We were required to learn about Aztec mathematics for the competition. The mathematical works of the Aztecs are among the most complex of any pre-Columbian culture. The Aztecs represented numerals with symbols for hands, hearts, and arrows. The researchers invested a great deal of time and energy into deciphering Aztec agricultural documents in an attempt to discover how the seemingly clever inhabitants of that culture arrived at their area estimations. [1] Once they included the frequently used and significant glyphs, the calculations made sense. The ethnic tribes that ruled Mexico politically and socially from the 1330s to the early 1500s are the origin of the word Aztec.
For four years beginning in the 1540s, University of Wisconsin geographer Barbara Williams and Universidad Nacional Autonoma de Mexico math prodigy Maria del Carmen Jorge Y Jorge pored over two texts that detailed the agricultural holdings of Tepetlaoxtoc residents[2]. Dr. Jorge's research shows that perimeter and area data are rare in pre-Mexican era documents. Most records from this era have been destroyed or lost. When scientists first attempted to replicate the area projections, they ran into some unexpected difficulties. The Aztecs were able to make some forecasts after they learned that the arrow, hand, and head drawings represented ground distances. [3]
As Dr. Jorge said in an interview with LiveScience, the method they employ to keep track of the regions is so complicated that not even the brightest minds in current mathematics can get their heads around it. She was overjoyed to find that the symbols facilitated her exploration of the map.
A land rod was the conventional measurement of land area, and each sign represented a distance less than that. According to the research Dr. Jorge presented, the arrow, heart, and hand symbols were quite close to what we now call fractions. [4]
Smaller than the metre, they were simply referred to as units of measure. [5] There were unique methods of computation used by the Aztecs. Numbers from one to twenty were represented by dots, and the tens by bars, in the Aztecs' base-20 system. The Aztecs had a deeper understanding of numbers, or at least of the symbols to describe numerical ideas, than we do now. All land titles were drafted with tax purposes in mind. To ensure consistency with the well-known mathematics of the Aztec calendar, the sort of mathematics utilised to determine land ownership was made consistent. Calculating with proportions was a skill widely taught at the time among many civilizations (Moskowitz[6]). Standard practise called for pointing to the appropriate digit. In the case of the dots, one would be represented by a single dot;
1 = á§
And so forth with the number system;
2 = á§á§
3 = á§á§á§
Throughout the course of several hundred years, the Aztecs ruled over the rest of Mexico. The Aztecs had a long-established method of counting. In contrast to our decimal system, this one uses vigesimal numbers. There was a dot-based numerical system in use by the Aztecs. They left behind them extensive mathematical publications that continue to fascinate academics today. Despite the lack of evidence for a zero symbol, the Aztecs had a sophisticated understanding of the concept. However, what appears to be a straightforward arrangement of lines and dots was actually rather involved. The Aztecs were unusual in that they meticulously measured nearly every aspect of their society. Altitude and illustrative illustrations of particular fields may be found in the 1540 Codex Vergara. Previous research has established that they have an understanding of multiplication and division as well as a basic familiarity with geometry.
The Aztecs' mathematical system, which also employed pictures for numerals, had deep roots in older Egyptian mathematical systems. Like the Egyptian symbols, the pictures did not follow any particular pattern and could be written in several different ways while still referring to the same single number.
In the Aztec culture, measurements were taken from actual human bodies. Example: if you extended your left arm, the distance between your heart and the tip of your finger would be one unit of measurement (much like our current foot, inch, and mile). Weirdly, it's utilised to keep track of things like area and perimeter throughout architectural and other building processes. However, the sophistication of the measuring equipment at the time was unprecedented.
The Aztecs simply kept track of the overall landmass. The Codex Vergara has been examined by Dr. Williams (which is what they called the Aztec math). The Aztecs had a wide variety of methods at their disposal for figuring the area. Some of these involved nothing more complicated than a simple multiplication of length by breadth.
Multiple novel concepts were developed by the Aztecs, such as multiplying the average of two sides by an adjacent side. When the number of land rods utilised did not quite work, they rounded up to roughly 2.5 in order to use their customary unit of measurement.
