We consider a surface and a fixed point and direction (vector in the tangent space at that point. We then draw geodesics through that point making every possible angle with respect to that direction. Points along these geodesics form geodesic polar coordinates. We find the first fundamental form in these coordinates and prove that they are isothermal. We conclude with a discussion of geodesic circles.
#mikethemathematician, #mikedabkowski, #profdabkowski, #differentialgeometry
