Claudia Zaslavsky, “Africa Counts: Number and Pattern in African Cultures”, 1973 was the topic of an earlier blog post.
Here I present: George Gheverghese Joseph, “The Crest of the Peacock: Non-European Roots of Mathematics”, 1991.
This book consists of eleven (11) chapters; and, the “table of contents” is shown BELOW.
TABLE OF CONTENTS
Chapter One (1). The History of Mathematics: Alternative Perspectives.
A Justification for This Book.
The Development of Mathematical Knowledge.
Mathematical Signposts and Transmissions across the Ages.
Chapter Two (2). Mathematics from Bones, Strings, and Standing Stones.
Beginnings: The “Ishango” CONGO Bone.
Native Americans and Their Mathematics.
The Emergence of Written Number Systems.
A Digression: Mayan Numeration.
Chapter Three (3). The Beginnings of Written Mathematics: Egypt.
The Urban Revolution and Its African Origins.
Sources of Egyptian Mathematics.
Number Recording among the Egyptians.
Egyptian Arithmetic.
Egyptian Algebra: The Beginnings of Rhetorical Algebra.
Egyptian Geometry.
Egyptian Mathematics: A General Assessment.
Chapter Four (4). The Beginnings of Written Mathematics: Mesopotamia’.
Fleshing Out the History Sources of Mesopotamian’ Mathematics.
The Mesopotamian’ Number System.
Babylonian Algebra.
Babylonian Geometry.
Chapter Five (5). Egyptian and Mesopotamian’ Mathematics.
An Assessment Changing Perceptions.
Neglect of Egyptian and Mesopotamian’ Mathematics.
The Babylonian-Egyptian-Greek Nexus.
A Seamless Story or Three Separate Episodes?
Chapter Six (6). Ancient Chinese Mathematics.
Background and Sources.
The Development of Chinese Numerals.
Chinese Magic Squares (and Other Designs).
Mathematics from the Jiu Zhang (Suan Shu).
Chapter Seven (7). Special Topics in Chinese Mathematics.
The “Piling-Up of Rectangles”.
The Pythagorean Theorem in China Estimation of π.
Solution of Higher-Order Equations and Pascal’s Triangle Indeterminate Analysis in China.
The Influence of Chinese Mathematics.
Chinese Mathematics: A Final Assessment.
Chapter Eight (8). Ancient Indian Mathematics.
A Restatement of Intent and a Brief Historical Sketch Math from Bricks.
Evidence from the Harappan Culture Mathematics from the Vedas.
Early Indian Numerals and Their Development Jaina Mathematics.
Mathematics on the Eve of the Classical Period.
Chapter Nine (9). Indian Mathematics.
The Classical Period and After Major Indian Mathematician-Astronomers.
Indian Algebra.
Indian Trigonometry.
Other Notable Contributions.
Chapter Ten (10). A Passage to Infinity.
The Kerala Episode.
The Actors Transmission of Kerala Mathematics.
Chapter Eleven (11). Prelude to Modern Mathematics.
The Islamic Contribution.
Historical Background.
Major Medieval Islamic Mathematicians.
Medieval Islam’s Role in the Rise and Spread of Indian Numerals.
Arithmetic in the Islamic World.
Algebra in the Islamic World.
Islamic Algebra and Its Influence on Europe Geometry in the Islamic World.
Trigonometry in the Islamic World.
Mathematics from Related Sources.
The Islamic Contribution: A Final Assessment.
Here I presented: George Gheverghese Joseph, “The Crest of the Peacock: Non-European Roots of Mathematics”, 1991.
SUMMARY.
This book contains areas in the history of mathematic shown on the map BELOW.
NUMERALS and FARMING.
Farming is known to have begun in 10,000 BC with Homo sapiens, as shown ABOVE.
The regions shown on the ABOVE map were in need of term “Numeral” as agricultural economy’s. The twelve (12) regions, domesticated species listed shown BELOW.
Urban settlements were “farm markets” in Sumerian Mesopotamia’ with writing in the city of Sumer Mesopotamia’.
Writing began in Sumerian Mesopotamia’ in 3,500 BC; and, was independently invented in China (as shown schematically ABOVE). Egyptian contact with Mesopotamia’ transmitted Latin letters (abc’s) currently used globally.
Numerals can express relationships like quantity (cardinal numbers), sequence (ordinal numbers), frequency (once, twice), and part (fraction).
NUMERAL LINGUISTICS.
In linguistics, a “numeral” in the broadest sense is a word or phrase that describes a numerical quantity.
Some theories of grammar use the word “numeral” to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the “two” in “two hats”. Some theories of grammar do not include determiners as a part of speech and consider “two” in this example to be an adjective.
Some theories consider “numeral” to be a synonym for “number” and assign all numbers (including cardinal numbers like the compound word “seventy-fifth”) to a part of speech called “numerals“.
Numerals in the broad sense can also be analyzed as a noun (“three is a small number”), as a pronoun (“the two went to town”), or for a small number of words as an adverb (“I rode the slide twice”).
The Ishango Bone from Semliki, CONGO (shown BELOW) is a tool for linguistic emergence of writing.
