Gen Nav Questions

[keith williams]

I suggest that anyone who wants to debate question 1 should read these:


http://en.wikipedia.org/wiki/Great_circle

To prove that the minor arc of great circle is the shortest path connecting two points on the surface of a sphere, one has to apply calculus of variations to it.



http://mathworld.wolfram.com/GreatCircle.html


The shortest path between two points on a sphere, also known as an orthodrome, is a segment of a great circle.


http://en.wikipedia.org/wiki/Great-circle_distance



Through any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle.

Or for those wishing to concentrate on the definition of an arc

http://en.wikipedia.org/wiki/Arc


In geometry, an arc is a closed segment of a differentiablecurve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle. If the arc is part of a great circle (or great ellipse), it is called a great arc.