Three Ellipsoidal Identities at Giza, Teotihuacan, and Istria: A Common Geodetic Invariant Encoding the Rectifying Sphere

Three ancient monumental sites Giza, Teotihuacan, and the Picugi necropolis in Istria, Croatia) each occupy latitudes that satisfy a family of closely related ellipsoidal identities on the WGS-84 reference ellipsoid. Each identity is a minimal promotion of a simple spherical condition to the oblate Earth, corrected by a single factor: the normalized radius of the rectifying sphere.

Beyond the precision of the individual matches, the system exhibits a rich internal structure. Each identity naturally employs a different member of the classical latitude triad (geodetic, reduced, geocentric), exhausting the set. The three identities form a one-parameter family admitting exact, parameter-free inter-site relations, projective harmonic conjugation, simplex origins for two parent fractions, and a chain of Pythagorean means linking the site heights along the polar axis.