a short presentation about the rhind mathematical papyrus.

1. Rhind Mathematical Papyrus
Plane and Solid Geometry
-Kaycee

2. 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.

3. 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.

4. 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.

5. 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 Papyrus
1. Book I
2. Book II
2.1 Volumes
2.2 Areas
2.3 Pyramids
3. Book III

6. Book I
The 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.

7. 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.

8. 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.

9. Book IIThe second part of the Rhind papyrus consists of
geometry problems. Peet referred to these problems as
"mensuration problems".
Volumes
Problems 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.
Areas
Problems 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.
Pyramids
The final five problems are related to the slopes of pyramids.

10. Book III
The 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 been
written 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.

11. Reference:
http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus
http://www.math.uconn.edu/~leibowitz/math2720s11/RhindPapyrus.html
Thank You!