Chapter 14.1, Problem 18WE

To determine

To find: The distances near the equator distorted more than or less than distances near the Arctic circle.

Answer to Problem 18WE

The image of equator and Arctic Circle will be congruent.

Explanation of Solution

Given information:

It is given that a piece of paper is wrapped around a globe of earth to form a cylinder as shown. $O$ is the center of the earth and a point $P$ of the globe is projected along $\overline{OP}$ to a point $P\text{'}$ of the cylinder.

  

Calculation:

If the equator is the line of latitude that is the longest and lie along the circumference of the globe and divides the globe into the northern and southern hemisphere, the images of all points on the equator will lies on the paper as circle.

Similarly, Arctic Circle is one of the five major circles of latitude the images of all points of the Arctic Circle will lies on the paper in a form of circle. And because of the shape of the paper, a cylindrical shape, the circles will be congruent.

As the actual line of Arctic Circle on globe is smaller than the equator line but on the paper, their images are congruent with each other. Therefore, as the point moves from equator to Arctic Circle the distance distorted.

Thus, the distance near the equator is less distorted than distances near the Arctic Circle.

Therefore, the distance near the equator is less distorted than distances near the Arctic Circle.