
Steinhaus Longimeter - ColinWright
http://cstaecker.fairfield.edu/~cstaecker/machines/longimeter.html
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computator
He groans with disappointment in the video that the longimeter and the map
measurer don't give the same result, but we don't find out which was right.
When he measures the curve he drew, the longimeter gives 28.9 mm but the map
measurer (a.k.a. opisometer, a hand-held instrument for measuring curves on
paper) says 34.5 mm; that's a 16% difference, so pretty big.

To do a real test, you could print out a curve with a mathematically
calculated length, say a sine curve, then measure with both methods (and other
methods like placing a string on top) to find out what works best in practice.

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no_identd
Hm. That 16% difference reminds me of the 60% point Miles Mathis makes in his
infamous 'pi'='4' [single quotes INTENTIONAL.] paper (which ISN'T what people
think. Numerous people tried to debunk it and I would absolutely LOVE to see a
proper debunking of it, but each 'debunker' actually only skimmed his writing,
or only read one of his papers on it instead of all of them, and constructed
bad counter arguments as a consequence.)

[http://milesmathis.com/pi.html](http://milesmathis.com/pi.html)
[http://milesmathis.com/pi2.html](http://milesmathis.com/pi2.html)
[http://milesmathis.com/pi3.html](http://milesmathis.com/pi3.html)
[https://sagacityssentinel.wordpress.com/](https://sagacityssentinel.wordpress.com/)
(the debunk reply there is from 2011 and doesn't factor in the fact that
Mathis indeed didn't realized the rather obvious link to the Hilbert/Taxicab
metric until 2012, see the pi2.html page there.)

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mannykannot
The short version has a simple but fundamental error in the use of limits, and
so as long as the author claims that this contains the essence of his
argument, there seems little point in wading through the full work, especially
as it is written in an extremely discursive manner, to put it charitably.

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jaclaz
The interesting part is the explanation on how it works and on the accuracy
you can expect:

[https://books.google.it/books?id=sFzCAgAAQBAJ&pg=PA121#v=one...](https://books.google.it/books?id=sFzCAgAAQBAJ&pg=PA121#v=onepage&q&f=false)

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2dollars27cents
This is a great youtube channel as well! I liked this review on a planar
planimeter and how it ties in to Green's Theorem.

[https://www.youtube.com/watch?v=jMvEOmpy8Kw](https://www.youtube.com/watch?v=jMvEOmpy8Kw)

~~~
xinyhn
Wow it really is great. Plan to share with everyone I know who would find this
interesting. Already watched a few of them and they are all just as enjoyable.
Hope he gets a bunch more subs and keeps making videos.

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rhaps0dy
Presumably this is the length of some discretisation of the curve, perhaps one
of millimeter-long line segments. (The exact length is uncomputable!) Really
cool though!

~~~
adrianN
It also has the corner cases of curves that exactly align with the overlay and
hence never cross any lines.

~~~
dmurray
For increased accuracy, one can displace the overlay slightly and measure
again, and take the average of multiple measurements.

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defen
See
[https://en.wikipedia.org/wiki/Crofton_formula](https://en.wikipedia.org/wiki/Crofton_formula)

Also see page 41 of _Differential Geometry of Curves and Surfaces_ by Manfredo
Do Carmo

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kozak
Also interesting is
[https://en.wikipedia.org/wiki/Opisometer](https://en.wikipedia.org/wiki/Opisometer)

~~~
Someone
That one is easy to understand. hettps://en.wikipedia.org/wiki/Planimeter is
more interesting: trace the perimeter to measure an _area_.

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iooi
How is this better than using a string? (Actual piece of string, not text).

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kumarvvr
This is brilliant.

