4 ms·
Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of t
by tedunangst 3y ago
Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.
- ClassyJacket 3y agoNope. Edges do not work that way. Mathematically a fractal outline can have infinite length but finite area.
- rdlw 3y agoDo this with Gabriel's horn and you'll observe that it has an area of pi, which does not reflect the fact that its perimeter is infinite.
- tedunangst 3y agoYeah, I'm not sure how I concluded you could go from volume to area.
- ClassyJacket 3y agoIt does seem intuitive that you'd be able to, I can certainly understand how you'd think that. But no!
- paulddraper 3y ago> the area of the edge No, it will give you the area of the island (more precisely, the area of the sea-level cross section of the island).
- cozzyd 3y agoConsider a short portion of shoreline in Fourier space. By keeping the "DC" term constant (i.e. the integral), you have complete freedom to change all other terms. By increasing high frequency terms the length of shoreline can tend to infinity without changing the area of the island.