On 07/06/2014 00:15, Dan Asimov wrote:
The first rigorous description of the Mercator projection was apparently given by Edwin Wright in 1599 -- it's a lovely geometric description I hadn't heard before: Imagine a vertical cylinder tangent to the globe at the equator. Now inflate (uniformly expand) a perfectly spherical balloon that initially coincides with the globe, stopping each point at the moment it reaches the cylinder. The correspondence between a point on the globe and the point it reaches on the cylinder is the Mercator projection, and can readily be seen to be conformal.
I'm not sure I understand this. The simplest interpretation of "uniformly expand" would seem to be that each point moves radially outwards, but that gives exactly the interpretation you said the Encyclopaedia Britannica wrongly gave for years: central projection from the sphere to the cylinder. So maybe you intend some fancier (more physically realistic?) notion of uniform expansion, but I can't tell what. What am I missing? -- g