Steinhaus Longimeter

#1

Post by ColinWright » Thu, Mar 22, 2018, 12:01 PM UTC

Steinhaus Longimeter
cstaecker.fairfield.edu

Re: Steinhaus Longimeter

#2

Post by rhaps0dy » Thu, Mar 22, 2018, 1:11 PM UTC

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!

Re: Steinhaus Longimeter

#3

Post by tantalor » Thu, Mar 22, 2018, 1:22 PM UTC

rhaps0dy wrote: post #2

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!

> uncomputable

[citation needed]

Re: Steinhaus Longimeter

#4

Post by XaspR8d » Thu, Mar 22, 2018, 1:24 PM UTC

rhaps0dy wrote: post #2

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!

Yeah, one could draw a tight spiral in any of the open spaces of unbounded length. But "discretization" is probably a good angle to interpret it, since such a counterexample would be discretized to a point.

Re: Steinhaus Longimeter

#5

Post by jaclaz » Thu, Mar 22, 2018, 1:42 PM UTC

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...

Re: Steinhaus Longimeter

#6

Post by tgb » Thu, Mar 22, 2018, 1:59 PM UTC

tantalor wrote: post #3

rhaps0dy wrote: post #2

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!

> uncomputable [citation needed]

There exist plenty of mathematical curves whose lengths are undefined. The term to search is "non-rectifiable curve".

Re: Steinhaus Longimeter

#7

Post by tantalor » Thu, Mar 22, 2018, 2:16 PM UTC

tgb wrote: post #6

tantalor wrote: post #3

Earlier quoted context omitted.

> uncomputable [citation needed]

There exist plenty of mathematical curves whose lengths are undefined. The term to search is "non-rectifiable curve".

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

Re: Steinhaus Longimeter

#8

Post by adrianN » Thu, Mar 22, 2018, 2:32 PM UTC

rhaps0dy wrote: post #2

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!

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

Re: Steinhaus Longimeter

#9

Post by tgb » Thu, Mar 22, 2018, 2:34 PM UTC

tantalor wrote: post #7

tgb wrote: post #6

Earlier quoted context omitted.

There exist plenty of mathematical curves whose lengths are undefined. The term to search is "non-rectifiable curve".

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...

Re: Steinhaus Longimeter

#10

Post by MS-DDOS » Thu, Mar 22, 2018, 3:04 PM UTC

I can imagine the practical appeal of a device like this when applied to something like a map. Especially over large journeys, this could likely cut down on your error considerably.