Since phys-l has been somewhat listless lately, here
is a riddle:
Dr. Livingstone starts out at a place which we call
Point A. He then undertakes a journey consisting
of three legs:
-- he travels precisely southward for one mile;
-- then he turns and travels precisely eastward
for one mile;
-- then he turns and travels precisely northward
for one mile.
He discovers that as a result of this journey, he
has returned to Point A.
Note: He travels by airship, at an appropriate constant
altitude, so you don't need to worry about obstructions
or other nonidealities.
The questions are:
1) Where is Point A?
2) Are you sure? How do you know?
Usual ground-rules: The right answer depends on
understanding the physics of the situation. This may
require some outside-the-box thinking. Everything
I've said is intended to be true and helpful. I expect
a strong consensus as to the correctness of the answer.