Resumen: Se plantea una posible metodología de como se realizaban las operaciones aritméticas de la suma, resta, multiplicación y división de los números enteros y decimales, en el imperio incaico con el uso de la Yupana Inca.
[ENGLISH] We introduce the Atipanakuy methodology for the development of the Tawa Pukllay method, also known as “The 4 Sacred Games of Inkas”, developed by the Yupanki Association (Peru) and validated by Universidad de Lima (Peru), which... more
[ENGLISH]
We introduce the Atipanakuy methodology for the development of the Tawa Pukllay method, also known as “The 4 Sacred Games of Inkas”, developed by the Yupanki Association (Peru) and validated by Universidad de Lima (Peru), which allows to convert the learning of arithmetic operations into a playful system of mutual empowerment, in which students participate on a tournament of effectiveness and speed in solving arithmetic challenges through the use of the Andean method Yupana Inka Tawa Pukllay and using tools developed for this purpose like the Kamachiq, which is the software that generates the challenges and Pachaq, which is a clock that allows to manage the dynamics of time between “competitors”.
[ESPAÑOL]
A continuación, presentamos la metodología Atipanakuy para el desenvolvimiento del método Tawa Pukllay, conocido también como “Los 4 Juegos Sagrados de los Inkas”, desarrollada en la Asociación Yupanki (Perú) y validada por la Universidad de Lima (Perú), la cual permite convertir el aprendizaje de las operaciones aritméticas en un sistema lúdico de empoderamiento mutuo, en el que los aprendices participan de un torneo de efectividad y velocidad en la solución
The work singles out a multiplication in the yupana by Guaman Poma de Ayala: unique example of computing carried out with the method used by ancient Incas, that nowdays we can observe. Conseguently the deciphering revealed the method of... more
The work singles out a multiplication in the yupana by Guaman Poma de Ayala: unique example of computing carried out with the method used by ancient Incas, that nowdays we can observe. Conseguently the deciphering revealed the method of computing and the number system used by Incas. By surprise, the number system resulted a decimal additive number system and no a decimal positional number system as we supposed.
What color were the favorite by the Incas? The Incas combine colors? Will we be able to decipher the signs tokapu if we know about the color? What colors did not see the Spaniards? Pedro de Cieza de Leon and Pachakuti Yamki Yupanqui... more
What color were the favorite by the Incas?
The Incas combine colors?
Will we be able to decipher the signs tokapu if we know about the color?
What colors did not see the Spaniards?
Pedro de Cieza de Leon and Pachakuti Yamki Yupanqui were color-blind?
Why was used a color naranjado by Guaman Poma de Ayala and nobody others?
El cronista jesuito, el autor de varias investigaciones históricas sobre la historia de los incas. Tenía un hermano teólogo Jerónimo Valera. También compiló un diccionario de signos tocapu, supuestamente la criptografía de los Incas. Fue... more
El cronista jesuito, el autor de varias investigaciones históricas sobre la historia de los incas. Tenía un hermano teólogo Jerónimo Valera. También compiló un diccionario de signos tocapu, supuestamente la criptografía de los Incas. Fue co-autor del Catecismo en quechua y aymara.
The Incas used large numbers on the abacus. Diego Gonzalez Holguin mentioned in his dictionary not only about a trillion (1 000 000 000 000), but also about a quadrillion (1 000 000 000 000 000)! In Europe, have not yet been... more
The Incas used large numbers on the abacus.
Diego Gonzalez Holguin mentioned in his dictionary not only about a trillion (1 000 000 000 000), but also about a quadrillion (1 000 000 000 000 000)!
In Europe, have not yet been invented names of these numbers.
At the moment, until the work is only in Russian, but I plan to translate into English. Even from the images you will understand that we were able to solve many issues of the yupana and quipu. Of course, this is just a hypothesis… I want... more
At the moment, until the work is only in Russian, but I plan to translate into English. Even from the images you will understand that we were able to solve many issues of the yupana and quipu. Of course, this is just a hypothesis…
I want present my draft about decipherment of yupana (co-author A. Bondarenko). The study is illustrated with numerous images, explaining the essence of our discoveries, interactive tables, etc. And also: black counters means no value, and white - the presence of value. We understand how to add a number from the yupana in a quipu, and vice versa. The multiplication table is short and it has an advantage over the decimal system. It represents the multiplication of the numbers. We understand how a curaca counted on the yupana its population. In contrast to other decipherments we realized how to multiply and divide. Working with the Yupana for the Incas require a translation of numbers in the decimal system of the Quipu. The Yupana more convenient to process of information than we use binary and decimal system due to unusual "nonlinear logic” of the number representation. The Yupana so universal that it can be used for vigesimal and sexagesimal system. We understand how to use Yupana together with a calendar of 328 and 360 days, and both were located the Wakas on the yupana because they have a numeric value and color.
The system of numbers and mathematical categories A "calculator" of ancient Americans Yupana A version of Niccolini de Pasquale The proposed decoding of the Yupana The device Yupana Terms of grouping and replacement Promotion of digits General Principles Appendix 1. An interactive example of the numbers on the YUPANA Advantages of presenting the number on the Yupana An addition rule Terms of subtraction Deciphering of Poma de Ayala’s picture The following categories of numbers Interactive examples of addition Mnemonic account on the Yupana Multiplication Multiplication of counters A multiplication table Interactive examples of multiplication Simplified methods of multiplication Table of squares Divisibility Division Appendix 2. An interactive example of arithmetic operations Arithmetic operations on Yupana A counting Yupana for the everyday counting How could count on a simple accountant Translations into decimal system Incas: Yupana and Quipu Transferring numbers: Yupana - Quipu Transferring numbers: Quipu - Yupana An interactive example: how input numbers on the Yupana and Quipu Nonlinear logic of Yupana Ability to work with different counting systems: visual patterns and paradoxes Appendix 3: Historical information about the Inca yupana Literature
