Catenary and Mercator projection (2401.12991v1)

Abstract: The Mercator projection is sometimes confused with another mapping technique, specifically the central cylindrical projection, which projects the Earth's surface onto a cylinder tangent to the equator, as if a light source is at the Earth's center. Accidentally, this misconception is rather close to a truth. The only operation that the map needs is a free bending in a uniform gravitational field if the map's material is dense and soft enough to produce a catenary profile. The north and south edges of the map should be parallel and placed in the same plane at the appropriate distance. In this case, the bent map been projected onto this plane gives the Mercator projection. This property is rather curious, since it allows to make such a sophisticated one-to-one mapping as the Mercator projection using simple tools available in the workroom.