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# History on Egyptian Algebra

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on 18 September 2012#### Transcript of History on Egyptian Algebra

Egyptian Algebra By Tori Shannon •The Egyptians could solve three different types of equations; linear (ax = b) quadratic (ax2 + bx = c) and indeterminate equations such as x2 + y2 = z2.

•The method the Egyptians used was what is now called, the "method of false position” and the way the way the method worked made it almost impossible to divide and multiply.

•The Egyptians stated and solved their “problems” or equations verbally and never used symbols and although it was VERY difficult to divide and multiply, they were very good with fractions and made it possible by editing errors later. With the knowledge the Egyptians had, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. With this they were able to build the Great Pyramid with extreme accuracy.

Most of our knowledge on ancient Egyptian algebra came from the “book;” Rhind papyrus which was written about 1650 B.C.

Culture started to make its contribution towards their algebraic studies in 250 B.C. The End! Hope You Enjoyed :) Work Cited!

Aleff, Peter. "Math Contributions from Ancient Egypt." Contributions from Egyptian Math.

Recovered Science, 2012. Web. 18 Sept. 2012. <http://www.recoveredscience.com/const130egymathcontributions.htm>.

Boyer, Carl B. "Egyptian Mathematics." Wikipedia. Wikimedia Foundation, 09 Aug. 2012. Web.

18 Sept. 2012. <http://en.wikipedia.org/wiki/Egyptian_mathematics>.

Counter, Hit. "The History of Algebra." Highlights in the History of Algebra. © Copyright 2000

by the University of Louisiana at Lafayette Computing Support Services, 12 Nov. 2002. Web. 18 Sept. 2012. <http://www.ucs.louisiana.edu/~sxw8045/history.htm>.

"Films for the Humanities and Sciences - Culture and Math: The Egyptians." Culture and Math:

The Egyptians. © Films Media Group, n.d. Web. 18 Sept. 2012. <http://ffh.films.com/id/15947/Culture_and_Math_The_Egyptians.htm>.

Gardner, Milo. "When Did Algebra Begin?" When Did Algebra Begin? Blog at WordPress.com.

RSS Entries and RSS Comments Powered by WordPress.com, 13 Dec. 2011. Web. 18 Sept. 2012. <http://profkeithdevlin.org/2011/12/13/when-did-algebra-begin/>.

"History of Algebra." History of Algebra. Algebra.com, n.d. Web. 18 Sept. 2012.

<http://www.algebra.com/algebra/about/history/>. One of the key contributors to Egyptians algebra studies was Herodotus.

Another key contributor was Proclus in his Commentary on Euclid.

Aristotle was another key contributor in Egyptian algebra.

Democritus was also credited with studies in Egyptian algebra.

Lastly there was Abu Kamil, who was an ancient egyptian mathematician. The “book” Rhind papyrus was written in 1650 B.C., but their achievements so far placed them in the mathematics state of 1850 B.C. This book contained, what are called, “Aha problems,” but only four.

Although they have the Rhind papyrus, there is also the Moscow Mathematical papyrus that was used for algebra. This “book” also included “Aha problems” which involve finding unknown quantities.

One of the greatest ways the Egyptians used there algebraic skills was in the building process of a pyramid. There most successful pyramid was the Great Pyramid at Giza. The algebraic writings show that the scribes used (least) common multiples to turn problems with fractions into problems using integers.

The multiplicative factors were often recorded in red ink and are referred to as “Red auxiliary numbers.”

The Egyptians were the first civilization to develop and solve second-degree, quadratic, equations. This information was found in a fragment of the Berlin Papyrus.

The great Abu Kumal stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and z such that x + y + z = 10, x2 + y2 = z2, and xz = y2.

A result of using algebra was pleasure. There was a game that Plato would play with young children to teach them. It was a “think of a number, and i will get it” type game.

The Egyptians had a decimal system using seven different symbols.

1 is shown by a single stroke.

10 is shown by a drawing of a hobble for cattle.

100 is represented by a coil of rope.

1,000 is a drawing of a lotus plant.

10,000 is represented by a finger.

100,000 by a tadpole or frog

1,000,000 is the figure of a god with arms raised above his head.

A key contributor in the culture was the Nile River. The Egyptians made all these calculations around the Niles flow, etc.

Another key contributor in the culture was pleasure for the pharaohs. The mathematicians would create games to puzzle you pleasingly.

One key contributor that really had the Egyptians pumped was they needed algebra for science. Because of this, they needed to get ahead in math so they could keep up embalming, etc.

A key contributor that has to do with culture and everyday life is the fact that, they needed to know math like the back of their hand if they were to be building afterlife homes for their pharaohs, or living gods to live in for eternal life.

