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# Alhazen's problem expanded

Started by BMAD, Apr 13 2013 06:39 PM

1 reply to this topic

### #1

Posted 13 April 2013 - 06:39 PM

Consider a terrestrial spheroid to be a sphere, and let our given points be A of which the latitude =x1, and longitude y1, and B of which the latitude =x2 and longitude y2. The shortest distance between these points on the surface of the sphere is along the arc of the great circle joining them. Suppose this great circle track passes, north of a given parallel of latitude x; Find the minimum path between A and B on the spherical surface which does not pass to the north of latitude x. The shortest path consists of two arcs of great circles drawn from A and B to a point P in latitude x in such a manner as to make equal angles with the parallel x at P. Determine this point P.

### #2

Posted 14 April 2013 - 07:14 AM

Spoiler for The basic problem

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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