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    Showing a Mercator Projection is not a perspective projection
    From: David Pike
    Date: 2016 Dec 31, 10:14 -0800

    Robin Stuart you wrote:

    "Wright also offered an interesting physical model. Consider a cylinder tangent to the earth’s equator and imagine the earth to “swal {swell] like a bladder.” Then identify points on the earth with points on the cylinder they come in contact with. Finally unroll the cylinder; it will be a Mercator map. This model has often been misinterpreted as a cylindrical projection (where a light source at the earth’s center projects the unswollen sphere onto its tangent cylinder), but this is not conformal."

    For this physical model to work I think you'd have to add the requirement that once a point on the surface of the bladder touches the inside of the cylinder it sticks and can move no more.

    I like this model, which sounds a bit like “Charlie in the Chocolate Factory”, but I wonder if it’s a bit too neat and plausible to be true.  While I’m quite prepared to accept that a real Mercator projection is non-perspective and therefore not quite the simple cylindrical projection often shown, I’m still trying to get my head round the difference between a swelling Earth and a projection from the centre.  The only explanation I can think of is that the swollen Earth is not swelling evenly from the centre.  Otherwise, what’s the difference?  Thinking of a round bread loaf, does it somehow creep up the sides of the tin expanding in both directions as it goes?  I think that would be so complicated no one would dare question it.  DaveP

       
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