Sorry - guys - I've been temporarily overwhelmed with work over the past few days - hence little time for FET disproofs.

You can't do this calculation with just triangles. Any three lengths will make a triangle (So long as A+B<C, etc)!

Mr Bishop's "Proof" is silly.

STEP 3:

You have to use TWO triangles. Take four cities that make a quadrilateral (basically, any four so long as they aren't "colinear").

Let's call them A, B, C, D.

Using the "cosine law" (which Mr.Bishop clearly accepts) you can say that IF the world is flat, then calculating the angle BAD from the lengths A-B, B-D and A-D will give you the same answer as if you calculate the angle CAD plus BAC. After all BAD must equal CAD + BAC - right?

If the world is flat then all of the geometry will work out nicely - you can calculate all of the angles and the'll all add up more or less perfectly...right?

If the world is not flat then there will be wildly different results from calculating the angle BAD directly and from the sum of CAD and BAC.

(Clearly "BAD" is well named!)

When I have time, I'll find four suitable cities and do the math. But if someone else wants to give it a shot first, there is a handy triangle calculator here:

http://www.calculator.net/triangle-calculator.htmlJust be sure to find four cities that are WIDELY spread. The further apart they are, the more convincing the answers will be.