The myocardial fiber of the heart has its unique orientation everywhere in the thin-layered atria and multi-layered three-dimensional ventricles. In the diffusion-reaction system, it means that the diffusivity tensor always has off-diagonal terms at every point. In analysing the behaviour of the cardiac action potential propagation, most difficulty arises due to the complex alignment of strong anisotropy induced by this myocardial fiber. In principle, this problem is not restricted to cardiologists, but can be applied to cosmologists because the cardiac action potential shares the same Lagrangian as the electrodynamic radiation such as light. One solution is to regard the anisotropic heart as a Riemannian geometry, but understanding the derived Riemannian geometry for complex anisotropic alignment seems to open other problems for practical implications. Cartan's method of moving frames (MMF) is introduced in this context as Euclidean glasses to understand the Riemannian geometry of the heart. In this talk, I will explain the past results for the new numerical methods to use the MMF and future works for new analytic tools based on the MMF in cardiac electrophysiology.