Inca Mathematics

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Inca Mathematics
Physics 001 Fall 2004

• Adam Benson
• Caleb Morrell
• Dominic Nardone
• Cory Sargeant
• Joshua Surdykowski

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Do the Inca

• Typically, a civilization must develop a form of
  writing before they can come up with one for
  counting or math.
• This was not true for the Incas.
• Their enormous empire stretched from what is the
  present-day northern border of Ecuador to
  west-central Argentina, which meant that they
  spoke about 20 different languages because they
  were from such diverse ethnic groups.
• Because there were so many different languages
  spoken among the same tribe, they had to come up
  with a language they would all understand, which
  turned out to be mathematics.

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Developing Quipus

• The Incas were very advanced for their time. In
  addition to roads, they also had agriculture,
  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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About Quipus

• The way a quipu was used was by putting knots in
  different positions on a string.
• These different positions represented a base 10
  counting system.
• For the units digit, knots were placed near the
  end of the string.
• A space was left, then there would be knots for
  the tens.
• Another space was left for the hundreds, and so
  on.
• For example, the number 395 would have 5 knots
  near the end of the string, then a space, then 9
  knots and another space, and finally 3 knots for
  the hundreds.
• The quipu could also represent a zero by putting
  no knots in that position.
• This meant that the spaces left between had to be
  very distinct so a zero was discernable.

Incan Quipu
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More about Quipus

• Just having hundreds of strings with numbers on
  them would be confusing, so different colors of
  strings would be used depending on what the
  number represented.
• For example, stalks of corn may have been shown
  by a yellow string, and apples might have been
  shown by a red string.
• With this system, any time you saw a certain
  color string, you would immediately know what it
  was recording.

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Statisticians

• The Incas also had a form of statisticians they
  called quipucamayocs.
• These quipucamayocs were the ones who interpreted
  the quipus and kept records which they would send
  to the capital, Cuzco.

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Conclusion

• Nobody knows for sure whether or not the Incas
  applied these devices to solving mathematical
  problems.
• It may have just been for record keeping.
• Either way, it was the most efficient form of
  counting at the time and would eventually lead to
  other mathematical discoveries.
• Without a system to count, math would be
  impossible.

DONE