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This youtube video video from How Round is Your Circle? claims you can estimate area with a tool created from a bent coat-hanger.

I am a little skeptical about the claim which is why I am posting this here as opposed to math.se.

Is this really a way to measure area, and if so what is it called (and maybe why it works)?

  • 1
    It is now crossposted to Math.SE. – Bill Dubuque Jun 16 '11 at 0:41
  • Planimeters are among those instruments that have to be seen to be disbelieved. They come in several varieties and can be staggeringly beautiful. A dear friend gave me a good one for my thirtieth birthday and it has pride of place among my office display pieces---yes, even ahead of my slide rule and artillery spotter's calculator. – dmckee Jun 16 '11 at 1:21
  • @picakhu -- hi picakhu. Pika, pika! :) Based on your comments below you seem to "not believe" that a planimiter is a completely normal everyday real instrument. You can easily buy one say here engineersupply.com/… or here amazon.com/Lasico-MECH-POLAR-PLANIMETER-ENG-CAL/dp/B001E0FHCQ. You can see many photos of it here ... en.wikipedia.org/wiki/Planimeter (Of course, the "cheap" planimeter in the youtube video would not be very accurate.) Yes, it is a totally normal thing. They are used every day by draftsmen. – Fattie Jun 16 '11 at 13:12
  • @Bill Tags don’t have to be specific; tags should be general enough to group subjects into categories. The tags suggested by you don’t really do this. I think even in a few years the number of questions about “measuring-devices” can be counted on one hand. – Konrad Rudolph Jun 16 '11 at 16:22
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    @konrad: Speaking as a mathematician with decades of experience in math and computation, I've encountered much skepticism about the correct function of various analog computational devices. So I wouldn't be surprised to see more than a handful of such questions here over many years time. Why throw away expert-contributed knowledge (here tags) that could later prove difficult to duplicate? – Bill Dubuque Jun 16 '11 at 16:51
15

Yes, this particular device is known as a hatchet planimeter - invented by Captain Prytz. See this Encyclopædia britannica page.

For the mathematical theory of the device see Robert L. Foote: Geometry of the Prytz Planimeter. See also Mark Levi and Serge Tabachnikov On bicycle tire tracks geometry, hatchet planimeter, Menzin’s conjecture and oscillation of unicycle tracks, and Tom Apostol and M. Mnatsakanian: The method of sweeping tangents.

7

It is, the device is called a planimeter and it works because of... a whole bunch of terrifying maths

  • @david from your first source "It does not correctly measure the area when the pointer traces the perimeter of a figure", so does it work? – picakhu Jun 16 '11 at 0:07
  • 2
    Did you catch the next paragraph? "Provided that certain rules are observed when it is used, the other factors will be minimised or eliminated and the planimeter will give an adequate estimate of the area" – david w Jun 16 '11 at 0:31
  • I did, but I am still skeptical. Sorry... – picakhu Jun 16 '11 at 1:13
  • What determines the final angle? Is it just that the hatchet end drags on the paper and kind of stays put while tracing the perimeter? I see a ton of human error, since the end calculation is based entirely on the final angular displacement from the starting position. What makes that displacement reliable? – Hendy Jun 16 '11 at 2:36
  • Of course, I gathered the question was about wether this method was logically sound - rather than if a particular user will be able to get a reliable result from it. I think, absent human error, the 'hatchet' end will follow a pursuit curve and that's the basis of the method. – david w Jun 16 '11 at 3:02

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