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Major concept ancient egyptian mathematics
Papers on mathematics in Ancient Egypt
The contribution of Egypt to the development of mathematics
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Introduction
Both ancient Egypt and Babylon had great civilizations and were the first to use numbers for more than just counting and record keeping, and they both developed systems of arithmetic (Allen, 2001, p.1). They used computation to find area, volume, circumference, and both used fractions. For both, the arithmetic was used for distribution of goods and the geometry for building. Their mathematics was very practical. What survives from both civilizations is records of problems solved by example. There is no record of generalizing principles or teaching principles supported by examples. This lack of mathematical theory limited the expansion of mathematics. These ancient civilizations developed practical ways to solve systems of equations and quadratic equations. Their math was practical, not theoretical. They did not represent the linear function as a line on a coordinate plane. They did not create theories to explain its behavior. They presented answers, not principles on the relationship between the numbers. They never developed the conic sections because they did not need to teach the mathematical principles of the parabola or ellipse. Math was taught “by example rather than by principle”
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It contains exercises and mathematics problems designed for the instruction of math students or scribes. The papyrus includes problems with fractions, arithmetic, algebra, geometry and measurement (Allen, 2001, p.10). The Egyptian decomposed fractions into the sum of unit fractions – i.e. the reciprocals of whole numbers (Allen, 2001, p.9). The exact method for the decomposition into unit fractions “has been widely debated and no general method that works for all n has ever been discovered” (Abdulaziz, 2007). The Egyptians solved linear algebra equations. They found the unknown, called the “keep” using the false position method (Allen, 2001,
Abstract: This paper gives an insight into the Mathematics used by the American Indians. The history of American Indians and how they incorporated mathematics into their lives is scarce. However from the information retrieved by Archeologists, we have an idea of the type of mathematics that was used by American Indians.
The Mesopotamians and Egyptians are among the first civilizations to make a valuable contribution to Western Civilization. Both Babylonians and Egyptians managed to produce written systems of communicating ideas. The Babylonians created wedge-shaped cuneiform, and the Egyptians made pictographic hieroglyphics. This invention even allowed for Hammurabi’s Code of law to be written and preserved through the ages. The Phoenicians took this concept another step forward and fashioned the alphabet. The ability to record history is an exceptional achievement. Another development of the Ancient Near East was architecture. The Egyptian pyramids, and the Babylonian ziggurats stand as testimony to their society’s technological and architectural achievements. The Assyrians left a lasting impact on civilization with the advent of the idea of conquest which they took to ruthlessly brutal ends. Later the Persians would add a degree of tolerance into the conquest equation. The concept of conquest would leave an indelible mark on the West, for better or worse. These developments still play a role in contemporary society.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Egypt was one of the first River Valley Civilizations. In Egypt there were big advances in art, math and science and also pottery. We still use the same number system and they even had fractions back in that time. During the Old Kingdom times the pyramids were built. The pyramids were tombs for the pharaohs of Egypt. These pyramids are one of the most popular historical sites in the world.
The ancient cultures of Mesopotamia and Egypt are a factor of the evolution of civilizations in present-day. Though, it wouldn’t occur if both of these ancient civilizations didn’t develop into successful ones. There are three similar components that led Ancient Egypt and Ancient Mesopotamia to become prosperous. These are the locations, their way of life, and their beliefs. All of these elements will be explored more thoroughly throughout this essay.
Two of the earliest and greatest civilizations, Mesopotamia and Egypt, show the transition from a Paleolithic society into a settled civilization. Both cultures had established kings; however, the Pharaoh is the god-king of Egypt, while in Mesopotamia the monarchs are priest-kings whom serve the gods. Although Mesopotamia and Egypt have some characteristics in common, which bring them under the “First Civilizations” category, their different views and beliefs about divine authority and how it is practiced set these civilizations apart and make them unique.
According to history there existed two of many important ancient civilizations that left a significant mark in the history of human development that even today leaves modern society in awe of its greatness. In spite of being distant civilizations, Ancient Egypt and Ancient Greece share similarities and difference in terms of how they practiced religion,political structure, everyday life style, and how they built the monumental architectures that continued to amaze the modern world of today. These comparison and contrast explain their difference in history and their dynasty's long term success. Through the early developmental age these two ancient civilizations contrasted in many ways perhaps due to the geographical location that helped shape their diverse cultures.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
Euclid also came up with a number of axioms and proofs, which he called “postulates.” Some of these postulates relate to all sciences, while other postulates relate only to geometry. An example of a Euclidean postulate that relates to all sciences is “The whole is greater than the part.” An example of a Euclidean postulate relating only to geometry is “You can draw a straight line between any two points.” Although these postulates seem extremely simple and obvious to us, Euclid was the first person to state them, as well as prove them to be true without question. These simple postulates really help with more complicated math and sciences, such as advanced geometry. For example, when doing advanced geometry involving a lot of lines and shapes, it is extremely helpful to know for sure that any single line can never contain more than one parallel line.
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
In fact, Egyptians had a belief that the condition of the world was perfect from its creation and because of that, style was kept consistently preserved within religious functions in order to symbolize ritual and belief. (Teeter, 1994, 14) However, in everyday objects a trend of evolving forms are present. The uniformity of Egyptian art was due to a standardized proportional system that employed guidelines and grids. (Teeter, 1994 14) In fact, in 2700 BCE, human figures were proportioned from a figures hairline to the soles of ones feet, in an 18 square grid with the foot given three squares alone. By 700 BCE and the Roman Era, the grid was modified and figures were elongated. (Teeter, 1994, 15) This slight change demonstrates the minor changes Egyptian Art took within a tradition of consistent practice. More often than not, workshops would produce items that were official representations of kings and deities that were supervised by palace officials or temples. Everyday objects also reflected royal or religious symbolism that made a presence in individual life in every way. Art would often reflect the relationship the people had with the temples and royalty as the Pharaoh’s were Gods on earth. Art itself is a reflection of a kingdoms wealth; economy, trade relations, and political standing that will be elaborated throughout the
Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
Many mathematicians established the theories found in The Elements; one of Euclid’s accomplishments was to present them in a single, sensibly clear framework, making elements easy to use and easy to reference, including mathematical evidences that remain the basis of mathematics many centuries later. The majority of the theorem that appears in The Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematician such as Hippocrates of Chios, Theaetetus of Athens, Pythagoras, and Eudoxus of Cnidos. Conversely, Euclid is generally recognized with ordering these theorems in a logical ...