in theory the length of the surface doesn't become 5 just because the ridges are too small to measure physically
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Bobbob (Site Administrator)
Yeah..no. With the straight line (using diagonal) you're effectively traveling the shortest distance (in 2-space). Even with smaller staircase steps you'd be adding unecessary lateral movement (effectively adding a 3rd dimension) whose cumulative impact increases the total distance. Not a paradox. Just perfunctory thinking by the guy making the video.
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(Site Administrator)
in theory the length of the surface doesn't become 5 just because the ridges are too small to measure physically
(Site Administrator)
Yeah..no. With the straight line (using diagonal) you're effectively traveling the shortest distance (in 2-space). Even with smaller staircase steps you'd be adding unecessary lateral movement (effectively adding a 3rd dimension) whose cumulative impact increases the total distance. Not a paradox. Just perfunctory thinking by the guy making the video.