Some mathematical and geometrical interpretations of the Sator Square

Abstract

In 1738, the King of Naples and future King of Spain, Carlos III, commissioned the Spanish military engineer Roque Joaqu\'in de Alcubierre to begin the excavations of the ruins of the ancient Roman city of Pompeii and its surroundings, buried by the terrible explosion of Vesuvius in AD 79. Since that time, archaeologists have brought to light wonderful treasures found in the among ruins. Among them, the Sator Square is one of the most peculiar, apparently simple but mysterious. Supernatural and medicinal powers have been attributed to this object and its use was widespread during the Middle Age. Studies to explain its origin and meaning have been varied. There are theories that relate it to religion, the occult, medicine and music. However, no explanation has been convincing beyond pseudo-scientific sensationalism. In this study, the author intends to eliminate the mystical character of the Sator Square and suggests considering it as a simple palindrome or a game of words with certain symmetrical properties. However, these properties are not exclusive to the Sator Suare but are present in various mathematical and geometric objects.