Chapter 14.1, Problem 17WE

To determine

To find: The congruency of image of the arctic circle to the image of the equator.

Answer to Problem 17WE

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.

Therefore, the image of equator and Arctic Circle will be congruent.