I should have added that if, in the demonstration, you put one point on the equator and move the other point above and below the equator, the curve alternates between concave and convex. Therefore, it must at some point (i.e. on the equator) be a straight line. So "always sinusoidal", no. Ever sinusoidal, or how to give a general description of the projected great circles, I don't know. Jeff On Fri, Jun 6, 2014 at 1:08 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
You might be interested in the Wolfram Demonstraton Project "Great Circles on Mercator's Chart".
http://demonstrations.wolfram.com/GreatCirclesOnMercatorsChart/
Jeff
On Fri, Jun 6, 2014 at 12:17 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Yes, I know this question is 400 years old, but what is the shape of the image of a great circle on a Mercator projection map?
I've seen it described as "sinusoid" shaped, but that can't be right, can it? (Yes, we've all seen those satellite location maps on TV, and they look pretty sinusoidal, but are they really?)
I'm not trying to measure lengths or angles, but am simply interested in the mathematical shapes of these great circle on the flat Mercator map.
I'm also not interested in the images of non-great circles.
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