Ancient Egyptian Numeral System 2024 PDF.pdf

Ancient EGYPTIAN NUMERAL SYSTEM  Greek Historian “My job is to report what people say, not to believe it all, and this principle is meant to apply to my whole work.” Herodotus (485-430 B.C.)...

Ancient EGYPTIAN NUMERAL SYSTEM  Greek Historian “My job is to report what people say, not to believe it all, and this principle is meant to apply to my whole work.” Herodotus (485-430 B.C.)  3 Principal Journeys Black Sea Asia Minor Egypt Herodotus (485-430 B.C.) History of Herodotus Chronicle of carefully recorded events. “Egypt is the gift of the Nile.” Speculations about the Great Pyramid Great Pyramid at Gizeh, erected about 2600 B.C. by Khufu, whom the Greeks called Cheops. According to Herodotus, 400,000 workmen labored annually on the Great Pyramid for 30 years—four separate groups of 100,000, each group employed for three months. (Calculations indicate that no more than 36,000 men could have worked on the pyramid at one time without hampering one another’s movements.) Speculations about the Great Pyramid Ten years were spent constructing a road to a limestone quarry some miles distant, and over this road were dragged 2,300,000 blocks of stone averaging 2.5 tons and measuring 3 feet in each direction. These blocks were fitted together so perfectly that a knife blade cannot be inserted in the joints. Speculations about the Great Pyramid it was the largest building of ancient times and one of the largest ever erected. When it was intact, it rose 481.2 feet (the top 31 feet are now missing), its four sides inclined at an angle of about 51°51’ with the ground, and the base occupied 13 acres—an area equal to the combined base areas of the cathedrals of Florence and Milan, St. Peter’s in Rome, and St. Paul’s Cathedral and Westminster Abbey in London. Speculations about the Great Pyramid Even more amazing was the accuracy with which it was put together. The base was almost a perfect square, no one of the four sides differing from the mean length of 755.78 feet by more than 4.5 inches. By using one of the celestial bodies, the Cheops builders were able to orient the sides of the pyramid almost exactly with the four cardinal points of the compass, the error being only fractions of 1°. 3 5 0 0 Soruce: https://www.google.com/imgres?imgurl=https%3A%2F%2Fupload.wiki media.org%2Fwikipedia%2Fcommons%2Fthumb%2F2%2F2b%2FMace- head_of_King_Narmer.jpg%2F512px-Mace- head_of_King_Narmer.jpg&tbnid=GCqE25rJV4RQvM&vet=12ahUKEwi a6PL475SBAxWCsVYBHY7cAIkQMygBegQIARBI..i&imgrefurl=https%3A %2F%2Fjoyofmuseums.com%2Fmuseums%2Funited-kingdom- museums%2Fashmolean%2Fnarmer- macehead%2F&docid=9yzdd3d5Vr8KnM&w=512&h=512&q=king%20n armer%20macehead&ved=2ahUKEwia6PL475SBAxWCsVYBHY7cAIkQM ygBegQIARBI  Horseshoe Curved Upright or heelbone rope bend finger Person holding up two hands in Vertical Lotus astonishment stroke flower tadpole Rising sun  Horseshoe Curved Upright Decimal bend or heelbone rope finger Number System (decem = ten) Person holding up two hands in Vertical Lotus astonishment stroke flower Non-positional number system tadpole Rising sun Example Non-positional number system Example 1 Example 2 Example 3  Example 4 Add 345 & 678 using Ancient Egypt Numeral Hieroglyphs  Example 5 Add 25,954 & 8,093 using Ancient Egypt Numeral Hieroglyphs  Example 6 Subtract 45 from 125 using Ancient Egypt Numeral Hieroglyphs  Example 7 Subtract 268 from 731 using Ancient Egypt Numeral Hieroglyphs “cipherization” Egyptian Multiplication Multiply: 11 x 73 11 x 73 1 73 = 73 2 146 +146 4 292 +584 8 584 803 x 16 1168 Egyptian Multiplication Multiply: 11 x 73 11 x 73 1 11 1 73 = 73 = 11 2 22 2 146 +146 +88 4 44 4 292 +584 +704 8 88 8 584 803 803 16 176 32 352 x 16 1168 64 704 x 128 1408  Egyptian Division Divide: 53 ÷ 8 35 ÷ 9 = 2 1 8 +4 2 16 +1/2 4 32 +1/8 1/2 4 6 + 1/2 + 1/8 1/4 2 1/8 1 Egyptian Division Divide: 53 ÷ 8 35 ÷ 9 1 9 = 1 2 18 +2 2/3 6 +2/3 2/9 2 +2/9 1/9 1 3 + 2/3 + 2/9 Egyptian Geometry 2 6 Volume of Truncated Square Pyramid (Frustum) 4 Example: If you are told: a truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top: You are to square this 4; result 16. You are to double 4; result 8. You are to square this 2; result 4. You are to add the 16 and the 8 and the 4; result 28. You are to take 1/3 of 6; result 2. You are to take 28 twice; result 56. See, it is of 56. You will find it right. Egyptian Geometry Volume of Truncated Square Pyramid (Frustum) There are only 25 problems in the Moscow Papyrus, but one of them contains the masterpiece of ancient geometry. Problem 14 shows that the Egyptians of about 1850 B.C. were familiar with the correct formula for the volume of frustum where h is the altitude and a and b are the lengths of the sides of the square base and square top, respectively. Rhind Papyrus The Rhind Papyrus was written in hieratic script (a cursive form of hieroglyphics better adapted to the use of pen and ink) about 1650 B.C. by a scribe named Ahmes, who assured us that it was the likeness of an earlier work dating to the Twelfth Dynasty, 1849– 1801 B.C. Although the papyrus was originally a single scroll nearly 18 feet long and 13 inches high, it came to the British Museum in two pieces, with a central portion missing. Rhind Papyrus is a kind of instruction manual in arithmetic and geometry, and it gives us explicit demonstrations of how multiplication and division was carried out at that time. It also contains evidence of other mathematical knowledge, including unit fractions, composite and prime numbers, arithmetic, geometric and harmonic means, and how to solve first order linear equations as well as arithmetic and geometric series. The Berlin Papyrus, which dates from around 1300 BCE, shows that ancient Egyptians could solve second-order algebraic (quadratic) equations. Rhind Papyrus Problem 79 There are seven houses; in each house there are seven cats; each cat kills seven mice; each mouse has eaten seven grains of barley; each grain would have produced seven hekat (unit of volume). What is the sum of all the enumerated things. Rhind Papyrus A Curious Problem (Problem 28) Think of a number, and add 2/3 of this number to itself. From this sum subtract 1/3 its value and say what your answer is. Subtract 1/10 of your answer to your answer. The result is your original number. References THE HISTORY OF MATHEMATICS: AN INTRODUCTION, SEVENTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright c 2011 by The McGraw-Hill Companies, Inc. https://www.britannica.com/science/mathematics/Mathematics-in- ancient-Egypt https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_mathematics/ https://www.storyofmathematics.com/egyptian.html/ Google Images. www.pixabay.com