enricfemi said:it comes from the calculus of variation that the shortest path between two points on a surface must be geodesic.
then must the geodesic connected two points be the shortest path?
if not, what about the example?
Thanks for any reply!
enricfemi said:it comes from the calculus of variation that the shortest path between two points on a surface must be geodesic.
then must the geodesic connected two points be the shortest path?
if not, what about the example?
Thanks for any reply!
wofsy said:No. On a cylinder there are infinitely many geodesics between most points. The same is true of a flat torus.
A geodesic is the shortest path between two points on a curved surface, such as a sphere or a curved plane. It is the equivalent of a straight line on a flat surface.
A geodesic is calculated using the principles of differential geometry. It involves finding the shortest distance between two points, taking into account the curvature of the surface and minimizing the distance traveled.
Geodesics are important in various fields such as physics, engineering, and navigation. They provide the most efficient and accurate path between two points on a curved surface and are used in the design of structures, transportation routes, and satellite orbits.
No, geodesics only exist on curved surfaces. On a flat surface, the shortest path between two points is always a straight line.
Geodesics are used in the navigation of ships, planes, and satellites. They are also used in the design of bridges, roads, and other structures. In addition, geodesics are utilized in computer graphics for creating 3D models and animations.