# Book:Richard J. Gillings/Mathematics in the Time of the Pharaohs

## Richard J. Gillings: Mathematics in the Time of the Pharaohs

Published $\text {1972}$, MIT Press

ISBN 0-486-24315-X.

### Subject Matter

• History of Mathematics in Ancient Egypt

### Contents

Preface
$1$ Introduction
$2$ Hieroglyphic and Hieratic Writing and Numbers
$3$ The Four Arithmetic Operations
multiplication
division
fractions
$4$ The Two-Thirds Table for Fractions
problems 61 and 61b of the rhind mathematical papyrus
two-thirds of an even fraction
an extension of rmp 61b as the scribe may have done it
examples from the rhind mathematical papyrus of the two-thirds table
$5$ The G Rule in Egyptian Arithmetic
further extensions of the g rule
$6$ The Recto of the Rhind Mathematical Papyrus
the division of 2 by the odd numbers 3 to 101
concerning primes
further comparison of the scribe's and the computer's decompositions
$7$ The Recto Continued
even numbers in the recto: 2 $\div$ 13
multiplies of divisors in the recto
two divided by thirty-five: the scribe discloses his method
$8$ Problems in Completion and the Red Auxiliaries
use of the red auxiliaries or reference numbers
an interesting ostracon
$9$ The Egyptian Mathematical Leather Roll
the first group
the second group
the third group
the fourth group
the number seven
line 10 of the fourth group
the fifth group
$10$ Unit-Fraction Tables
unit-fraction tables of the rhind mathematical papyrus
problems 7 to 20 of the rhind mathematical papyrus
$11$ Problems of Equitable Distribution and Accurate Measurement
division of the numbers 1 to 9 by 10
cutting up of loaves
salary distribution for the personnel of the temple of illahun
$12$ Pesu Problems
exchange of loaves of different pesu
$13$ Areas and Volumes
the area of a rectangle
the area of a triangle
the area of a circle
the volume of a cylindrical granary
the details of kahun iv, 3
$14$ Equations of First and Second Degree
the first group
similar problems from other papyri
the second and third groups
equations of the second degree
kahun lv, 4
suggested restoration of missing lines in kahun lv, 4, and modernization of others
$15$ Geometric and Arithmetic Progressions
geometric progressions: problem 79 of the rhind mathematical papyrus
arithmetic progressions: problem 40 of the rhind mathematical papyrus
problem 64 of the rhind mathematical papyrus
kahun iv, 3
$16$ "Think of a Number" Problems
Problem 28 of the rhind mathematical papyrus
Problem 29 of the rhind mathematical papyrus
$17$ Pyramids and Truncated Pyramids
the seked of a pyramid
the volume of a truncated pyramid
$18$ The Area of a Semicylinder and the Area of a Hemisphere
$19$ Fractions of a Hekat
$20$ Egyptian Weights and Measures
$21$ Squares and Square Roots
$22$ The Reisner Papyri: The Superficial Cubit and Scales of Notation
appendix $1$
The Nature of Proof
appendix $2$
The Egyptian Calendar
appendix $3$
Great Pyramid Mysticism
appendix $4$
Regarding Morris Kline's views in Mathematics, a Cultural Approach
appendix $5$
The Pythagorean Theorem in Ancient Egypt
appendix $6$
The Contents of the Rhind Mathematical Papyrus
appendix $7$
The Contents of the Moscow Mathematical Papyrus
appendix $8$
appendix $9$
Horus-Eye Fractions in Terms of Hinu: Problems 80, 81 of the Rhind Mathematical Papyrus
appendix $10$
The Egyptial Equivalent of the Least Common Denominator
appendix $11$
A Table of Two-Term Equalities for Egyptian Unit Fractions
appendix $12$
Tables of Hieratic Integers and Fractions, Showing Variations
appendix $13$
Chronology
appendix $14$
A Map of Egypt
appendix $15$
The Egyptian Mathematical Leather Roll
bibliography
index