Egyptian Mathematical History Created by Christina Gomez Egyptian

Egyptian Mathematical History Created by Christina Gomez

Egyptian Numbering System The Egyptian numbering system was used for – – – – Measuring time Straight lines Level of Nile River flooding Calculating areas of land Counting money Working out taxes Cooking

Ahmes The beginning of Egyptian Math Who was Ahmes? – Before 1700 B. C. there was a well known priest by the name of Ahmes What did this priest do during that era? – During this era Ahmes created a collection known as “Directions for knowing all dark things” – His collection included problems in geometry and arithmetic – What his collection didn’t show was the solution to the problems What does his work show? – Ahmes states in his work that a circular field with a diameter of 9 units is equal in area to a square with sides of 8 units – Modern notation would show it as &pi(9/2)2=82 – This leads to the value of Pi equals to 3. 16049

Egyptian Engineering • Egyptians used Papyrus to write hieratic scripts used for engineering – Rhind Papyrus a mathematical textbook dated 1832 B. C. – Relics of the Rhind textbook show engineers calculated proportions of pyramids and other structures – This is evidence that algebra was already being used in the Nile Valley

Egyptian Numeral Hieroglyphs • Hieroglyphs are little pictures representing words. – An illustration of an English sentence: "an eye", "an ear", "bark of tree" + "head with crown", "a dog". • The Egyptians used a system 10 of hieroglyphs for numerals. – separate symbols were used for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million.

Hieroglyphs as fractions • • Adding numeral hieroglyphs is easy. Adding the one symbol but replacing 10 symbols by a single symbol of the next higher value. Fractions to Egyptians were limited to unit fractions (with the exception of the frequently used 2/3 and less frequently used 3/4). The unit fraction is 1/n meaning n is the integer but placing the symbol representing a “mouth, ” meaning “part” on top of the number.

Hieratic Numerals • Hieroglyphs did not continue all through the two thousand or the years of the ancient Egyptian civilization, instead they were broken down in three periods of time: – Old Kingdom - around 2700 BC to 2200 BC – Middle Kingdom - around 2100 BC to 1700 BC – New Kingdom - around 1600 BC to 1000 BC

Hieratic Numerals • • • The Egyptians also invented the Hieratic Numerals. The numerals were written in a more compacted form but also required more symbols to be remembered. Each had individual symbols for: – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000

Hypatia of Alexandria b. Alexandria, Egypt, c. 370 ce, d. Alexandria, 415 The only famous female woman Scholar in ancient Egypt • Studied under the tutoring of her father Theon of Alexandria • A teacher and wrote many books on mathematics along with criticisms of philosophical and mathematical concepts. • Teacher at Alexandria’s Neoplatonic School • History records report Hypathia helped to invent mechanical devices such as the plane astrolabe that was used by Greek astronomers to determine the position of the sun and the stars • Other works of Hypathia – brass hydrometer which measures specific gravity of liquid – Hydroscope which was used to observe objects under water

Sources Seawright Caroline, A. A. , March 10, 2001 The Ancient Egyptian Number System. March 10, 2001, http: //www. the keep. org/~kunoichi/themestream/egypt_maths. html pg 1, 2 O’Conner J. J. , A. A. , Robertson E F B. B. December 2000 Egyptian Numerals. December 2000, from http: //www-groups. dcs. st-and. ac. uk/~history/Hist. Topics/Egyptian_numerals. html pg. 3, 4, 5, 6 O’ Conner J. J. , A. A. , Robertson E F B. B. January 1997 Ahmes. January 1997. from http: //www-history. mcs. st-andrews. ac. uk/Biographies/Ahmes. html pg. 3 Hupatia of Alexandria Copyright 2009 http: //www. answers. com/topic/hypatia-of-alexandria pg 8