Lastly, a really big reason, or key contributor, for the Egyptians to study and know algebra, is because they had taxes and trades to deal with and algebra is created to take away a few steps and try and make long equations easier, so that was very helpful.

Full transcript•The method the Egyptians used was what is now called, the "method of false position” and the way the way the method worked made it almost impossible to divide and multiply.

•The Egyptians stated and solved their “problems” or equations verbally and never used symbols and although it was VERY difficult to divide and multiply, they were very good with fractions and made it possible by editing errors later. With the knowledge the Egyptians had, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. With this they were able to build the Great Pyramid with extreme accuracy.

Most of our knowledge on ancient Egyptian algebra came from the “book;” Rhind papyrus which was written about 1650 B.C.

Culture started to make its contribution towards their algebraic studies in 250 B.C. The End! Hope You Enjoyed :) Work Cited!

Aleff, Peter. "Math Contributions from Ancient Egypt." Contributions from Egyptian Math.

Recovered Science, 2012. Web. 18 Sept. 2012. <http://www.recoveredscience.com/const130egymathcontributions.htm>.

Boyer, Carl B. "Egyptian Mathematics." Wikipedia. Wikimedia Foundation, 09 Aug. 2012. Web.

18 Sept. 2012. <http://en.wikipedia.org/wiki/Egyptian_mathematics>.

Counter, Hit. "The History of Algebra." Highlights in the History of Algebra. © Copyright 2000

by the University of Louisiana at Lafayette Computing Support Services, 12 Nov. 2002. Web. 18 Sept. 2012. <http://www.ucs.louisiana.edu/~sxw8045/history.htm>.

"Films for the Humanities and Sciences - Culture and Math: The Egyptians." Culture and Math:

The Egyptians. © Films Media Group, n.d. Web. 18 Sept. 2012. <http://ffh.films.com/id/15947/Culture_and_Math_The_Egyptians.htm>.

Gardner, Milo. "When Did Algebra Begin?" When Did Algebra Begin? Blog at WordPress.com.

RSS Entries and RSS Comments Powered by WordPress.com, 13 Dec. 2011. Web. 18 Sept. 2012. <http://profkeithdevlin.org/2011/12/13/when-did-algebra-begin/>.

"History of Algebra." History of Algebra. Algebra.com, n.d. Web. 18 Sept. 2012.

<http://www.algebra.com/algebra/about/history/>. One of the key contributors to Egyptians algebra studies was Herodotus.

Another key contributor was Proclus in his Commentary on Euclid.

Aristotle was another key contributor in Egyptian algebra.

Democritus was also credited with studies in Egyptian algebra.

Lastly there was Abu Kamil, who was an ancient egyptian mathematician. The “book” Rhind papyrus was written in 1650 B.C., but their achievements so far placed them in the mathematics state of 1850 B.C. This book contained, what are called, “Aha problems,” but only four.

Although they have the Rhind papyrus, there is also the Moscow Mathematical papyrus that was used for algebra. This “book” also included “Aha problems” which involve finding unknown quantities.

One of the greatest ways the Egyptians used there algebraic skills was in the building process of a pyramid. There most successful pyramid was the Great Pyramid at Giza. The algebraic writings show that the scribes used (least) common multiples to turn problems with fractions into problems using integers.

The multiplicative factors were often recorded in red ink and are referred to as “Red auxiliary numbers.”

The Egyptians were the first civilization to develop and solve second-degree, quadratic, equations. This information was found in a fragment of the Berlin Papyrus.

The great Abu Kumal stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and z such that x + y + z = 10, x2 + y2 = z2, and xz = y2.

A result of using algebra was pleasure. There was a game that Plato would play with young children to teach them. It was a “think of a number, and i will get it” type game.

The Egyptians had a decimal system using seven different symbols.

1 is shown by a single stroke.

10 is shown by a drawing of a hobble for cattle.

100 is represented by a coil of rope.

1,000 is a drawing of a lotus plant.

10,000 is represented by a finger.

100,000 by a tadpole or frog

1,000,000 is the figure of a god with arms raised above his head.

A key contributor in the culture was the Nile River. The Egyptians made all these calculations around the Niles flow, etc.

Another key contributor in the culture was pleasure for the pharaohs. The mathematicians would create games to puzzle you pleasingly.

One key contributor that really had the Egyptians pumped was they needed algebra for science. Because of this, they needed to get ahead in math so they could keep up embalming, etc.

A key contributor that has to do with culture and everyday life is the fact that, they needed to know math like the back of their hand if they were to be building afterlife homes for their pharaohs, or living gods to live in for eternal life.

Lastly, a really big reason, or key contributor, for the Egyptians to study and know algebra, is because they had taxes and trades to deal with and algebra is created to take away a few steps and try and make long equations easier, so that was very helpful.