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

Prometheus Books

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...