AiS Challenge Team Abstract

Team Number: 092

School Name: Silver High School

Area of Science: Social Science

Project Title: An Ancient Calculator



Problem Statement

The ancient civilization of the Incas was very complex for its time. However, there was no real written language, therefore there is not much information regarding their culture. The only real artifacts we have today that could be considered a written record is the quipu. A quipu was a series of strings tied in knots to represent numbers, words, or even sounds. Quipus have been used to tell a story, keep inventory, count livestock, for census, or even looming patterns. The quipu maker was respected in the Inca community. The team will computerize a quipu using a C++ compiler. The program will allow the user to input information and it will separate the information and use matrix algebra and find sums or differences. This will hopefully allow for a better understanding of Incas and their quipus.

Progress to Date

We have researched the Incas and their quipus on the Internet and through the book, Mathematics of the Incas: Code of the Quipu by M. and R. Ascher. We did this in order to gain a better understanding and make an accurate computer program. We have also made multiple quipus that represent ages of the members of our class and the sum in order to understand the layout of the quipu. A skeleton of the computer program for the "virtual quipu" has been developed in C++. The first operation is to ask the user to input a series of numbers. The program then inserts the numbers into an array. Next, the program asks which operation to complete; either find the sum, difference, or product of the array. It will then output the correct data. It will repeat this process as many times as the user would like. The program will also tell the user the history of the quipu if they so desire. At this time, the program outputs how the Incas divided and found totals, since it is done differently than what Western civilization does now.

Expected Results

We will be adding code that will draw out a quipu and output the names of objects it is recording. Since, at this time, we do not know the code to do this, we have researched and conferred with our mentor, Daniel Houch. The computer program will simulate a virtual quipu once completed. It will allow the user to input specific information such as the number of livestock or the number of people living in a town. Once the data is inputted, it will be able to query information and find the sums or differences of the data. This may seem like an ordinary calculator, but the Incas thought differently than Eastern civilization. The Incas were primitive and could not understand the concept of decimals, so only whole numbers were used. Also, numbers greater than twenty were broken down in halves until a small enough number was acquired so that the operations could be easily performed. The program, like an Inca, will not use decimals and break down large numbers. However, the results of the calculations will not be correct by our standards. Hopefully this will give better understanding of the Incas and how they thought.

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