A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2015 Oct 7, 14:30 -0700
You are not matching the curvature at the poles you are actually matching the diameters.
Slice the Earth through a meridian and you get an ellipse that is wider at the equator that the poles. The curvature of this elliptical curve is greatest at the equator and least at the poles. If you are traveling along a meridian you have gone 1° in latitude when the direction of your vertical has changed by 1°. Because the curvature decreases the higher in latitude you go you need to move further on the ground for that to happen,