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

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## Richard J. Gillings:

## 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
- addition and subtraction
- 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*

- Regarding Morris Kline's views in

- 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 $8$
- A Papyritic Memo Pad

- 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

## Cited by

- 1986: David Wells:
*Curious and Interesting Numbers* - 1992: David Wells:
*Curious and Interesting Puzzles* - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.)

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $7$: Footnote - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $7$: Footnote