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	How Planimeters Work
		The surprising fact is that when a polar or linear planimeter is used to trace the boundary of a region, the amount the wheel rolls is proportional to the area of the region.
		When a planimeter is used to measure a region, the user moves the right endpoint of the rod, the tracing point, around the boundary of the region to be measured.
		The constant of proportionality is the length of the planimeter rod.
	persweb.wabash.edu /facstaff/footer/Planimeter/HowPlanimetersWork.htm (1197 words)

	Planimeter
		This area is equal to the area enclosed by K because the area between the circle and K is covered twice in opposite directions.
		Hence the area of K is proportional to the rotation of W, the constant of proportionality being determined by the dimensions of the planimeter.
		In the Siemens planimeter drawing, part 4 is an accessory used for calibrating the instrument.
	www.science.uva.nl /faculteit/museum/planimeter.html (362 words)

	Planimeter - Wikipedia, the free encyclopedia
		A planimeter is a technical drawing instrument used to measure the surface area of an arbitrary two-dimensional shape by tracing the perimeter.
		The concept having been pioneered by Hermann in 1814, Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, the operation of which can be justified by appealing to Green's theorem.
		The first planimeter was invented by Hermann in 1814 and there were many subsequent developments before Amsler's famous planimeter.
	en.wikipedia.org /wiki/Planimeter (187 words)

	The Planimeter
		The planimeter is a drafting instrument used to measure the area of a graphically represented planar region.
		In this sketch we have a planimeter tracing a boundary.
		Since the planimeter begins and ends in the same position, the net change in the angle is zero.
	whistleralley.com /planimeter/planimeter.htm (1916 words)

	How to Use A Planimeter (Site not responding. Last check: )
		A planimeter is a device, which mechanically integrates an area and records that area on a drum and disk as a tracing point moves over the boundary of the figure to be measured.
		A planimeter is most useful for irregular areas on maps such as lakes, field, etc. A common planimeter can be seen in Figure 1.
		The precision of using a planimeter is dependent upon operator skill, accuracy of the map, type of paper, and other factors.
	baen.tamu.edu /users/munster/agen_468_99/planimeter/planimeter.htm (919 words)

	How does the planimeter work?
		The planimeter is a mechanical device for measuring areas in the plane.
		The measurement consists of dragging (x,y) along the boundary of the region R. The wheel at (x,y) measures the motion in the direction orthogonal to the leg.
		The Planimeter lineintegral is therefore the area of the enclosed region.
	www.mathematik.com /Planimeter/explanation.html (252 words)

	Hatchet Planimeter as used by Walter Scott
		The Polar Planimeter is usually used, but for the field man, has the disadvantage of being rather cumbersome, expensive, and subject to breakage.
		The use of the Hatchet Planimeter was demonstrated at the recent meeting of the Ohio Academy of Science in Colombus, by Professor Andrew R. Weber and a group of his students from the University of Dayton.
		Locate, by inspection, the approximate centroid of the figure to be planimetered, and draw through it a pair of lines at right angles of each other, and intersecting the perimeter to be measured.
	www.stithvalley.com /pappaw/planimet.htm (962 words)

	Planimeter Applet Guide
		Description of the planimeter mechanically and mathematically, and the use of the applet.
		Ordinarily, the planimeter is outside the sample, so the wheel reading should be the area of the sample, but if the planimeter is inside then the zero circle must be added or subtracted from the wheel reading.
		In general, the planimeter lines invert all colors; the area swept by the tracer arm inverts red; and the area covered if the tracer arm were rotated about the wheel instead of the pivot inverts blue.
	www.hpmuseum.org /planim/guide.htm (4223 words)

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		These planimeters are powered by a built-in Ni-Cad storage battery that can be recharged with a 120V AC adapter (included).
		Tamaya digital planimeters are excellent tools to use when measuring irregular-shaped areas on plans or drawings.
		(polar planimeter) is attached to a weighted base by an arm that allows movement within a circular area.
	www.gpsforestry.com /planimeters.htm (686 words)

	Das Planimeter
		Ungläubig sah ich einem Bekannten zu, der mir sein frisch erworbenes Planimeter vorführte: Er umfuhr damit ein Quadrat und konnte dann an einem kleinen Rädchen den Flächeninhalt ablesen.
		Planimeter sind Messgeräte, mit denen man den Inhalt von Flächen in Landkarten und Zeichnungen bestimmen kann, indem man mit einem Fahrstift die gewünschte Fläche im Uhrzeigersinn umfährt und dann die Anzeige des Planimeters mit einem Tabellenwert multipliziert, der die Baumaße des Planimeters berücksichtigt.
		Mir ist nun klar geworden, wie ein Planimeter dazu in der Lage ist, den Inhalt einer Fläche zu bestimmen, indem einfach nur der Umfang der Fläche abgefahren wird.
	www.bluemich.net /rechner/rmplanimeter.htm (2350 words)

