Synopses & Reviews
In this carefully researched study, the author examines Egyptian mathematics, demonstrating that although operations were limited in number, they were remarkably adaptable to a great many applications: solution of problems in direct and inverse proportion, linear equations of the first degree, and arithmetical and geometrical progressions.
In the past, scholars have tended to dismiss the mathematics of the ancient Egyptians as "child's play," compared with the achievements of the Greeks and other later civilizations. Nevertheless, in a society that achieved the marvelous accuracy of construction revealed in the Pyramids, extensive systems of irrigation canals, the erection of large granaries, levying and collecting of taxes, and other evidences of a well-organized and highly developed culture, mathematics must have played a major role.
In this remarkably erudite work, the first book-length study of ancient Egyptian mathematics, Professor Gillings examines the development of Egyptian mathematics from its origins in commercial and practical computations to such accomplishments as the solution of problems in direct and inverse proportion; the solution of linear equations of the first degree; determining the sum of arithmetical and geometrical progressions, and the use of rudimentary trigonometric functions in describing the slopes of pyramids. Drawing on all the extant sources Egyptian Mathematical Leather Roll, the Reisner Papyri, the Moscow Mathematical Papyrus, and, most extensively, the Rhind Mathematical Papyrus, a training manual for scribes- the author shows that although the mathematical operations of the ancient Egyptians were limited in number, they were adaptable to a great many applications. Professor Gillings is also at pains to debunk such myths as the numerical mysticism that arose in connection with the construction of the great Pyramids, and the oft-repeated assertion that the Egyptians were conversant with the Pythagorean Theorem.
Enhanced with photographs of age-old papyri and other artifacts, as well as the author's own calligraphic renderings of hieroglyphic and hieratic words and numerals, this carefully researched and well-presented study will fascinate Egyptologists, mathematicians, engineers, archaeologists, and any student or admirer of the remarkable civilization that flourished on the shores of the Nile so many centuries ago.
First book-length study--from simple commercial computations to trigonometric functions used in construction of pyramids. Fascinating, provocative. Illustrated.
This carefully researched study examines Egyptian mathematics, demonstrating that although operations were limited in number, they were remarkably adaptable to a great many applications.
Table of Contents
Hieroglyphic and Hieratic Writing and Numbers
The Four Arithmetic Operations
ADDITION AND SUBTRACTION
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
The G Rule in Egyptian Arithmetic
FURTHER EXTENSIONS OF THE G RULE
The Recto of the Rhind Mathematical Papyrus
THE DIVISION OF 2 BY THE ODD NUMBERS 3 TO 101
FURTHER COMPARISONS OF THE SCRIBE'S AND THE COMPUTERS DECOMPOSITIONS
The Recto Continued
EVEN NUMBERS IN THE RECTO: 2 ÷ 13
MULTIPLES OF DIVISORS IN THE RECTO
TWO DIVIDED BY THIRTY-FIVE: THE SCRIBE DISCLOSES HIS METHOD
Problems in Completion and the Red Auxiliaries
USE OF THE RED AUXILIARIES OR REFERENCE NUMBERS
AN INTERESTING OSTRACON
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
UNIT-FRACTION TABLES OF THE RHIND MATHEMATICAL PAPYRUS
PROBLEMS 7 TO 20 OF THE RHIND MATHEMATICAL PAPYRUS
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
EXCHANGE OF LOAVES OF DIFFERENT PESUS
Area 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
Equations of the First and Second Degree
THE FIRST GROUP
SIMILAR PROBLEMS FROM OTHER PAPYRI
THE SECOND AND THIRD GROUPS
EQUATIONS OF THE SECOND DEGREE
"SUGGESTED RESTORATION OF MISSING LINES OF KAHUN LV 4, AND MODERNIZATION OF OTHERS"
Geometric and Arithmetic Progressions
GEOMETRIC PROGRESSIONS: PROBLEM 79 OF THE RHIND MATHEMATICAL PAPYRUS
ARITHMETIC PROGRESSIONS: PROBLEM 40 OF THE RHIND MATHEMATICAL PAPYRUS
"Think of a Number" Problems"
PROBLEM 28 OF THE RHIND MATHEMATICAL PAPYRUS
PROBLEM 29 OF THE RHIND MATHEMATICAL PAPYRUS
Pyramids and Truncated Pyramids
THE SEKED OF A PYRAMID
THE VOLUME OF A TRUNCATED PYRAMID
The Area of a Semicylinder and the Area of a Hemisphere
Fractions of a Hekat
Egyptian Weights and Measures
Squares and Square Roots
The Reisner Papyri: The Superficial Cubit and Scales of Notation
The Nature of Proof
The Egyptian Calendar
Great Pyramid Mysticism
"Regarding Morris Kline's Views in Mathematics, A Cultural Approach"
The Pythagorean Theorem in Ancient Egypt
The Contents of the Rhind Mathematical Papyrus
The Contents of the Moscow Mathematical Papyrus
A Papyritic Memo Pad
"Horus-Eye Fractions in Terms of Hinu: Problems 80, 81 of the Rhind Mathematical Papyrus"
The Egyptian Equivalent of the Least Common Denominator
A Table of Two-Term Equalities for Egyptian Unit Fractions
"Tables of Hieratic Integers and Fractions, Showing Variations"
A Map of Egypt
The Egyptian Mathematical Leather Roll