The Inca Number System

End

Sources:

Yapas

• Yapas (also known as yapans) was a supposed representation of the Quipu in written form. However, the Incas did not write, which creates controversy among researchers today over whether or not it was the original process of Quipu and it's function as a number system (some researchers claim that it served dually as the Incas' texts), or plain misinterpretation by the scribe Filipe. Not only is there controversy to it's purpose (the possible representation of this system), but also the entire break down of the pair (the Yapas and the Quipu). According to the Yapas, as to however it is chosen to be interpreted, the Quipu would not be set to bases of ten, but they would follow the basis of Fibonacci's Sequence. This is because the Yapas, on paper, look like dots that shaded according to the previous numbers of dots added together...
• See Ex. off to the side.

http://www-history.mcs.st-and.ac.uk/HistTopics/Inca_mathematics.html

http://people.wku.edu/darlene.applegate/newworld/webnotes/unit_4/inca.html

http://www.abc.net.au/science/articles/2004/02/02/1036168.htm

http://www.amathsdictionaryforkids.com/qr/b/base10system.html

http://www.purplemath.com/modules/numbbase.htm

http://math.about.com/library/blpowers.htm

http://www.nytimes.com/2003/08/12/science/string-and-knot-theory-of-inca-writing.html?pagewanted=all

http://www.ancient.eu/Inca_Civilization/

Bases of 10

What This Looks Like

• The result should leave each set of knots separated while the knots within the sets touch one another.

• The biggest unit placement should be on top, while the smallest should be on bottom. In this example, our biggest measure of units are our thousands, so they are located up top.

• So, how do units with a base of 10 tie into this?

• Well, what exactly are bases of 10?

• The decimal system: #'s 0-9...

• This base of 10 is set to the power of something; so, let's think back to our number 3, 643.

• If we were to look back at our smallest unit, which is a 3 in the ones place, we would punch 10^0 in our calc. What would it say? 1. We would then just do 3 times 1 to find our 1's unit place.

• How would we find what's in our 10's unit place? We would do 10^1. Which would give us?___. We would then multiply ___ times 4, giving us our ___.

• THE PATTERN WILL CONTINUE. Except, what do you think will happen if we decided to create an example that utilizes decimal placements as well? Try these examples...

How To Use Quipu

• Quipu use a fairly simple concept it seems; and, this concept connects with base ten units.

• Let's use an example: We have a #, let's say, 3,643.

• On a Quipu, we would pick whichever color we desire for a representation of something... Let's pretend we pick a blue string, and say that this string is a representation of how many people pass through a city within a specific time.

1.) We would start from the top of that string and make 3 knots.

2.) We would then slide down the string, creating a noticeable space between that 1st set of knots. Then we start on a 2nd set, which should have 6 knots.

3.) We continue this process. The next set having 4 knots, while the one after consists of 3 knots.

Quipu

• How can a rope be considered documentation; and, how can this documentation be connected to math?

• Quipu could, often times, consist of different colors. These colors could either be representative of an object/idea.

• According to most researchers, Quipu were used in placement of written text/numbers; therefore, they used rope as a sort of storage for documentation of numbers.

The Inca Number System

The History and Development:

• The Incan civilization lasted between c. 1400 and CE 1533; although, some textbooks state 1534.
• One of the most widely known artifacts of the Inca civilization is called a Khipu, (also known as a Quipu, noted within the findings of Felipe Guaman Poma de Ayala to the King of Spain's chronicles), which is a rope/pieces of rope kept for documentation.
• Another piece of documentation, written by the scribe Felipe rather than the Incans, was the yapas (also known as yapans).

By: Jackie, Carlos, and Keegan