NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Pi Problem for CN
From: John Karl
Date: 2015 Mar 20, 15:11 -0700
From: John Karl
Date: 2015 Mar 20, 15:11 -0700
Well, Pi day is well past, along with it's various interpretations. But here's a problem more relevent to us navigators operating on a sphere: We all know the ratio of the circumference of a circle to its diameter is that famous number, Pi. But now calculate that same ratio of circumference to diameter for that sphere that we CN guys are so familiar with. Find an expression for that ratio, and show that for the largest possible circle that ratio is a prime rational number, and that as the circle appoaches zero diameter, the ratio monotonically shrinks to an irrational number.
Happy living on a sphere,
J Karl
