A geometric–computational framework for teaching and visualising parallel transport in curved spaces

Parallel transport is a fundamental concept in differential geometry and underpins the mathematical structure of spacetime in general relativity. However, its abstract formalism presents substantial cognitive challenges for students encountering relativity for the first time. This work introduces a geometric–computational framework for teaching parallel transport, complemented by a practical approach that enables systematic analysis and interactive visualisation in an educational setting. The proposed method generalises the intuitive notion of transport along geodesics to arbitrary curves by discretizing them into successive geodesic segments. Numerical simulations on spherical manifolds demonstrate that the approximation converges rapidly to the exact solution, with angular deviations becoming negligible even for moderate discretizations. By translating abstract geometric structures into interactive visualisations and computational exercises, the framework strengthens students’ intuition, integrates digital tools into the learning of geometry and physics, and broadens access to advanced concepts – fostering a deeper engagement with the geometric essence of General Relativity. The article concludes with a detailed discussion of potential implications for physics and mathematics teaching, curriculum design, and future research, highlighting the method’s broader relevance for both physics education and the practice of numerical modelling in curved spaces.