Since the commencement of human existence, personal qualities such as: the pursuit of knowledge, the desire to expand ones horizons, and the inclination to establish and follow a dream, has significantly impacted society. From the earliest days, right up until the present time, a number of accomplishments have filled the vast expanse of time. Such accomplishments span from exemplary literary works, such as those of Cicero, Virgil, and Goethe; to philosophical breakthroughs of men like Rene Descartes who said, “I think therefore I am”, and finally to the unprecedented discoveries in the fields of mathematics and science. Among all the civilizations of time, those of the Pre-Columbian Era seem to have successfully applied mathematical concepts, mainly geometry and algebra, in a somewhat uncanny manner. One cannot all but question how engineers of today’s time, men and women with almost limitless resources, suffer periodic setbacks, while structures of the primitive Pre-Columbians have remained largely intact up until the present day. Clearly no one can compare the Golden Gate Bridge, Lincoln Tunnel, and Empire State building to Pre-Columbian structures, yet the simplistic success of these ancient people causes substantial curiosity. It seems, although only a personal conjecture, that through the analysis of modern day mathematics, insight into the minds of the long lost masterminds behind some of the worlds greatest architecture and the mathematics emphasized in their extraordinary works, can be ascertained. The ancient Maya, although a civilization that first emerged during the pre-classic period, actually have a lot of similarities to the people of the modern era. Socially, politically, and even creatively, they were far more advanced then many may have assumed. However, the advancements that the Mayans made in mathematics were both intriguing and impressive. Formally, the Mayans are credited with the development of a number system based on a combination of lines and dots, and although not literally known to be geometers, like Euclid for example, geometry was an important part of their culture (Schele 82). Through simply looking at the structures of the Mayans, and then studying the geometry available to the world of academia, a precise realization of almost every form of this ancient math that the Mayans capitalized on, can be discovered. The first and most obvious geometric structures are the ancient pyramids. These temples were built mainly for religious purposes and the glorification of the king. Yet, regardless of how observative, or lacking, the everyday Mayan may have been to their surroundings, the pyramids were an expression and home of the era’s geometric beauty (Schele 105). While building pyramids, the Mayans, whether they realized it or not, were applying some very important geometric related concepts. Although there are probably countless books written on the geometry of a pyramid, three main focuses seem intertwined in most of the Mayans work. Those areas that seem to be the most important are: center of gravity, parallel lines, and congruent sides. Although such focuses may seem rather basic, they are in fact some of the most important concepts surrounding the world of pyramids. The first of these three main areas, center of gravity, may at a glance be puzzling in the sense of its relation to geometry, or even a pyramid for that matter. Yet, a center of gravity is not only geometric, but also played a paramount role in the Mayan pyramids. Consider a tall pyramid with a terrible center of gravity, caused by, for example, one side of the pyramid consisting of a stone that weighs three times more then that used for the other sides. Although it may be fine for the first one hundred years, or even two hundred, a tall structure with a poor center of gravity is bound to crumble over time, and certainly will not last hundreds upon hundred of years. The fact that they are still standing...

...Long before any white man ever set foot in this hemisphere, there were fully functional and highly developed societies here. These civilizations were sophisticated, could even be considered more advanced than the European nations at the time. While the rest of the Eastern world was in the dark Middle Ages, the people here were flourishing.
The Aztecs were the Native American people who dominated northern México at the time of the Spanish conquest led by Hernan CORTES in the early 16th century. According to their own legends, they originated from a place called Aztlan, somewhere in north or northwest Mexico. At that time the Aztecs (who referred to themselves as the Mexica or Tenochca) were a small, nomadic, Nahuatl-speaking aggregation of tribal peoples living on the margins of civilized Mesoamerica. Sometime in the 12th century they embarked on a period of wandering and in the 13th century settled in the central basin of México (Encarta). Continually dislodged by the small city-states that fought one another in shifting alliances, the Aztecs finally found refuge on small islands in Lake Texcoco where, in 1325, they founded the town of Tenochtitlan (modern-day Mexico City).
Fearless warriors and pragmatic builders, the Aztecs created an empire during the 15th century that was surpassed in size in the Americas only by that of the Incas in Peru. As early texts and modern archaeology continue to reveal, beyond their conquests and many of their religious...

