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A very similar situation, with a similar answer, is this:
Two runners run a square marathon, along the same street. One
runner hugs the inside gutter of the street, arguing that he'll save
lots of distance. The other runner says the distance saved
is negligible, compared with his course that follows the outside
gutter. Who is right ?
Well, I like to think of it this way. As they run side-by-side (across
the street from each other), clearly during the entire straight edge of
the square they run exactly the same distance. The only savings is at
the *corners* of the square, where the inside runner merely turns 90 degrees,
while the outside runner must run a distance of two road widths (forming an L
shape at the corner). Assuming four such corners, the outside runner runs 8 road
*widths* longer than the inside runner, regardless of how long a "marathon" is.
Is that clear enough without a picture ?
/Eric
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