Rhind Mathematical Papyrus

Plane and Solid Geometry-Kaycee

The RHIND PAPYRUS

The Rhind Mathematical Papyrus, which is also known as the Ahmes Papyrus, is the major source of our knowledge of the mathematics of ancient Egypt.

It was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1650 BCE.

Mr. A. Henry Rhind, a Scottish lawyer, visited Egypt.Rhind purchased the papyrus in Luxor, Egypt, in 1858. In later years, it was willed to the British Museum, where it remains today. A piece missing from the center of the papyrus was located in New York City many years later and was restored to the Rhind Papyrus after 1922.

The papyrus is in the form of a scroll about 12-13 inches wide and 18 feet long, written from right to left in hieratic script on both sides of the sheet, in black and red inks. After identifying himself as the writer, the scribe Ahmes begins by saying that he has copied this work from a very old scroll from the period of the Middle Kingdom, a couple of hundred years earlier.

Ahmes begins with an announcement, that he will provide a "complete and thorough study of all things" and will reveal "the knowledge of all secrets.“.

Contents Of Rhins Papyrus1. Book I2. Book II 2.1 Volumes 2.2 Areas 2.3 Pyramids3. Book III

Book IThe first part of the Rhind papyrus consists of reference tables and a collection of 20 arithmetic and 20 algebraic problems. The problems start out with simple fractional expressions, followed by completion (sekhem) problems and more involved linear equations.The first part of the papyrus is taken up by the 2/n table.

The first fraction table occupies a large part of the manuscript. For each odd integer n from 5 through 101, it gives a decomposition of twice the unit fraction 1/n into a sum of distinct UNIT FRACTIONS, fractions whose numerator is 1. This table is not just a list of facts; every entry is either derived from scratch or is verified in detail.The second fraction table decomposes one tenth of n as a sum of distinct unit fractions, for n = 1, 2, ..., 9.

After these two tables, the scribe recorded 84 problems altogether and problems 1 through 40 which belong to Book I are of an algebraic nature.Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 and 1 + 2/3 + 1/3 by different fractions. Problems 21–23 are problems in completion, which in modern notation is simply a subtraction problem. The problem is solved by the scribe to multiply the entire problem by a least common multiple of the denominators, solving the problem and then turning the values back into fractions. Problems 24–34 are ‘’aha’’ problems. These are linear equations. Problem 32 for instance corresponds (in modern notation) to solving x + 1/3 x + 1/4 x = 2 for x. Problems 35–38 involve divisions of the hekat. Problems 39and 40 compute the division of loaves and use arithmetic progression.

Book IIThe second part of the Rhind papyrus consists of geometry problems. Peet referred to these problems as "mensuration problems".VolumesProblems 41 – 46 show how to find the volume of both cylindrical and rectangular based granaries. In problem 41 the scribe computes the volume of a cylindrical granary.AreasProblems 48–55 show how to compute an assortment of areas. Problem 48 is often commented on as it computes the area of a circle. The scribe compares the area of a circle (approximated by an octagon) and its circumscribing square. Each side is trisected and the corner triangles are then removed.PyramidsThe final five problems are related to the slopes of pyramids.

Book IIIThe third part of the Rhind papyrus consists of a collection of 84 problems. Problem 61 consists of 2 parts. Part 1 contains multiplications of fractions. Part b gives a general expression for computing 2/3 of 1/n, where n is odd. In modern notation the formula given.Problems 62–68 are general problems of an algebraic nature. Problems 69–78 are all pefsu problems in some form or another. They involve computations regarding the strength of bread and or beer. Problem RMP 79 sums five terms in a geometric progression. It is a multiple of 7 riddle, which would have beenwritten in the Medieval era as, "Going to St. Ives" problem. Problems 80 and 81 compute Horus eye fractions of henu(or hekats). Problem 81 is followed by a table.The last three problems 82–84 compute the amount of feed necessary for fowl and oxen.

Reference:http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrushttp://www.math.uconn.edu/~leibowitz/math2720s11/RhindPapyrus.html

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