Steinhaus Longimeter • Hacker News Board

Re: Steinhaus Longimeter

#11

Post by taneq » Thu, Mar 22, 2018, 3:24 PM UTC

tgb wrote: post #9

tantalor wrote: post #7

Earlier quoted context omitted.

This tool is for measuring curves drawn on a piece of paper, not abstract curves.

Oh, that doesn't make it any easier: https://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Brita...

Well, it doesn't in theory, but it does in practice. Natural phenomena are only fractal over a certain range of scales. Outside that range they follow normal rules.

Re: Steinhaus Longimeter

#12

Post by iooi » Thu, Mar 22, 2018, 3:26 PM UTC

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

Re: Steinhaus Longimeter

#13

Post by kumarvvr » Thu, Mar 22, 2018, 3:41 PM UTC

This is brilliant.

Re: Steinhaus Longimeter

#14

Post by 2dollars27cents » Thu, Mar 22, 2018, 5:14 PM UTC

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

Re: Steinhaus Longimeter

#15

Post by tantalor » Thu, Mar 22, 2018, 5:40 PM UTC

tgb wrote: post #9

tantalor wrote: post #7

Earlier quoted context omitted.

This tool is for measuring curves drawn on a piece of paper, not abstract curves.

Oh, that doesn't make it any easier: https://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Brita...

That doesn't fit on a piece of paper, either.

Re: Steinhaus Longimeter

#16

Post by tgb » Thu, Mar 22, 2018, 6:07 PM UTC

tantalor wrote: post #15

tgb wrote: post #9

Earlier quoted context omitted.

Oh, that doesn't make it any easier: https://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Brita...

That doesn't fit on a piece of paper, either.

A cartographer might disagree.

Re: Steinhaus Longimeter

#17

Post by kozak » Thu, Mar 22, 2018, 6:08 PM UTC

Also interesting is https://en.wikipedia.org/wiki/Opisometer

Re: Steinhaus Longimeter

#18

Post by cstaecker » Thu, Mar 22, 2018, 7:09 PM UTC

kozak wrote: post #17

Also interesting is https://en.wikipedia.org/wiki/Opisometer

I got you: http://www.youtube.com/watch?v=ifKrwF47uP8

Re: Steinhaus Longimeter

#19

Post by [deleted] » Thu, Mar 22, 2018, 7:33 PM UTC

tgb wrote: post #16

tantalor wrote: post #15

Earlier quoted context omitted.

That doesn't fit on a piece of paper, either.

A cartographer might disagree.

[deleted]

Re: Steinhaus Longimeter

#20

Post by computator » Thu, Mar 22, 2018, 8:32 PM UTC

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.