Egyptian Math
The use of organized mathematics in Egypt has been dated back to the third millennium BC. Egyptian mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry. With their vast knowledge of geometry, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. They were also able to build the Great Pyramid with extreme accuracy.
Early surveyors found that the maximum error in fixing the length of the sides was only 0.63 of an inch, or less than 1/14000 of the total length. They also found that the error of the angles at the corners to be only 12", or about 1/27000 of a
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Isis was Osiris's wife and their son was Horus. Seth was Osiris's evil brother and Nephthys was Seth's sister (Weigel 19).
The Egyptians divided their year into 3 seasons that were 4 months each. These seasons included inundation, coming-forth, and summer. Inundation was the sowing period, coming-forth was the growing period, and summer was the harvest period. They also determined a year to be 365 days so they were very close to the actual year of 365 ¼ days (Gillings 235).
When studying the history of algebra, you find that it started back in Egypt and Babylon. The Egyptians knew how to solve linear (ax=b) and quadratic (ax2+bx=c) equations, as well as indeterminate equations such as x2+y2=z2 where several unknowns are involved (Dauben).
The earliest Egyptian texts were written around 1800 BC. They consisted of a decimal numeration system with separate symbols for the successive powers of 10 (1, 10, 100, and so forth), just like the Romans (Berggren). These symbols were known as hieroglyphics. Numbers were represented by writing down the symbol for 1, 10, 100, and so on as many times as the unit was in the given number. For example, the number 365 would be represented by the symbol for 1 written five times, the symbol for 10 written six times, and the symbol for 100 written three times. Addition was done by totaling separately the units-1s, 10s, 100s, and so forth-in the numbers to be added.
“The Ancient Egyptians believed that there was more to life than just the life they had on earth. Much of their architecture inspired by these beliefs, including the pyramids and the houses they built were based on strict rules of mathematics and geography. (Parulekar pg 1)”. It has beendiscovered that the numbers of pi have been greatly incorporated in the building and design of Ancient Egyptian architecture. The Ancient Egyptians built their homes and monuments very symmetrically and with lots of greenery (Also thought to keep harmony among the people).
Ancient Egypt is one of the earliest civilizations in the world. Beginning with their Predynastic Period in circa 5000 BCE, the Egyptians began to cultivate their way of life. Independently ruling until the conquest of Alexander the Great in 332 BCE, the Egyptians continued to influence and be influenced by other cultures, like the Greeks and Romans. However, unlike the Greeks, the Egyptians incorporated their religious thinking into everyday life, believing that the sky was the heavens and the sun, moon, and stars were gods. During the thousands of years the ancient Egyptians lived, they developed calendars and constellations that inspired later calendars until the calendar that is used today was created. The ancient Egyptians used astronomy to create calendars, believing that the sun and the stars were their gods.
Ancient Egyptians developed a writing system based on pictures, known as hieroglyphics. The difference between cuneiform and hieroglyphics was hieroglyphics stood not only for ideas or objects, but also sounds. According to document four, Egyptians also created papyrus, the first paper, in order to keep records.
