Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism

TL;DR

This paper introduces Tawa Pukllay, a novel arithmetic method using pattern recognition and parallelism with the Inca Yupana, enabling quick calculations without memorization or trial and error, validated through rigorous proof.

Contribution

The paper presents a new arithmetic system, Tawa Pukllay, that leverages pattern recognition and parallel processing to perform calculations efficiently and accurately.

Findings

Tawa Pukllay produces correct numerical results.

The method allows multiple calculation paths and strategies.

It eliminates the need for memorization and trial-and-error procedures.

Abstract

Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), where arithmetic operations do not require mental calculations: no carries, no borrows, no memorization of multiplication tables, nor trial and error procedures for divisions. Instead, user recognizes patterns and makes predefined movements to perform the four basic arithmetic operations very quickly; moreover, the result of the operation can be reached by multiple paths and in parallel, allowing each user to create his own strategies. This paper proves with mathematical rigor that TP produces correct numerical results.