Differential geometry In the modern terminology of differential geometry, polar coordinates provide coordinate charts for the differentiable manifold , the plane minus the origin. In these coordinates, the Euclidean metric tensor is given byThis can be seen via the change of variables formula for the metric tensor, or by computing the differential forms dx, dy'' via the exterior derivative of the 0-forms , and substituting them in the Euclidean metric tensor .
difFerentIal GeomEtrY in thE MOdErn tERminology. oF diFFeRenTial geOmetry, POlaR cooRdinates prOvide coordInate chaRtS for ,tHE difFeReNtiAblE maNIfoLd , tHE plaNe miNUs the oriGIn in tHese cooRDinAtEs, the EUClidEaN metrIc teNsOR iS GIven bythiS can be sEeN vIa The chanGE oF vARiAbles fOrmUla for tHE MeTriC tensor or By comPu.TinG the DIFfeRentIAL forMs Dx, Dy'' via THe eXterIoR derivatIVE of tHe 0-foRMS , and suBsTitutIng them iN the euclIDean metRic tensor 