Among the many scholars working in the House of Wisdom, there was Al-Khawarizmi, known as the father of algebra. Born around 800 in Baghdad, al-Khwarizmi worked in the House of Wisdom as a scholar. Being involved in the center’s translation of ancient scientific knowledge helped him develop a unique knowledge of the accumulated wisdom of the world. His importance lies in his discoveries of mathematical knowledge which was later transferred to Arab and European scholars. His masterpiece, a book of clear explanations of what would become algebra, was his entire life’s work compiled into one collection of information. The word algebra comes from the Arabic word, al-jabr, which means “completion”. In his work, al-Khwarizmi explains the principles of solving linear and quadratic equations, the concept that an equation can be created to find the value of an unknown variable. Another crucial work of al-Khwarizmi’s was The Book on the Art of Reckoning of the Hindus, which introduced the numbering system used in the Islamic culture to the west. This is the numerical system that is still used today and offered many advantages over the existing Roman numerals. An
Religion was not a monolithic institution, it consisted of a large variety of different beliefs and practices, all of which were linked by the common focus on the interaction between the Egyptian people and the divine realm, as the gods of this realm linked the Egyptian understanding of the world. As the Ancient Egyptian Religion was an integral part of ancient Egyptian society. Polytheism the belief of multiple deities usually assembled into a pantheon of gods and goddesses along with their own mythologies and rituals was an essential aspect of ancient Egyptian religion. As the Ancient Egyptian religion included a large and diverse pantheon of gods and goddesses, and around these deities arose a rich mythology that helped explain the
Geb’s son, Osiris, was the god of afterlife. He was murdered by his own brother Seth, which they think was the cause of the droughts, but his miraculous rebirth caused the flooding of the Nile valley. He was married to his sister Isis and had a son named Horus. Osiris also had another sister, Nephthys. It was said that Osiris was the one who brought civilization to the ancient Egyptian. He left and showed the Egyptians many things, but while he was gone Seth planned to kill him. His plan worked, he killed Osiris and threw him into the Nile River, but Isis found his body only to let Seth rip it into 14 pieces. Isis and Nephthys worked together and found every piece except one, which was eaten by the Nile fish. Isis recovered him just long enough to have Horus, which would be the future king of Egypt.
The map and map key on “Document A: Ancient Egypt,” reveals that it had two deserts in the east and in the west, the Mediterranean Sea in the north, and the first and second cataract in the south. Most, if not all, of the settlements and cities were located in or very close to the Fertile Nile Valley because of the Nile’s plentiful water sources and silt, fertile soil carried by the river which was perfect for farming. Three main seasons revolved around the river: Akhet, Peret, and Shemu. Akhet was the flood season, which was between mid-June and mid-October. During this time of year, farmers would work off their public-labor tax since all the floodplains were heavily flooded. Mid-October to mid-February was called Peret, or the planting and growing season. This is when the Nile was high enough to fill irrigation canals and farmers were able to plant and tend crops. Last was the harvest season, known as Shemu, which takes place mid-February to mid-June. Without the seasons the river provided, it would be impossible for the people to grow crops for them to eat and
According to Document B, the Egyptians followed a calendar of three seasons,: Akhet, Peret, and Shemu. Akhet was mid June- mid October which was also known as the flooding season. Since it was the flooding season, the Ancient Egyptians could not farm,
A similarity between the ancient Egyptians and Greek is the use of what is now known as geometry. It is currently thought that the Egyptians had introduced the earliest fully-developed base-ten numeration system, this system was introduced around 2700 BCE, and was based. On people having ten fingers (story of mathematics). A famous document of the time was the Rhind Papyrus, created 1650 BC, and contained information and exercises to show the “Correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.” (Washington.edu). The Egyptians had also approximated the area of
Instead, their seasons were consisted on the basis of when was the optimum time to plant their crops and cultivate the land. One expert points out that, “Between June and September in a season the Egyptians called akhet” (Seawright). This was not an optimum time for harvesting because the lands were all flooded from the Nile waters and people tended to stay indoors due to the high tide of the waters. The remaining seasons consisted of, according to a researcher, “peret (growing), and shemu (harvesting)” (Seawright). During the growing season, the Egyptians used different forms of irrigation in order to grow the crops more efficiently. Followed by the growing season, came the harvest season. The Egyptians would cultivate the land from what they had grown in order to feed their families as well as to make offerings. They made offerings to the pharaoh in hopes of future success in farming and with the flood waters, as well as to the multiple gods that they worshiped such as Hapi. They gave offerings to him in hopes that he would once again allow the Nile to flood again to allow the farmers to have another successful attempt at harvesting and providing for the many inhabitants that lived in the Nile River Basin. Climate was only the first aspect that ruled.