Astronomy was another area where the Aztecs utilised mathematics. Although most of their mathematical astronomical data was destroyed, Anthony Aveni's book "Skywatchers" does a superb job of synthesising what we do know about them. Using this method, the Aztecs learned that Venus's orbital period is 584 days. Even without knowledge of Earth's form or size, the Aztecs were able to calculate the eclipse season using mathematics. Time of the eclipse had been determined, but whether or not it would be a complete eclipse was still up for debate.
Natural calamities would be recorded numerically. As far as we can tell, the Aztecs are the only pre-Columbian people to have left behind technical writings. When it came to taxes, the Aztecs were quite precise with their measures. There was a lot of structure and intricacy in the Aztecs' writings.
In the year 1540, the Codex Vergara was compiled with the use of schematic drawings and precise measurements of specific fields. It was out that familiarity with basic arithmetic and geometry principles was required.
Even though we only have records from the Aztecs, it's not unreasonable to assume that other advanced early American civilizations, like the Maya, utilised equivalent recording methods. The Aztecs were said to have relied heavily on their religion, which is said to have influenced their scientific pursuits and other areas of knowledge. Researchers have concluded that the Aztecs placed a premium on precision in all aspects of life, including taxation. Evidence from the past suggests that they were familiar with basic arithmetic operations like multiplication and division as well as the principles of geometry.
As one of the earliest developed mathematical systems, Aztec mathematics holds great historical significance. A tax period dating back to antiquity. Aztec mathematics is fascinating since it is so different from the mathematics that is commonly practised now. The calendar and hieroglyphic writing system were both developed with the aid of Aztec mathematics.
Around the year 1100 A.D., after the fall of the Toltecs, the Aztec civilisation began to flourish. In 1325, they discovered Tenochtitlan in the valley of Mexico and quickly rose to prominence as one of the region's most powerful military forces. The Aztec empire, as it was often called, was a dominant political entity that oversaw several subordinate groups, collected massive tax revenues, used human sacrifices, and held their accomplishments tightly in their hands. Diamonds are worth ten, flags twenty, feathers hundreds, and a bundle of cacao beans eight thousand.
The Aztec Empire consisted of a loose confederation of principality-like kingdoms. By forming an alliance with the nearby city-states of Tetzcoco and Tlacopan, they eventually became so strong that they dominated most of modern-day Mexico. The Aztec monarch claimed divine descent and exercised power through a council of nobility and bureaucrats. The military, the administration, and the church all relied on individuals of noble birth. Most Aztecs were members of the commoner and slave castes.
Once the region of the forms was discovered, the Aztecs documented it. The Aztecs were exceptionally bright, and they pushed themselves to reach the current level of mathematical sophistication. The study of the stars and planets is called astronomy. The Aztecs created a complex calendar they named the Sun Calendar to keep track of the cosmological cycles venerated by their religion.
It's no secret that the Aztecs had brilliant minds as well. The Aztecs placed a premium on education. To date, their mathematical approach has proven to be the most sophisticated of its kind. The Aztecs' proficiency in both mathematics and science undoubtedly aided them in some of their decision-making. On sometimes, they needed to rely on their scientific knowledge to complete their mathematical tasks.
The Aztecs created their math system in part to ensure accurate measurements were taken while building structures and to facilitate the collection of taxes, two areas in which modern society relies heavily.
The Aztec Empire was renowned for its might and its ability to tax, capture, and absorb the technological advances of the many nations it conquered. This is how the Mayans had an indirect impact on them, through the Toltecs, who had learned this information decades earlier.
There is no definite record of Aztec mathematics, although it is generally accepted that the Aztecs learned a kind of Mayan mathematics that shared the same worldview and symbols. Not only did astronomers utilise calendars to aid in their crucial sky and space searches, but they also used them in the marketplace to facilitate the exchange of products.
