A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John Karl
Date: 2015 Mar 23, 13:47 -0700
As I said, I thought Dave did a great job. Norm did too in his explaination of the limit Pi sin x/x as x goes to zero, I just thought of the series sine x = x - x3/3! + ... (the 1st term in that seires comes from L'Hospital's rule.)
Herbert, I made two "slips" (wish I could claim them typos). Of course a prime number is also a rational number. And 2nd, I should have said the ratio of c/d increases to Pi, not decreases, as the circle goes to zero.
And yes, I didn't go into details about what the diameter of a circle might mean on a sphere. Maybe I should have, but I thought that might be intuitive for spherical navigators. If I were to suggest a simple definition, I might say that the cord of a circle on a spherical surface is the minimum distance between two points on that circle. And the diameter is the maximim cord on the circle. (Yes the max of a min ... contradictory?)
Just to drift off the topic of CN a bit more, anyone on the List willing to tackle the same problem for the Schwarzchild metric of general relativity, the curved space we all navigate in? With his background, Frank should be able to address this.
Wishing none of us have to use this in navigating clear of a black hole,