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 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 The beginning of Egyptian Math

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 how 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

b. Alexandria, Egypt, c. 370 ce, d. Alexandria, 415 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, keep.org/~kunoichi/kunoichi/themestream/egypt_maths.html pg1,2 O’Conner J. J., A. A., Robertson E F B. B. December 2000 Egyptian Numerals. December 2000, from pg.3,4,5,6http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Egyptian_numerals.html O’ Conner J. J., A. A., Robertson E F B. B. January 1997 Ahmes. January from pg. 3 Hupatia of Alexandria Copyright pg8