# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Finding great circle apex?
From: David Pike
Date: 2019 Jan 19, 06:50 -0800

Sean you wrote: I'm about the farthest thing from a mathematician that you can find.

I sympathise with you.  I thought I was quite good at maths at school, but when I got to college I realised I’d only been doing ‘sums’ until then, and ‘clever maths’ was a different kettle of fish altogether.  Unless I could draw a picture to explain it, I found it a struggle.  I still do.  Even when I’ve made the effort to understand in the past to complete a project or an exam, I’m afraid I remember it for no more than about 30 minutes once I no longer need it.  I believe that’s what they say about higher education. The important thing is not to be able to remember everything you've learned, but that it teaches you how to go about finding the answer.

I woke up thinking about your first formula,  cos(Latv) = cos(Lat1) ∙ sin(C).

There’s nothing wrong with just a starting point and no particular destination.  You could put in any value for a starting course you wished from 001 to 360.  All you’d get were 360 great circles.  All would have a northerly and a southerly vertex.  The one which started heading 360 would be a special case.  It would go though the poles, and the spherical triangle would be just the arc of a circle, a bit like in a Mer Pas calculation.   What could you use the formula for except for passing exams?  Well I suppose it might help you to know what cold weather gear to take with you, or if you were likely to encounter pack ice. Maybe it could be used in broadcasting or to predict satellite orbits. DaveP

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