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