: A visual representation of the resulting manifold and the geodesics (shortest paths) between two user-defined points. Educational Visualization: Geodesic on a Sphere
d2xkdt2+Γijkdxidtdxjdt=0d squared x to the k-th power over d t squared end-fraction plus cap gamma sub i j end-sub to the k-th power d x to the i-th power over d t end-fraction d x to the j-th power over d t end-fraction equals 0 Riemannian Geometry.pdf
To illustrate this, consider a simple case: a 2D sphere where we want to find the shortest path between two points. In Riemannian geometry, these are "Great Circles." Why this is helpful: : A visual representation of the resulting manifold
, which represent how the coordinate system twists and turns across the manifold. Riemannian Geometry.pdf