Exercise 18. Show the following concerning the exponential map .
18 (d). The image
of the vertical line segment , where is
half a circle.
Solution 18 (d).
See text and/or instructor's solution manual.
Substitute into the equations and and obtain
Notice that and and .
This set is the parametric representation of half a circle of radius subtended by the angles
We are done.
Aside. We can let Mathematica double check our work.
image the horizontal strip ,
is the half circle .
This solution is complements of the authors.
(c) 2008 John H. Mathews, Russell W. Howell