Sphere–Ellipsoid Consistency at the Menkaure Pyramid Latitude Under the Polar-Axis Split Ratio
Abstract
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.
Fields of Study & Subjects
Historical Geography and Cartography
Mathematics and Applications
Historical and Architectural Studies
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint