Chapter PL, Problem 8P

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4th Edition

James Stewart + 2 others

ISBN: 9781305071742

Textbook Problem

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**Ending Up Where You Started **A woman starts at a point *P* on the earth’s surface and walks 1 mi south, then 1 mi east, then 1 mi north, and finds herself back at *P*, the starting point. Describe all points *P* for which this is possible. [*Hint: *There are infinitely many such points, all but one of which lie in Antarctica.]

To determine

**To describe:**

All the possible points *P* for which the problem hold.

Explanation

The given problem can be viewed in two possible ways.

*Case 1:*

From the given data the path tracked by the women can be viewed as a triangle.

That is, the women starts from the north pole and heads towards south pole(Antarctica is in situated in south pole), then walks towards west and walks back north.

This can be diagrammatically represented as

Therefore, the possible points are one such point in north pole and infinitely many points near the south pole.

*Case 2:*

From the given data the path tracked by the women can be viewed as a Circle.

That is, the women starts from the north pole and heads towards south pole(Antarctica is in situated in south pole), then walks towards west and walks back north...