sPad of Super Accuracy and Geometry in Old Babylon. -- sPad de S\'uper Exactitud y Geometr\'ia en la Antigua Babilonia

TL;DR

This paper analyzes the ancient Plimpton-322 tablet, revealing geometric relations of right triangles, introduces sPad as a super-accurate calculation tool, and presents key physical constants in sexagesimal base.

Contribution

It introduces the concept of sPad as a super accuracy calculation tool based on ancient geometric relations and calculates its machine accuracy, also presenting physical constants in sexagesimal.

Findings

Identified geometric relations in Plimpton-322

Calculated sPad's machine accuracy $psilon_m$

Presented physical constants in sexagesimal base

Abstract

Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a super accuracy calculation tool, in this work we have called it sPad by stone pad, and we have calculated its machine accuracy $\epsilon_m$. Additionally, we present the physical and astrophysical constants most used in science and engineering in sexagesimal base. ----- Reci\'entemente se ha descubierto que en una tableta de piedra de m\'as de 3800 a\~nos de antig\"uedad, la Tabla Plimpton 322, est\'an ta\-lla\-das las relaciones geom\'etricas que existen entre los lados de 15 tri\'angulos rect\'angulos escogidos de manera muy especial. Debido a su propiedad como herramienta de c\'alculo s\'uper preciso, en este trabajo la hemos llamado sPad por \emph{stone pad}, y hemos calculado su exactitud de m\'aquina $\epsilon_{m}$. Adicionalmente presentamos las constantes f\'isicas y astrof\'isicas m\'as usadas en ciencia e ingenier\'ia en base sexagesimal.