A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2020 May 15, 01:57 -0700
Hello to all,
In our current quest to know whether there are one or more solutions to our EAL's Challenge , I am hereby confirming that I have been able to fully duplicate Peter Hakel's [re?]discovery and results about the existence of 2 "real world" solutions for some specific environments.
I have also noticed that for some other configurations - which could be the more "frequent" case - there is only one valid solution. For example, Dave Walden's initial problem seems to have only 1 such valid "real world" solution since the 2nd solution yielded by Peter's method does not make sense (at least in our "real world").
So, Peter's method seems a reliable tool to check whether there are 1 or 2 "real world" solution[s].
Nonetheless, and other than performing a limited number of spot checks - which might show us that the existence of 2 real world solutions only happens in the vicinity of the Poles, hence with the involved EAL's and EAC's also in the vicinity of the Poles - it looks difficult to perform checks onto all possible configurations on Earth, as we all know that such configurations are infinite in number.
Hence it would be great to get hold of a publicly available solid mathematical study showing and depicting the various shapes of all different families of EAL's. This would greatly help us visually identifying which are the general cases when EAL's and EAC's cut oneanother in either 1 point or 2 points or maybe more ?
Are they such publicly available mathematical studies ?
Best Isoazimuthal Regards to all,