The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclid
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The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclid

by Peter S. Rudman
     
 

ISBN-10: 159102773X

ISBN-13: 9781591027737

Pub. Date: 01/26/2010

Publisher: Prometheus Books

A physicist explores the history of mathematics among the Babylonians and Egyptians, showing how their scribes in the era from 2000 to 1600 BCE used visualizations of plane geometric figures  to invent geometric algebra, even solving problems that we now do by quadratic algebra. Rudman traces the evolution of mathematics from the metric geometric algebra of

Overview

A physicist explores the history of mathematics among the Babylonians and Egyptians, showing how their scribes in the era from 2000 to 1600 BCE used visualizations of plane geometric figures  to invent geometric algebra, even solving problems that we now do by quadratic algebra. Rudman traces the evolution of mathematics from the metric geometric algebra of Babylon and Egypt—which used numeric quantities on diagrams as a means to work out problems—to the nonmetric geometric algebra of Euclid (ca. 300 BCE). From his analysis of Babylonian geometric algebra, the author formulates a "Babylonian Theorem", which he demonstrates was used to derive the Pythagorean Theorem, about a millennium before its purported discovery by Pythagoras.

He also concludes that what enabled the Greek mathematicians to surpass their predecessors was the insertion of alphabetic notation onto geometric figures. Such symbolic notation was natural for users of an alphabetic language, but was impossible for the Babylonians and Egyptians, whose writing systems (cuneiform and hieroglyphics, respectively) were not alphabetic.

This is a masterful, fascinating, and entertaining book, which will interest both math enthusiasts and students of history.

Product Details

ISBN-13:
9781591027737
Publisher:
Prometheus Books
Publication date:
01/26/2010
Pages:
248
Product dimensions:
6.10(w) x 9.00(h) x 1.00(d)

Related Subjects

Table of Contents

Contents

LIST OF FIGURES....................9
MATHEMATICAL SYMBOLS....................15
PREFACE....................17
ACKNOWLEDGMENTS....................23
Chapter 1. NUMBER SYSTEM BASICS....................25
Chapter 2. EGYPTIAN NUMBERS AND ARITHMETIC....................39
Chapter 3. BABYLONIAN NUMBERS AND ARITHMETIC....................47
Chapter 4. OLD BABYLONIAN "QUADRATIC ALGEBRA" PROBLEM TEXTS....................61
YBC 6967....................63
AO 8862....................75
[Db.sub.2] 146....................77
VAT 8512....................80
Chapter 5. PYTHAGOREAN TRIPLES....................85
OB PROBLEM TEXT BM 85196 #9....................85
BERLIN PAPYRUS 6610 #1....................86
PROTO-PLIMPTON 322....................89
PLIMPTON 322....................93
Chapter 6. SQUARE ROOT CALCULATIONS....................99
EGYPTIAN CALCULATION....................99
OB PROBLEM TEXT YBC 7289....................99
OB SQUARING-THE-RECTANGLE (Heron's Method)....................102
OB CUT-AND-PASTE SQUARE ROOT (Newton's Method)....................104
OB PROBLEM TEXT VAT 6598....................108
PYTHAGORAS CALCULATES SQUARE ROOTS....................109
ARCHIMEDES CALCULATES SQUARE ROOTS....................111
PTOLEMY CALCULATES SQUARE ROOTS....................116
Chapter 7. PI([pi])....................119
RMP PROBLEMS 48 AND 50....................120
OB PROBLEM TEXT YBC 7302....................122
A SCRIBE FROM SUSA CALCULATES [pi] (ca. 2000 BCE)....................123
ARCHIMEDES CALCULATES [pi] (ca. 200 BCE)....................126
KEPLER CALCULATES THE AREA OF A CIRCLE (ca. 1600)....................131
EVERYBODY CALCULATES THE AREA OF A CIRCLE (ca. 2000)....................132
Chapter 8. SIMILAR TRIANGLES (PROPORTIONALITY)....................135
RMP PROBLEM 53....................135
OB PROBLEM TEXT MLC 1950....................137
OB PROBLEM TEXT IM 55357....................140
Chapter 9. SEQUENCES AND SERIES....................145
ARITHMETIC SEQUENCES AND SERIES....................145
OB PROBLEM TEXT YBC 4608 #5....................145
RMP PROBLEM 64....................147
RMP PROBLEM 40....................148
GEOMETRIC SEQUENCES AND SERIES....................149
OB PROBLEM TEXT IM 55357-REVISITED....................151
Chapter 10. OLD BABYLONIAN ALGEBRA: SIMULTANEOUS LINEAR EQUATIONS....................155
AMODERN ELEMENTARY ALGEBRA PROBLEM....................156
OB PROBLEM TEXT VAT 8389....................158
Chapter 11. PYRAMID VOLUME....................161
HOW THEY KNEW V(pyramid)/V(prism) = 1/3....................162
EUCLID PROVES V(pyramid)/V(prism) = 1/3....................166
TRUNCATED PYRAMID (FRUSTUM) VOLUME....................169
Chapter 12. FROM OLD BABYLONIAN SCRIBE TO LATE BABYLONIAN SCRIBE TO PYTHAGORAS TO PLATO....................179
LATE BABYLONIAN (LB) MATHEMATICS....................179
PYTHAGORAS (ca. 580-500 BCE)....................181
PLATO (427-347 BCE)....................189
Chapter 13. EUCLID....................195
WHO WAS EUCLID?....................195
EUCLID I-1....................197
EUCLID I-22....................199
EUCLID I-37....................202
EUCLID I-47: THE PYTHAGOREAN THEOREM....................204
EUCLID II-22....................206
EUCLID II-14: THE BABYLONIAN THEOREM....................207
APPENDIX A. ANSWSERS TO FUN QUESTIONS....................213
APPENDIX B. DERIVATION OF EQUATION (11.2)....................227
APPENDIX C. PROOF [square root of 2] IS AN IRRATIONAL NUMBER....................231
NOTES....................233
REFERENCES....................239
INDEX....................245

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