Department of Mathematics
Christopher Newport University
Math 355 Project 1 (Extra Credit)
Due February 16, 2007
Consider the unit sphere centered at the origin in the xyz-plane. We know N= (0,0,1) is on the surface of the sphere
and let Q= (x0, y0,0) be a point of xy-plane. Draw a line from Nto Q. The line intersects the unit sphere at a
point P= (u, v, w) .
a. Find the coordinates of Pin terms of x0and y0.
b. Show that there is a bijective map from the points on the xy plane to points of the unit sphere except N..
c. Find the image of the line x−y= 2 on the unit sphere under the bijection found in part (b).