Points A and B are on a plane surface, 1 mile apart. Suppose you must walk in a path consisting of N straight lines from point A to point B, such that at all times your (Euclidean) distance to point B is decreasing. What is the longest possible route length (as a function of N)?
(In reply to re: But....
Another interesting thing about the process is how easily it can be reversed.
Begin at B and walk in some direction a distance 1/N mile
[This is the solution for N=1]
turn arccos(sqrt(0/1))=90 walk another 1/N mile,
[This is the solution for N=2]
turn arccos(sqrt(1/2))=45 walk another 1/N mile,
[This is the solution for N=3]
and so on.
The limit as N goes to infinity is the spiral.
Posted by Jer
on 2019-01-16 13:43:17