Sphere–Ellipsoid Consistency at the Menkaure Pyramid Latitude Under the Polar-Axis Split Ratio

On a perfect sphere, latitude 30° is where the polar-axis split ratio and the meridional-to-equatorial circumference ratio both equal unity — a unique geometric identity. On the WGS-84 ellipsoid, these two ratios reconverge at 29°58′20″ N — the latitude of the Pyramid of Menkaure — agreeing to within 2.57 parts per million. The closed-form ellipsoidal generalisation converges exactly to 30° on a sphere and places the exact WGS-84 solution 4.7 meters from the pyramid, outperforming all five standard auxiliary latitudes by factors of 2,600 to 4,600.