Egypt of the pharaohs is best known for its great monuments and feats of engineering (such as the Pyramids), but it also made great advances in many other fields too. The Egyptians produced early forms of paper and a written script. They developed the calendar too and made important contributions in various branches of mathematics, such as geometry and algebra, and it seems likely that they understood and perhaps invented the use of zero. They made important contributions in mechanics, philosophy, irrigation and architecture. In medicine, the Egyptians understood the body’s dependence on the brain over 1000 years before the Greek scholar Democritus. Some historians now believe that ancient Egypt had an important influence on ancient Greece, and they point to the fact that Greek scholars such as Pythagoras and Archimedes studied in Egypt, and that the work of Aristotle and Plato was largely based on earlier scholarship in Egypt. For example, what is commonly known as Pythagoras’ theorem, was known to the ancient Egyptians hundreds of years before Pythagoras’ birth.
The mathematics had been developed for four thousand years, and Muslim inherited mathematics from Egyptian, Mesopotamians, Sumerian and Babylonian. Greek geometry and Hindu arithmetic and algebra reached at an early stage in Muslim lands and were translated in centers such as Gondeshapur and Baghdad. Starting out at intellectual center of Islam, they soon criticizing those concepts and formulation by finding inaccurate and inconsistent information and adapt their own ideas. At the same period in Western Europe, they still use Roman numerals and abacus to calculate numbers. The Babylonian already had concept of bases sixty computation with place value numerals. Muslim then developed a decimal arithmetic based on place value and joint concept of zero. In the ninth century, Banu Musa brothers who were three gifted sons of Musa, Muhammad, Ahmad, and Hassan ibn Musa lived in Baghdad studied problems in constructing interrelated geometrical figures. Later the characteristic of those line, space of geometrical shape was given intense study and utilized sophisticated geometry in designing waterwheels, in improving farming equipment, in developing new type of weapon used at war. Another person who make significant contribution on mathematics is Muhammad ibn al-Khwarizmi, a Persian born in the eighth century. He was the first person who originated both terms “algebra”, and
Omar was also a poet, philosopher, and astronomer. Omar’s works were translated in 1851, which was research on Euclid’s axioms. In the medieval period, he expanded on Khwarizmi’s and the Greeks mathematic works. He only worked with cubic equations only and focused on geometric and algebraic solutions of equations. In 1145AD, Al-Khwarizmi’s book was translated by Robert Chester, which made it possible for algebra to be introduced to Europe. After algebra was introduced in Europe, European mathematicians developed and expanded on algebra concepts. Even though algebra began in the Arabic countries, once European mathematicians obtained the information of algebra, they became the leaders of mathematical discoveries in the world (“Mathematics”).
There are many civilizations in history that contributed to the rise of modern day society. All of the things that we see today have been in some way shape or form improved upon to stand the test of time. From the structures of buildings, religion and pyramids, to the influence of art, it all played a part. The ancient civilization of the Egyptians was one of the most significant and well known cultures to ever have existed and technology wise, they were light years ahead.
The Egyptians used sums of unit fractions (a), supplemented by the fraction B, to express all other fractions. For example, the fraction E was the sum of the fractions 3 and *. Using this system, the Egyptians were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra. In geometry, the Egyptians calculated the correct areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. To find the area of a circle, the Egyptians used the square on U of the diameter of the circle, a value of about 3.16-close to the value of the ratio known as pi, which is about 3.14. The Babylonian system of numeration was quite different from the Egyptian system. In the Babylonian system-which, when using clay tablets, consisted of various wedge-shaped marks-a single wedge indicated 1 and an arrowlike wedge stood for 10 (see table). Numbers up through 59 were formed from these symbols through an additive process, as in Egyptian mathematics. The number 60, however, was represented by the same symbol as 1, and from this point on a positional symbol was used. That is, the value of one of the first 59 numerals depended henceforth on its position in the total numeral. For example, a numeral consisting of a symbol for 2 followed by one for 27 and ending in one for 10 stood for 2 × 602 + 27 × 60 + 10.