The Theodorus of Cyrene Spiral Geometry and Its Application to Antenna Design

Abstract

In this article, we introduce for the first time the radiation properties of a spiral shape that is obtained from the work on irrational numbers by Theodorus (465 BC–398 BC) of Cyrene (presently near Shahhat, Libya). In the past, this piecewise continuous spiral shape has been erroneously introduced in the literature as the Root, Pythagorean, or Einstein spiral. In addition, we use here P. J. Davis’s interpolation function to obtain the continuous version of this spiral, and we present both the discrete and the continuous Theodorus spiral antenna radiation properties. Finally, we fabricate and perform measurements on the Theodorus spiral, and we present a comparison with its theoretically obtained radiation properties as well with those obtained for the standard Archimedean shape of the same diameter.