PLATO’S TRIANGLE AND GNOMONIC FACTOR: AN APPLICATION TO HERODOTUS’ ORACLES

Abstract

A modification to the gnomonic factor (fg) (Perez-Enriquez 2000) using the concept of Plato’s triangle is presented. With the aid of the platonic gnomonic factor (fgp) as we called it, we found that the oracles mentioned by Herodotus in his History (Dodona in Greece and Ammon in Oasis Siwa, Egypt) could have been placed there because the noon shadow of the sun of a vertical gnomon formed Plato’s triangle the former, and the Egyptian “sacred triangle” (sides 3:4:5) the latter; sites where the value of fgp is equal to 1/1 and 1/3, respectively. This could mean that both concepts were known by Egyptians in Thebes long before, they were formalized by the Greeks. The priestesses, about whom Herodotus talks, knew the right angle triangle concept as an idealization of the sun’s observation as it was proposed by Magdolen (2001), i.e., the triangle is the shadow casted by a gnomon. We consider that the idea of the use of a gnomon for site location could be found in other regions along the Valley of the Nile.