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Inca

Mathematics

Adam BensonCaleb MorrellDominic Nardone

Cory SargeantJoshua Surdykowski

Physics 001

Fall 2004

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Typically, a civilization must develop a form of writingbefore they can come up with one for counting or math.This was not true for the Incas.Their enormous empire stretched from what is thepresent-day northern border of Ecuador to west-centralArgentina, which meant that they spoke about 20different languages because they were from suchdiverse ethnic groups.

Because there were so many different languages spokenamong the same tribe, they had to come up with alanguage they would all understand, which turned out tobe mathematics.

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The Incas were very advanced for their time. In addition to roads, they also hadagriculture, textile design, and administration.This made it all the more incredible that they never developed a writing system.However, none of this would have been possible without a system to count.Their system of writing did not require any counting.All they needed were strings and knots, which they used to make quipus.Quipus were not calculators. They were for recording, not adding or subtracting.

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The way a quipu was used was by puttingknots in different positions on a string.These different positions represented abase 10 counting system .For the units digit, knots were placed nearthe end of the string.A space was left, then there would be knotsfor the tens.Another space was left for the hundreds,and so on.For example, the number 395 would have 5knots near the end of the string, then aspace, then 9 knots and another space, andfinally 3 knots for the hundreds.The quipu could also represent a zero byputting no knots in that position.

This meant that the spaces left between hadto be very distinct so a zero wasdiscernable.

Incan Quipu

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Just having hundreds of stringswith numbers on them wouldbe confusing, so differentcolors of strings would be useddepending on what the number

represented.For example, stalks of cornmay have been shown by ayellow string, and apples mighthave been shown by a redstring.With this system, any time yousaw a certain color string, youwould immediately know whatit was recording.

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The Incas also had a form of statisticians they calledquipucamayocs.These quipucamayocs were the ones who interpretedthe quipus and kept records which they would send tothe capital, Cuzco.

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Nobody knows for surewhether or not the Incasapplied these devices tosolving mathematicalproblems.It may have just been forrecord keeping.Either way, it was the mostefficient form of counting atthe time and wouldeventually lead to othermathematical discoveries.Without a system to count,math would be impossible.

DONE