The Aztec stone was a sacrificial stone created in the 1470s at the temple of the war god Huitzilopochtli, but it also represented the Aztec universe, since the Aztecs were deeply religious and guided themselves via offerings, human and animal sacrifices to the gods. It was the priests, who were also the astronomers, who were tasked with this obligation. Given the importance of mathematics in the study of the heavens and the interpretation of the calendar, it is clear that arithmetic was a fundamental element of the education of the future priests.
The Aztecs' calendars were a synthesis of preexisting calendars and the Aztecs' own religious tenets. The Aztecs thought that the conclusion of every 52-year cycle marked the beginning of a new era or the impending end of the world.
The Earth-Sun Era, the Age of Great Winds, the Age of Fire, the Age of Floods, and the Present-Day Earthquake Era are all distinguished by distinctive processes. The current sun is in the middle, and the other four, along with their respective end dates, surround the fifth sun, which represents an Aztec god (one of the Aztec gods), likely the sun god. The stone did not celebrate the beginning of the fifth sun, but rather its destruction at the hands of earthquakes. The Aztecs thought that their gods needed new human hearts so that they could continue to function.
The Aztecs used their calendars for more than just keeping track of the dates; they also used them to learn more about the universe and the planet we call home. The calendars were used to keep track of the optimal times for seeing the stars and constellations (see them best). Their system was comparable to that of the Egyptians (as was said), as well as the Hindus and Babylonians.
We have a very high regard for the Aztecs and their mathematical prowess. We believe mathematics is relevant in the present day. They had an impact by paving the way for the growth of contemporary mathematics in our culture. It's possible that we wouldn't have made any progress in mathematics without the Aztecs' contributions. The use of zeroes as placeholders, decimal notation, monetary units, and the concept of time itself might not have been invented.
When it comes to numbers, we find that the Aztecs' approach to them to be rather useful. The mathematical concepts developed by the Aztecs are being used today in academia, instruction, and industry. It's possible that the mathematical advances of the Aztecs will determine the course of our professional lives in the future.
Delaney finds it fascinating since the progress made by the Aztecs in mathematics is useful for solving modern math problems. Jaysiya, on the other hand, feels it's great since technology lets us function in the twenty-first century (career, historian, and etc wise). Raquel finds it amusing because it has been around for a while and continues to be useful in the present day. Olivia believes it's brilliant because of all the unique symbols it employs. Kalyna considers the sophisticated equations and computations of Aztec mathematics to be a major step forward in the field at the time they were developed. Katelyn believes it would be fascinating to learn more about Aztec mathematics. Destiny says she enjoys learning about it and agrees that it may have been challenging to devise such a system.
We will wrap up this article as follows:
Where do the mathematical ideas of the Aztecs fit into modern life? Inventions as diverse as the automobile, the key, television, the internet, and computers would not exist without the mathematical foundations laid by the Aztecs, whose legacy has been carried down through the ages.
In what ways did the Aztecs' mathematical practises evolve? Aztec writing evolved from and built upon earlier systems such as Egyptian hieroglyphs and the Mayan dot-and-bar system. However, they independently produced a wide range of innovations, such as calendars, decimals, and the late invention of zeros as placeholders.
Works Cited
Andrei, Mihai. “Science ABCs – How Aztecs did the Math.” http://www.zmescience.com, 9 Apr. 2008, www.zmescience.com/other/science-abc/science-abc-how-aztecs-did-the-math/
Holden, Constance. “How Aztecs did the Math.” http://www.sciencemag.org, 3 Apr. 2008
Leon, Araceli. “Math Use During Maya and Aztec Civilizations.” http://www.hermetic.ch, www.hermetic.ch/cal_stud/maya/mathuse.htm
Moskowitz, Clara. “Amazing Aztecs were Math Whizzes Too.” www.livescience.com, 2 Apr. 2008, www.livescience.com/2427-amazing-aztecs-math-whizzes.html
Siddiqui, Ajaz. “Aztec Number System.” www.math.temple.edu, 8 Feb. 2004, www.math.temple.edu/~zit/Native%20American/9%20Aztecs_num.pdf
