Rhind Papyrus Problems
Date: 03/23/99 at 10:37:41 From: Byron Subject: The Rhind Papyrus equations We would like to know the equations on the Rhind Papyrus.
Date: 03/23/99 at 13:35:53 From: Doctor Rick Subject: Re: The Rhind Papyrus equations Hi, Byron, welcome to Ask Dr. Math! I have been reading about Egyptian and other ancient math lately - I find it fascinating! The Rhind papyrus, named for the man who discovered it in 1858, is sometimes called the Ahmes papyrus for the scribe who wrote it around 1650 BC. It is a roll 1 foot high and 18 feet long. It starts, as I understand it, with some numerical tables - tables of "Egyptian fractions." After these come 84 math problems with solutions. A lot of the problems would look pretty simple to you - for instance, if you have 1, 2, 6, 7, 8, or 9 loaves and you want to divide them equally among 10 men, what fraction of a loaf does each man get? This kind of problem was harder for the Egyptians because of the way they wrote fractions. An Egyptian fraction is a sum of fractions that all have 1 in the numerator (as we write it). Actually they would also use 2/3; they had a special symbol for it. Other problems are multiplication and division problems. Problem 13, for instance, is to multiply 1/16 + 1/112 by 1 + 1/2 + 1/4. Problem 70 is to find the quotient of 100 divided by (7 + 1/2 + 1/4 + 1/8). Still other problems deal with proportions. Problem 63: How do you divide 700 loaves among 4 people in the ratio 2/3 : 1/2 : 1/3 : 1/4. There are a few problems that might be called algebra, although I think some math historians would not want to call it this. These were still pretty simple given our algebraic methods, for instance, problem 24 (in algebraic terminology): what is x if x + x/7 = 19? They didn't use the distributive property as we would. Instead they guessed a value for x; say, 7. With this value, x + x/7 = 8. If you multiply x by 19/8 (2 + 1/4 + 1/8 as an Egyptian fraction), you get the correct value of x, which is 133/8 or 16 + 1/2 + 1/8. But my source says that there is one such problem that is solved by the distributive property: Problem 30, x + 2/3 x + 1/2 x + 1/7 x = 37, is solved by dividing 37 by (1 + 2/3 + 1/2 + 1/7). That's about it, but remember, this is from 1650 BC, and it is supposed to be a copy of a document 200 or more years older! The math you learn in school has been built over many generations on foundations like what we find in the Rhind papyrus. If you were left to figure out math on your own, you might never come up with the things the Egyptians had figured out. My source is a book, _A History of Mathematics_, 2nd ed., by C. Boyer and U. Merzbach, 1988. You can find some on-line material on Egyptian mathematics here: History Topics Index, MacTutor Math History Archives (look for Babylonian and Egyptian Mathematics) http://www-groups.dcs.st-and.ac.uk/~history/HistoryTopics.html Egyptian Math (Interlochen Arts Academy) http://www.interlochen.k12.mi.us/Math/EgyptianMath/MathInEgypt.html This last site includes this page on the Rhind papyrus (differing in some minor details from what my source said): http://www.interlochen.k12.mi.us/Math/EgyptianMath/Rhind.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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