Math Help - Questions about points on the surface of a sphere & great circles...

Hi,

Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points?

I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture

B

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

source ...

Great Circle -- from Wolfram MathWorld

Originally Posted by Bwts

Hi,

Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points?

I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture

B

Of course, any three points form a plane (your two on surface and the center of sphere)

Thanks my follow up question is this, if using the same 2 points I construct a another circle on the sphere's surface (not a great circle this time) how would I prove that the segment of this new circle is greater then the great circle segment between the same points?

I think it must have something to do with the curvature of the circles but am having trouble visualising it?

Originally Posted by Bwts

Thanks my follow up question is this, if using the same 2 points I construct a another circle on the sphere's surface (not a great circle this time) how would I prove that the segment of this new circle is greater then the great circle segment between the same points?

I think it must have something to do with the curvature of the circles but am having trouble visualising it?

the shortist distance between points on the earths surface is along a great circle.Navigators have to change course regularlyto follow such a route.Points are places like New york and London and are not changable

Yes but how do I prove this is the case?

There are many arcs on the surface of a sphere that will pass through the same two points.

Originally Posted by Bwts

Yes but how do I prove this is the case?

There are many arcs on the surface of a sphere that will pass through the same two points.

Look up the definition of great circle and remember that 3 points create a plane. Two surface points and center of sphere.Take a ball and mark two points less than a diameter apart.Measure the distance by using a string. Try to find a route shorter than the string