For an ellipsoid, the geodesic curve is a curve

For an ellipsoid, the geodesic curve is a curve

• A. A straight line
• B. Having double curvatures
• C. Lying entirely in a plane
• D. A closed circle

Answer: (B)

Geodesics on a curved surface are the locally straightest paths on that surface, so on an ellipsoid the path must bend to follow the surface’s shape. The ellipsoid curves in two independent directions, which means the spatial embedding of a geodesic isn’t confined to a single plane and its bending isn’t captured by a single constant curvature. In space, such a curve typically shows two aspects of bending—curvature and how the curve twists through space (torsion)—often described as having double curvature. That’s why it isn’t a straight line, isn’t generally planar, and isn’t typically a closed circle (only in the special case of a sphere do geodesics become planar great circles).

Geodesics on a curved surface are the locally straightest paths on that surface, so on an ellipsoid the path must bend to follow the surface’s shape. The ellipsoid curves in two independent directions, which means the spatial embedding of a geodesic isn’t confined to a single plane and its bending isn’t captured by a single constant curvature. In space, such a curve typically shows two aspects of bending—curvature and how the curve twists through space (torsion)—often described as having double curvature. That’s why it isn’t a straight line, isn’t generally planar, and isn’t typically a closed circle (only in the special case of a sphere do geodesics become planar great circles).