Athena B.
Jacobs 1/2
February 29, 2012

Introduction
Meso-American civilizations made many advanced achievements in astronomy and mathematics. The Mayans made several breakthroughs in these fields. This includes the invention of the Mayan calendars, one with 260 days and the other with 365 days. The Aztecs made many other inventions, as they made advances in math and astronomy, as well. The Incas also made discoveries in math, which led to the making of the quipu and other tools.


This is a map of the Mayan and Aztec empires.


Mayan Mathematics and Astronomy
The Mayans were, “One of the most brilliant and powerful cultures in ancient America” (Day 10). The Mayans developed a highly advanced number system. Their system was similar to ours in the way that they used place values. Instead of a base-ten system, though, they used a system based on 20. For example, there were place values for 20's, 400's and so on. They also discovered the importance of using zero, a discovery few other civilizations made. The Mayans made a system for writing these numbers; a dot was one, a bar was five, and a shell meant zero. To add and subtract, they would align two numbers and then combine or take away dots, bars, and shells.
Through this advanced understanding of mathematics, they made many discoveries in astronomy. Priests studied the sky and the stars from observatories and were able to track the movements of the planets and stars. This included tracking the sun. As they became aware of the paths of the sun and changes in the weather due to its location, they discovered the seasons. The Mayans used this knowledge of seasonal changes to improve their agriculture. They knew that as the distance from equator to the sun decreased, their growing season would be coming closer. As it came closer to the end of the season, they would know when they needed to harvest their crops.


This picture shows the symbols the Mayans used for math.

The Mayan Calendar
Along with all their other accomplishments, the Mayans invented a calendar of amazing accuracy and complexity. They used mathematics and their knowledge of astronomy to create this involved system. The Mayans used these calendars to help determine the best days to hunt, battle, cure, and perform religious ceremonies.
The first type was a daily calendar based on the sun. This divided the year into 18 months, with each month consisting of 20 days. The Mayans believed there were also five “unlucky days”, adding up to 365 days in all. We also have 365 days in our year, but with twelve months with an average of 30 days.
The second type of calendar was the sacred calendar. It was called the Sacred Round, or tzolkin. This calendar had 13 months with 20 days in each. The Sacred Round was based on two cycles that would identify a specific day. The first cycle had the numbers one through 13. The other consisted of names of 20 days. Each of theses names represented a certain god.
Every 260 days, a specific set of numbers and day names would occur. Priests were the only ones who could read these combinations and interpret the secret meaning of the Sacred Round. They used these meanings to know when to perform important things like battling and hunting. “The Sacred Calendar is the main entry to the thinking of the advanced civilizations that existed in the Western world” (Calleman 2). Some priests in southern Mexico still use this calendar system today.


The Mayans created an amazingly accurate calendar.

Aztec Mathematics and Astronomy
The Aztecs also had an advanced mathematical system. Like the Mayans, they had a vigesimal system, (base-20 system). The Aztecs also used dots for ones and bars for five, like the Mayans. In addition, they had rhombuses for ten, flags for twenty, and used hand, heart, and arrow symbols to show fractional distances. This helped when they calculated areas of land for farming and building. The hand, heart, and arrows symbolized individual units, like feet or inches that we use today. Along with their advanced method of doing math, they carefully tracked the movements of celestial bodies. This included the sun, moon, stars, and other planets. This practice was mostly done by priests and nobles at fixed locations in buildings, such as temples. They tracked the rising and setting of the sun, moon, stars and other planets by placing sets of crossed sticks along their site line. These alignments helped layout plans for cities and buildings.
Through these advanced ways of math and astronomy, the Aztecs could invent and adapt things such as the sun stone and calendar. The sun stone was a huge stone calendar. It was twelve feet wide and weighed almost 25 tons. It was covered in beautiful carvings and showed the Aztec’s dedication to the sun god by having its face carved into the center. This calendar represents the Aztec belief that the universe had passed through four world creations.
The Aztecs also adapted the solar and sacred calendar made by the Mayans. The solar calendar, with 365 days was very useful for farming because it tracked the seasons. They also used the sacred calendar to determine when certain events would occur and know the lucky days for cases like going to war, planting crops, and hunting.


This shows the symbols the Aztecs used for math.