...true history. Knowledge about pre-Columbiancivilizations comes from two main sources: archaeological remains and the accounts written by European white men. A result of the Conquest by the Europeans they Aztec, Mayan, and Inca Civilizations were virtually wiped out. There was a major loss to humanity here, first of all it destroyed many Ideas of these people that do not affect or Present day thinking. The history of thesecivilizations mysterious and as a result of the Conquest people of today know little of nothing about these Grand Civilizations that once flourished the new world.
Knowing that we are getting our history from either the white man or the remains of a person of that time period to one is a shame, it makes one feel that these cultures must have had something perfect that scared the white man, because they didn’t waste much time getting rid of anybody that had knowledge about the land prior to the invasion. They also didn’t mind teaching the young Indians to what they believed was the proper way to live. Of course this was only possibly if the Indians were captured and left over after a big battle.
Furthermore cultures had been flourishing thousands of years before the Europeans arrived to the New World. Great empires such as the Aztecs, Mayans, and Incas inhabited the vast lands of Central and South America. These three major powers controlled the land before Columbus or...

...DISCRETE MATHEMATICS
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.
Research in discrete mathematics increased in the...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest...

...“Pre – Columbian Americas”
The New World before Columbus, was not empty and unknown before his discoveries. Europeans had explored in the New World, they came into contact with people whom Columbus by mistaKE called them Indians. It is unknow where they came from and when these first Americans came to the North and South America, but it is cleared that they lived in the new world centuries before the Europeans came. The Indians were not unified they were divided into hundreds of clans or tribes, each had its own language, lifestyle, and leader. Some Indians were called Nomadic, constantly looking out for game, fish, and wild plants. They lived in portable shelters such as tepees Others, settled in one area and farmed the land, raising crops such as maize, potatoe, squash, and beans. More often Indians lived in more permanent housing such as dome shaped wigwams covered with leaves and bark, or adobe houses built of sun dried bricks. Eventhough, most of the Indians were scattered in small villages there were three groups that built large civilizations before the white man came. In Central and South America, the Mayas, the Aztecs, and the Incas lived in large cities and developed many skills.
The Pre-Columbian era was a time that Indians or Indegenous cultures flourished to maintain there traditions. The Mayan civilization, located in the Yucatan Peninsula of Mexico and in...

...Introduction
Mathematics is one of the fundamental tools in analyzing and understanding astronomy. Astronomers use mathematics to do basic conversion, calculate brightness, density and temperature and improve the understanding of astronomical images.
Most ancient astronomers views celestial objects on behalf of gods. They studied celestial objects with the hope of discovering the unknown of the world. In ancient China, astronomer is an occupation that works for the imperial family. They determine the calendar and divine by astrology. Astronomers are responsible to explain the reason of natural disaster and the health condition of imperial family. The duties of ancient Chinese astronomers make it to be a mysterious job. It is so sacred that there is a law that if an astronomer was commit to a crime, the judge should penalize him in the lighter way than usual in Qing Dynasty. It is a very special job that astronomers could be very useful in power struggle because natural disaster could be explained as the emperor or officials did not perform his duties and they have to be punished or even die. However, in the Chinese history, there are some extraordinary astronomers who are curious about the secrets of the universe. They use science to explore the laws of universe and the relationship between movement of stars and climate change with the purpose of giving the instruction for people to farming and avoid natural disasters.
In this...

...Pre-Columbian America
There is no certain answers as to how precolumbian natives got to America. There are many theories based on hard evidence. The Paleo-Indians, archaeologists refer to as the first americans. At this point there was no official scripture in their society. Paleo Indians seemed to have paved the way for many other cultures to settle. All though in many cases these native settlers were very different from one another, they also had a plethora of similarities.
Most of the tribes in the new world all believed in the same work ethic. Woman would gather, care for their children, and maintain the household, while men hunted for food. When Paleo Indians, or other tribes would run into each other along the way, they followed the principle of reciprocity. This means they would have a mutual bestowing of gifts, favors, etc. Rather than the notion that one party accumulate profits or power at the expense of the other. These encounters enabled Paleo Indians to develop a broad cultural life that transcended their small bands (5).
When hunting, American natives preferred to travel in groups capable of taking down big mammals. Mammals such as Mammoths, Mastodons, and giant species of horses, camels, bison, caribou, and moose. All the settlers had to eventually deal with climate change over time, which could affect the food chain, and cultivation of the areas crops. around 4000 B.C.E. Natives began to...

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