...As the shortest distance between two points on a plane surface is the straight line joining them, so the shortest distance between two points on the surface of a sphere is the shorter arc of the great circle passing through the points. In Fig. 4 the black line passing through...

...The foregoing can be formulated as follows: for the problem formulated verbally as a request to show "the shortest distance" between two points on the surface of a sphere, the orthodromic line and the line of vision play the role of "vectors" determining the position of...

...sail in a curve to the northwards. Actually, however, the path is that of a great circle, which is the shortest distance between two points on the surface of a sphere. We all remember Lindbergh's path to Paris, which was along a great circle, and crossed Nova Scotia,...

...neighboring points on a smooth surface, a geodesic curve is the shortest path connecting them. Thus, the shortest distance between two points on the surface of a sphere is along the arc of a great circle, while on the surface of a cylinder the shortest path is an arc of...

...of the sphere with the surface of the sphere, as shown in Figure 2l.3. (Trans-Atlantic Figure 21.3. The shortest distance between two points on the surface of a sphere is defined by the cut on the sphere's surface (DEAC) made by a plane that passes through the center of...

...equation dy dxdy' = 0. (2.9b) Next, we show how to use a variational principle to formulate and find the shortest distance between two points on the surface of a sphere. The arc-length ds on a sphere of radius r is given by ds2 = (rd0)2 + (rsin0d</>)2 = (rd0)2[l + (/'(0)sin0)2],...

...= mx + c back in Equation (4. 1 8) and show that J attains a minimum value. PROBLEM 4.3. Show that the shortest distance between two points on the surface of a sphere (the curve is called a geodesic) is an arc of a great circle. (The boundary curve obtained by cutting...

...York does not correspond to a straight line on the map in the central pages of the in-flight magazine. The shortest distance between two points on the surface of a sphere is a circle. What complicates our understanding of this curvature in general applications of the theory...

...Members of higher income households, howev11 These are great circle distances. Great circle distance is the shortest distance between two points on the surface of a sphere. er, took trips of shorter duration than did persons in lower income households. The average length...

...straight line. Scientists are going to be unchallenged when they tell us the earth is a sphere - and that the shortest distance between two points on the surface of a sphere is an arc, not a line. If you think this is an unimportant distinction take a look at the introduction...