A man is standing in a flat field 1 rod ( more than 5 yards) directly east of a post, and facing north.?

Question

He walks straight north until he is directly northeast of the post; then -always in a straight line- he walks northwest until he is directly north of the post; then west until he is west of it; then southwest until he is west of it; and so on, in a kind of segmented spiral. when he is again due east of the post, how many rods is he from it? show a diagram with all work including the answer and give the formula, with d = distance from post in rods and n = number of segments walked.

Answer 1

Interesting:
He moves in such a way that every turn is exactly 45 degrees and walks such that the angle from the center is increased counter clockwise by 45 degrees each time

The distance from the post is
d=sqrt(2)^n
where n is the number of segments walked.
Note that when n=0, d=1
He walks a total of eight segments and
d=16 when he is again dues East of the post
the angle θ from horizontal that the next segment will be walked is
θ=90+45*n

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