Also interesting is https://en.wikipedia.org/wiki/Opisometer
It's like a small version of a Rolatape (used for measuring race courses etc)
Steinhaus Longimeter
21–27 of 27 posts
Re: Steinhaus Longimeter
#22See https://en.wikipedia.org/wiki/Crofton_formula
Also see page 41 of Differential Geometry of Curves and Surfaces by Manfredo Do Carmo
Re: Steinhaus Longimeter
#23Presumably 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!
It also has the corner cases of curves that exactly align with the overlay and hence never cross any lines.
For increased accuracy, one can displace the overlay slightly and measure again, and take the average of multiple measurements.
Re: Steinhaus Longimeter
#24He 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 m…
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/pi2.html http://milesmathis.com/pi3.html 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.)
Re: Steinhaus Longimeter
#25This 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
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.
Re: Steinhaus Longimeter
#26Also interesting is https://en.wikipedia.org/wiki/Opisometer
That one is easy to understand. hettps://en.wikipedia.org/wiki/Planimeter is more interesting: trace the perimeter to measure an area.
Re: Steinhaus Longimeter
#27He 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 m…
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 co…
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.