Cartographic projection is the mapping of an ellipsoid or sphere onto a plane. Given the Euler’s result from the 18th century which demonstrated that a projection that is simultaneously conformal (preserves the angles) and equal-area (preserves area measures) does not exist, we conclude that we cannot faithfully represent the Earth on a plain.
Let us look at the 3D Earth model designed by David Bachman and its stereographic projection. Stereographic projection is conformal mapping. Check this claim!
We notice that, through stereographic projection, meridians are mapped into directions that contain the projection of the centre of the sphere, and parallels are mapped into circles whose centre is the projection of the centre of the sphere.
Notice also how not all areas are deformed equally. Try to adjust the sphere so that the stereographic projection deforms Europe as little as possible!
