February 29, 2012
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
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.
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
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.
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.
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.
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.
Mathematics and Astronomy
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
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.
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.
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
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.
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..
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.
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.
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.
7. Moskowitz, Clara. Aztecs Were
Whizzes at Math. msnbc.com, April 3, 2008. Web. December 8, 2011.
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.
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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