Link to a pdf file that you don't need an institutional login for.
I did an activity in a basic maths class based on this paper years ago. Each student had an A3 map of the main island of the UK. Some set their compasses to 5cm radius and counted the number of radii around the island. Others tried 2.5cm, and 1cm and half a cm. Worked ok, good lesson.
Actually ... Not infinitely long. You wont have a precise value since each measure can be increased by taking a smaller "step" or "ruler", but it won't be infinite.
this is also why the GPS on your watch will reports different distances the more frequently it samples, ie. once per second vs once per every few seconds, think curves becoming diagonal lines
it's also why they measure official distances using a wheel on a stick
7 comments:
https://gsp.humboldt.edu/OLM/courses/GSP_510/Articles/Mandel...
Link to a pdf file that you don't need an institutional login for.
I did an activity in a basic maths class based on this paper years ago. Each student had an A3 map of the main island of the UK. Some set their compasses to 5cm radius and counted the number of radii around the island. Others tried 2.5cm, and 1cm and half a cm. Worked ok, good lesson.
Infinitely long. You can't trick me with the coast paradox
Actually ... Not infinitely long. You wont have a precise value since each measure can be increased by taking a smaller "step" or "ruler", but it won't be infinite.
Unbounded, at least. If you give me a measurement, I can give you a larger one that's more precise.
This guy* Mandelbrots
*presumably, but maybe not
Depends on your measurements. If you measure with 1 cm it is longer than if measure with 10 cm.
ah the coastline paradox
https://en.wikipedia.org/wiki/Coastline_paradox
where the sampling rate affects distance measured
this is also why the GPS on your watch will reports different distances the more frequently it samples, ie. once per second vs once per every few seconds, think curves becoming diagonal lines
it's also why they measure official distances using a wheel on a stick