NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Spherical triangles versus plane triangles
From: Alexandre Eremenko
Date: 2025 Sep 17, 07:23 -0700
From: Alexandre Eremenko
Date: 2025 Sep 17, 07:23 -0700
Dear Frank,
I would like to correct the mistake in your message. You wrote: "Of course, celestial navigation deals in spherical triangles instead of plane triangles, and arguably the 3:4:5 triangle doesn't exist!"
This is obviously wrong. Such triangles exist (but none of the angles in them is 90 degrees). In general a small stiangle with sides a,b,c (in the plane or in the sphere, does not matter!) exists if and only if a<b+c, b<a+c, c<a+b. "Small" means that each side has length less than 90 degrees.
I do not write the solution of your puzzle (it is to simple for a professional mathematician), to let other people figure this out. Just wanted to correct the statement.
