problem) show that the shortest distance between two points in three dimensional space is a straight line?
problem) Finding the shortest path between any two points on the surface of a sphere but use the method of the Euler equations with an auxiliary condition imposed?
problem) Find the shortest path between the (x,y,z) points (0,-1,0) and (0,1,0) on the conical surface z=1-(x^{2}+y^{2})^{1/2} what is the length of the path?
problem)
(a) Find the curve on the surface z=x^{3/2} joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc length?
(b) Use a computer to produce a plot showing the surface and the shortest curve on a single plot?