Fastest time between two points by walking under some constraints

Asked Mar 25 '21 at 17:35

Active Mar 26 '21 at 06:12

Viewed 63 times

So the problem, is that I want to walk A to B under the fastest time. If I had no constraints, then the answer is simple, simply a straight line from A to B but here I have some constraint which makes it complicated.

Here are my rules and set up: I can make along the purple path from A to B, but I can also move in the region enclosed by ABC in the following ways:

I can move a 'step' to the right (however steps crossing BC is not allowed)
Similarly I can step directly in the direction of B
I can take a step 'up' so I get closed to AB (though I can never cross it)

You may take step size as large or small as you want.

I want to rigorously prove that for any sequence of the three steps I have described above which terminates with ending at B from starting at A, the amount of distance I travel will be less than if I walked by going along AD then to DB

edited Mar 26 '21 at 06:12

asked Mar 25 '21 at 17:35

tryst with freedom

11,538

Oh , I had changed pic in middle which made it wrong. I fixed it now @LinAlg – tryst with freedom Mar 25 '21 at 19:21
hmm how do I prove the steps commute? @LinAlg – tryst with freedom Mar 26 '21 at 06:13
1

I think the problem is that the type of 'step-2' depends on where exactly you are on the grid, because the vector pointly directly to B is position dependent – tryst with freedom Mar 26 '21 at 14:35

Fastest time between two points by walking under some constraints

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