Riemannian geometry is famous for its complexity, often requiring students to manually compute Christoffel symbols and solve differential equations to find the shortest paths (geodesics) on a curved surface. This feature would automate those grueling steps. Useful Feature: Metric Tensor & Geodesic Visualizer This feature would allow you to input a metric tensor gijg sub i j end-sub and automatically generate the following:
: You can use it to check manual calculations for textbooks like M. Spivak's Calculus on Manifolds . Riemannian Geometry.pdf
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 is famous for its complexity, often
, which represent how the coordinate system twists and turns across the manifold. Spivak's Calculus on Manifolds
: A visual representation of the resulting manifold and the geodesics (shortest paths) between two user-defined points. Educational Visualization: Geodesic on a Sphere
: Calculation of the symbols of the second kind, Γijkcap gamma sub i j end-sub to the k-th power