Summary: HOME-MADE HOMEWORK
FOR WEEK 14
MATH 2573H, FALL 2011
UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
Problem from the textbook
Problem 8 on page 385 of the text is assigned.
Home-made problem 1
Verify the Gauss-Bonnet formula for the sphere by using it to calculate the area
of the part of the unit sphere with 0 0 and then calculating that same
area the usual way.
Home-made problem 2
Find the area of the part of the earth's surface inside the geodesic triangle with
vertices Los Angeles, Paris and the North Pole. Look at page 17 of the text to be
reminded of the latitudes and longitudes for Los Angeles and Paris. And as on that
page of the textbook, take 4000 miles as the radius of the earth.
Remark The law of sines from spherical trigonometry can be helpful here. But
you can do all the calculations using vector calculus that you learned this semester
along with the Gauss-Bonnet formula.
Home-made problem 3