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

Rudman, Peter S.

Hardcover

ISBN 10: 159102773X ISBN 13: 9781591027737

Verlag: Prometheus Books, 2010

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Peter S. Rudman (Tel Aviv, Israel), a retired professor of physics at the Technion-Israel Institute of Technology, is the author of How Mathematics Happened: The First 50,000 Years, which was selected in 2008 as an Outstanding Academic Text by the American Library Association.

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THE BABYLONIAN THEOREM

THE MATHEMATICAL JOURNEY TO PYTHAGORAS AND EUCLIDBy PETER S. RUDMAN

Prometheus Books

Copyright © 2010 Peter S. Rudman
All right reserved.
ISBN: 978-1-59102-773-7

Contents

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

Details zur Ausgabe

• Verlag: Prometheus Books
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 159102773X
• ISBN 13: 9781591027737
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 248
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Simon and Schuster Netherlands BV; info@simonandschuster.nl; ; Herculesplein 96; Utrecht; 3584 AA; Niederlande