Rae Steinheiser
Grubisic
Honors Algebra I Period 6
1 May 2014
Writing Assignment: Math of the Ancient Egyptians
Introduction
The Ancient Egyptians are commonly known as the first people to use geometry. Not only did they use it, but they were masters of it. Their work constructing the pyramids only provides evidence of their vast mathematical knowledge. The Ancient Egyptians invented many different mathematical techniques in order to make daily life easier. Luckily, there are still records from the Egyptians that have been decoded so that we may learn how they invented their version of math.
The Reason for Math
The Egyptians used math very heavily in their daily life. Since the Egyptians at that time had no money, participating in trade and market required knowledge of fractions. Since the Egyptians need the most precise calculations, they only used unit fractions, aside from the fraction 2/3. Because they didn’t round off their numbers, the closest possible answer was produced. Another peril of life in Egypt that was solved by math was the need for a calendar. Since the Nile flooded every season, a calendar was developed in order to specify the times of the floods, the planting season, and the harvest season.
The Egyptian Number System
The very first numbers were symbolized using simple tally marks. But as time went on, the number system became more complex. It evolved into a numeric decimal system based on the number ten because of our ten fingers. This system had symbols for a wide range of numbers starting at one and reaching up to one million. The system the Ancients used had no place-system and no number for zero. It also had no symbols for an equal sign, a plus sign, a minus sign, and so on. These attributes make this s...
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... division tables, as well as the measurements of areas and volumes. However, everything in this papyrus was only in an equation form; there were no mathematical theorems.
In the Rhind Papyrus is found the earliest known algorithm. This problem shows how to find 2/3 of 1/5. There is also an explanation of how to use multiplication. The table shows that on one half of the paper is the factor you are multiplying by. On the other half is the factor being multiplied. With each increasing number, the factor being multiplied simply shows continuous addition.
The math of the Ancient Egyptians is both simple and complex. With their methods of math usage, they could find complex and definite solutions to any problem. This especially came in handy for everyday challenges, not just record keeping and pyramid building. The math of the Egyptians is both extensive and accurate.
Thoughts regarding math was on a very basic level and was simple for the Yupiaq. The Yupiaq do not think in additive or qualities of things. Since the Yupiaq were a tribe of hunter-gatherers, to use fish as an example, they would estimate what could fulfill their needs by acquiring enough that could fit in a box. They knew that the women could not clean any more fish than that in one day, so there was no need to take more than that. They also used math in the concept of time for traveling, basically how long it would
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 calendars and the calculations made are very important to the people’s culture and the importance of time. The Egyptians, Gregorian's, and the Mayans calendar all represent the importance of time in their culture. Each of these has different forms of finding the times and the creations of the calendars. The Egyptians created their calendars based on the Sirius, the Gregorian's creation was based on the Julian calendar, and the Mayans calendar was due to their astronomical table calculations. Each of these shows the different creations based on the people's cultures and beliefs.
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.
Like the Mesopotamians, the Egyptians also believed in god and goddesses and was one of the first to develop their unique writing system called hieroglyphics. Egyptian’s also were the first to construct triangular pyramids with magnificent tombs to bury their dead pharaohs and queens. These pyramids were very comparable to the ziggurats built by the Mesopotamians. The Egyptians unlocked more access when they started using papyrus to make paper in order to communicate. They also inven...
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, who lived from about 330 B.C.E. to 260 B.C.E., is often referred to as the Father of Geometry. Very little is known about his life or exact place of birth, other than the fact that he taught mathematics at the Alexandria library in Alexandria, Egypt during the reign of Ptolemy I. He also wrote many books based on mathematical knowledge, such as Elements, which is regarded as one of the greatest mathematical/geometrical encyclopedias of all time, only being outsold by the Bible.
Geometrical Progressions Model of Base 10 numeration. The use of Horus eye fractions or just “Fractions” shows geometrical Progression. For example, the egyptians used to simplify fractions like ½=50% or Half of a loaf of bread. These terms were also used with exponents like ½+n=?. We in fact still use the
The foundations of mathematics are strongly rooted in the history and way of life of the Egyptian people, dating back to the fourth millennium B.C. in Egypt. Egyptian mathematics was elementary. It was generally arrived at by trial and error as a way to obtain desired results. As such, early Egyptian mathematics were primarily arithmetic, with an emphasis on measurement, surveying, and calculation in geometry. The development of arithmetic and geometry grew out of the need to develop land and agriculture and engage in business and trade. Over time, historians have discovered records of such transactions in the form of Egyptian carvings known as hieroglyphs.
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
Due to archeological evidence we know that the African people were the first people in the world to use counting to keep track of their things, or time. Around 35,000 BC, in South Africa the earliest known tally stick was made, and was left in Lebombo Cave. 29 notches were cut into the stick. We don't know exactly what they were counting. Some people think they were counting the days from one moon phase to the next, but it could have been something else. Just as well. Now, what we do see is that by 35,000 BC people in South Africa had the idea of keeping records by making marks. “The Lebombo bone is a baboon fibula with a set of 29 notches carved in it. Archeologists believe these marks are evidence of a primitive calendar, measuring either the lunar or the menstrual calendar. This artifact is incredibly important for unders...
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics (“Archimedes”).
By the time the Babylonians and Egypt developed their mathematics; Indians had worked independently and made an advanced mathematical discovery. During the early time of Indian, they were already familiar with arithmetic operations such as addition, multiplication, subtraction, multiplication, fractions, squares, cubes and roots. The evidence of using Pythagorean triples was also traced as part of Hindu mathematics long before Pythagoras. The Indian text known as “Sulba Sutras” contains a geometric approach in finding the solutions of linear and quadratic equations. The use of circle to represent zero is usually attributed to Hindu mathematics. Early Indians are also known to be the first to establish the basic mathematical rules for dealing with zero. They had also established the laws that could be used to manipulate and perform calculation on negative numbers, something that was not manifested in unearthed mathematical works of other ancient mathematics. Brahmagupta, a Hindu mathematician, showed that quadratic equations could have two possible solutions and one of which could be negative.
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.