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to define two important curvatures in English the Gaussian curvature and the mean curvature so for any surface if you consider at any point try to look at its normal and the way that this normal varies are turn around the point P will actually let us know how the surfaces say for example if you have a point and if you look at its normal if it is varying in a faster way I turn around the point it means that the surface is highly curved and suppose if the same normal is being present everywhere around the point P if it is the same that enables us to know that the surface is a plane so keeping this normal in fact specifically keeping this unit normal into the picture we will try to relate the points of the surface to its normal and this the mapping that means that relation that we are going to define for the points of the surface to the normals so in fact weamp;#39;ll do it by using a map and that map is nothing but our Gauss map so letamp;#39;s try to see what is the definition