	Ben Meadows Company - Tech Info - Document #1350, Planimeters (Site not responding. Last check: )
		Planimeters are used to measure areas on maps of any kind and scale, as well as plans, blueprints, or any scale drawing or plan.
		The mechanical (non-digital) planimeters we stock have some differences, but all feature a pole arm, tracer arm, tracer magnifier, recording dial, and vernier measuring wheel.
		To use a mechanical planimeter, a "constant" is first determined by choosing the shortest possible arm length which will cover the area to measure, and tracing the boundary of a known area(a 2 x 3 business card for example).
	www.benmeadows.com /refinfo/ezfacts/ezf1350.htm (932 words)

	Planimeters
		A planimeter is a mechanical instrument used to compute the area of a planar region.
		Using a planimeter to prove the isoperimetric inequality.
		Try using one of the web search engines to search for "planimeter." You will get lots of "hits," most of which will illustrate the variety of ways planimeters are used in science, technology, medicine, archeology, and many more areas.
	persweb.wabash.edu /facstaff/footer/Planimeter/PLANIMETER.HTM (186 words)

	Plancom Basic Mechanical Planimeter
		For evaluating plane areas of any shape or contour from maps, blueprints, photos, etc., this economical, rugged and easy-to-use planimeter is one of the most precise instruments of its type.
		Planimeter features include: a lens tracer, built-in vernier magnifier for measuring wheel, zero setting wheel, pole weight, fixed pole arms, fixed tracer arm, and an exclusive tilted body design that permits convenient operation without bending over the instrument during tracing or readout.
		Planimeter packed in a 12" x 6" x 2" carrying case with test rule and complete instructions.
	www.nationwidedrafting.com /store/plancombasic.html (89 words)

	Digital Planimeters
		Planimeters are measuring instruments that are best known for their ability to calculate the area of an irregularly shaped figure by simply tracing the perimeter of the object.
		Planimeters are used to measure and make calculations from maps, aerial photographs, x-rays, blueprints, drawings and many other types of documents.
		Planimeters are used in a surprising number of applications, in everything from determining the size of real estate parcels by tax appraisers to measuring the cross-section size of a tumor by doctors.
	www.calistar.com /DM/planimeter.asp (369 words)

	Planimeter Operator: A description for the planimeter operator job
		Planimeter Operator: Traces boundary lines of land plots on aerial photographs to determine acreage, using planimeter: Centers tracer point of planimeter arm on plot to be measured and places pivot arm at right angle to tracer point.
		Moves tracer point to starting point on photograph according to shape of area to be measured and traces boundary until point of beginning is reached.
		Records figures shown on dial and measuring wheels of planimeter at beginning and ending of tracing and subtracts figures from each other to determine acreage.
	www.job-descriptions.org /planimeter-operator.html (135 words)

	US Patent 783,568, February 28, 1905
		These parts are all in common use on planimeters of the Coffin type.
		A planimeter having a scale adjacent to the end of the tracer-arm, and a pointer movable along and overlapping said scale and adapted to be controlled in its movements by the said tracer-arm, said pointer being separate from but adjacent to the tracing-point of said arm.
		With a planimeter one can determine the mean effective steam pressure in the engine or, when the stroke and diameter of the cylinder and the number of revolutions per minute are known, the power of the engine.
	www.geocities.com /andriesdeman/patchas.html (1244 words)

	Citebase - Geometry of the Prytz Planimeter
		Authors: Foote, Robert L. The Prytz planimeter is a simple example of a system governed by a non-holonomic constraint.
		The motion of the planimeter is realized as parallel translation for a connection on this bundle and for a connection on a principal SU(1,1)-bundle.
		As a consequence, the planimeter is an example of a system with a phase shift on the circle that is not a simple rotation.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9808070 (337 words)

	IMPROVED WILLIS PLANIMETER by JAMES L. ROBERTSON & SONS (Site not responding. Last check: )
		Made of nickel plated brass, 9 1/2" long overall x 6 1/2" wide, with 1 1/4" diameter recording wheel mounted on sliding tracer bar and triangular recording scale with six graduated edges.
		Mathematically, the two approaches are equivalent, but the Willis planimeter's approach was never generally accepted.
		This unusual planimeter is in fine overall condition, in its original velvet lined leather case.
	www.gemmary.com /add/Add-0901.html (91 words)

	⊙ AntiQuark: Prytz (Hatchet) Planimeter
		The Prytz planimeter is undoubtedly the simplest of these.
		The Prytz planimeter is a simple example of a system governed by a non-holonomic constraint.
		It is unique among planimeters in that it measures something more subtle than area, combining the area, centroid and other moments of the region being measured, with weights depending on the length of the planimeter.
	www.antiquark.com /2004/12/prytz-hatchet-planimeter.html (397 words)

