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

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.