Consider a flat 2-dimensional plane. This can be described by standard Cartesian coordinates (x,y). We establish a oblique set of axes labelled p and q. p coincides with x but q is at an angle θ to the x-axis. At any point A has unambiguous co-ordinates (x,y) in the Cartesian system. In the (p,q) system we can measure the axes either perpendicular or parallel to the axes. For the perpendicular system find a relationship between (x,y) and (p,q). Establish differential coefficients and metric tensor. The attempt at a solution Now I have read that any flat 2 dimensional plane has a metric tensor gμ[itex]\nu[/itex] of I2 As for the differential coefficients would they simply be: ∂f=∂f/∂x . ∂x + ∂f/∂y . ∂y for (x,y) and ∂f=∂f/∂p . ∂p + ∂f/∂q . ∂q for (p,q) Any help would be greatly appreciated!