	Amsler biography
		He began to study the construction of precision mathematical instruments and quite quickly he had an idea for the design of a new type of planimeter.
		He invented the polar planimeter, a device for measuring areas enclosed by plane curves.
		None of his other inventions came close to the polar planimeter in importance, but they were of sufficient quality to win him prizes at the world exhibition at Vienna in 1873, at Paris in 1881, and again in Paris in 1889.
	www-history.mcs.st-and.ac.uk /history/Biographies/Amsler.html (686 words)

	eBay: PLANIMETER, Technik Photographica, Antiquarische Bücher, Technik Geräte (Site not responding. Last check: )
		Antique Polar Planimeter by KEUFFEL and ESSER, K&E
		Keuffel & Esser K&E Compensating Polar Planimeter 4236
		Keuffel & Esser K&E Compensating Polar Planimeter N4242
	search.ebay.de /PLANIMETER_W0QQsofocusZbsQQsbrftogZ1QQfromZR10QQsatitleZPLANIMETER*QQsoloctogZ9 (198 words)

	The Polar Planimeter
		Chapter X has all the pictures and is probably the best place to start if you are unfamiliar with the Polar Planimeter.
		A non-trivial planimeter has an adjustable arm, whose length is proportional to the planimeter reading.
		The tables use 3 planimeters, none of which seem to be the planimeter sited in the text.
	www.leinweb.com /snackbar/planimtr/wheatley/index.htm (640 words)

	Water Quality
		Catchment area can be measured on a topographic map using a planimeter.
		A planimeter is a piece of clear plastic covered with evenly-spaced dots.
		The investigator places the planimeter on the topographic map and counts the number of dots that lie within the watershed's boundaries.
	www.cotf.edu /ete/modules/waterq3/WQassess4a.html (176 words)

	Trig Instruments
		The KP90N planimeter measures the area by pulse count of 6 - digit.
		The KP90N is a roller-type planimeters and has full calculation functions.
		This planimeter can measure a larger area by 100 times than an ordinary planimeter, the conventional planimeter has a maximum cumulative area to measure only 0.1 m2.
	www.triginstruments.co.nz /catalog/product_info.php?cPath=101&products_id=278 (161 words)

	Anleitung Digital (Site not responding. Last check: )
		The planimeter is a highly sensitive instrument and must be handled carefully.
		The planimeter is not ready for use untill a scale is displayed.
		The user can calibrate the planimeter to match the working surface in use by means of the test area (8) supplied.
	www.haff.de /manual_digitalplan_330_e.htm (1415 words)

	Area by planimeter
		The most commonly used instrument is called the polar planimeter.
		the planimeter is a simple instrument to operate.
		You should remember, though, that the accuracy obtained with the planimeter depends mostly on the skill of the operator in accurately tracing the boundary lines of the figure with the tracing point of the planimeter.
	www.tpub.com /inteng/7k.htm (965 words)

	Planimeter - LEMAG - MIP, engine indicator, diesel indicator, Power calculator, Pi-Meter, Peak pressure, ...
		Planimeter - LEMAG - MIP, engine indicator, diesel indicator, Power calculator, Pi-Meter, Peak pressure, firing pressure, Spitzendruckmesser, Stabfederindikatoren, Maschinenindikatoren, Marinfloc
		Planimeters types PT1 and PT2 are perfect tools for accurately measuring indicator diagrams.
		The planimeters are delivered in solid instrument cases to ensure safe handling and maintain accuracy.
	www.lemag.de /planimeter.0.html (130 words)

	Amazon.com: Planimeter (Site not responding. Last check: )
		The Coradi planimeters: Description and instructions for the use and testing with a general elementary explanation of their operation by G Coradi (Unknown Binding - 1917)
		The polar planimeter and its use in engineering calculations: Together with tables, diagrams and factors for the immediate adjustment of the instrument...
		A treatise on the Calkins steam-engine indicator: With descriptions of Calkins' improved graduated pantograph, polar planimeter, speed measure, revolution...
	www.amazon.com /s?ie=UTF8&keywords=Planimeter&index=blended&page=1 (328 words)

	Geog380 Lab 8
		Use your dot planimeter to count the area of each cover type.
		If a dot falls on a line, let us count it as the cover type to the north of the line (there are other possible rules, but this one will do for us).
		You may have to move the dot planimeter to cover large areas, in which case mark your ending boundary with the grease pencil, then erase the mark afterward.
	www.sonoma.edu /users/f/freidel/remote/380lab8.htm (770 words)

	Planimeter Basic Mechanical Metric AND English PL30 - Planimeters Map Measuring
		Planimeter Basic Mechanical Metric AND English PL30 - Planimeters Map Measuring
		Double Readout Plan Measuring WheelDigital Planimeter Plancom Roller Free ShippingPlanimeter Basic Mechanical PL10Planimeter Basic Mechanical Metric AND English PL30Scale Master ClassicScale Master IIScale Master II with PC Interface Kit Combo CA325Two Face Inch Counter WheelTwo Face Map, Plan, or Curve Measuring WheelScalex PlanWheel Protective Case SC00100Scalex Map Wheel SC00700Scalex Scale Link USB SC02001
		Planimeter Basic Mechanical Metric AND English PL30: Same as No. PL10, but with an adjustable pole arm and adjustable graduated tracer arm.
	www.draftingsteals.com /21433.html (630 words)

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