Question

how can you prove that the Earth is spherical by looking at the pole star

Answer 1

The pole star can be seen at ninty degree at the north pole . It lies in the line with the axis of the earth , and its angle decrease toward the equator. At the equator , the angle is zero degree. This can happen only in an arc of a circle . If the earth was flat the pole star would have been the same height for all latitude.