Incan Math Tools
The way the Incas did their math was very unusual, yet impressive. The Incas had no written language, so they used tools like yupanas and quipus to help them. A yupana was a type of stone calculator. They were approximately 20cm. by 30cm. large and had carved or sculpted quadrants inlaid into the tablet. The Incas would place small pebbles or corn seed on the quadrants and then would use it like an abacus.
Another tool they used was the quipu. This was a cord held horizontally where knots on the strings hanging down would represent particular things. The placement of these knots also held information. These different positions represented a base-10 counting system. The units digit was near the end of the string, the tens near the middle, the hundreds little after that, and so on.
As you can imagine, looking at hundreds of strings would be confusing, so they used different colors to represent different things. For example, yellow might represent corn while brown meant grain. Quipucamayocs, the Inca statisticians, would interpret these quipus and keep records that would be sent to the capital, Cuzco. “This remarkable system helped the Incas manage their far-flung empire.” (Frey 289).
It is still unknown whether or not the Incas used the quipu to solve mathematical problems. It was most likely just a way to keep records. These two inventions were very efficient forms of counting and would lead to other mathematical discoveries later on.


This is a quipu that the Incans used to record various things..

Incan Astronomy
Astronomy was very important to the Incas. The stars gave the Inca detailed information about when to plant their crops and what the weather might be like in the near future. Some of the most important events to the Inca involved the risings and settings of the sun, moon, and stars. For example, when the Pleiades star cluster rose, it signaled the start of the new Incan year. The Inca also built carefully oriented pillars on hills overlooking Cuzco to know when to plant. When the sun rose or set between the pillars, they knew it was time to plant at a specific altitude. Astronomy greatly helped the Incas with their agriculture.



Conclusion
As you can see, these three Meso-American civilizations were highly advanced for their time. The Mayans and Aztecs had very involved ways of performing and studying math and astronomy. The Incas developed a complex counting system without any written language, and the Mayans even created an amazingly accurate calendar system. I wonder if it’s accurate enough to predict the end of the world.


Their magnificent temples are just one of the things to prove that the Aztecs, Inca, and Maya were some of the most advanced ancient civilizations.




Works Cited

1. Baquedano, Elizabeth. Aztec, Inca and Maya. New York: DK, 1993. Print.

2. Calleman, Carl. The Mayan Calendar and the Transformation of Consciousness. Rochester, Vermont: Bear and Company, March 25, 2004. Print.

3. Day, Nancy. Your Travel Guide to Ancient Mayan Civilization. Minneapolis, Minnesota: Lerner Publishing Group, October 1, 2000. Print.

4. Frey, Wendy. History Alive: The Medieval World and Beyond. Palo Alto, California: Teacher’s Curriculum Institute, 2005. Print.

5. Inca Empire. Wikipedia, n.d. Web. December 6, 2011. http://en.wikipedia.org/wiki/Inca-Empire.

6. Kimble, John. Inca Maya and Aztec Empire Achievements. Yahoo Voices, July 1, 2007. Web. December 8, 2011. yahoo.com/inca-maya-aztec-empire-achievements-359085.html?cat=37.

7. Moskowitz, Clara. Aztecs Were Whizzes at Math. msnbc.com, April 3, 2008. Web. December 8, 2011. http://www.msnbc.com/id/23940691/#.TurWUJhOXw4.



Author’s Page
Athena Byers lives in a small house by the beach in Santa Cruz, California. She was born on a sunny day in February about two years after her sister, Mikaela. She went to Bay View Elementary and is currently working on her second year at Mission Hill Middle School. Athena enjoys skiing, soccer, and volleyball, and has been on teams for all of these. She also loves hanging out with friends, going to the beach, and traveling. In fact, she has been to 17 countries including Belize, Austria, Ireland, Vietnam, and Qatar. She loves to experience all the different cultures and people and hopes to continue traveling her whole life. Some places she would love to visit would be Iceland, New Zealand, Australia, Chile, and Morocco. Athena also loves seeing her aunt, uncle, and two cousins in Qatar.
Athena would also love to learn more languages like French, Arabic, Spanish, and maybe even some sign language. Her family is actually planning a trip to visit a Spain over the summer so that they can all learn Spanish. Another goal of hers is to get better at drawing. She loves to sketch in her free time and doodle on the sides of her school papers or notes. Right now, she is in her school’s multi media class and is very excited for the new semester to get going so they can start new projects.





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