The Babylonian theorem: the mathematical journey to Pythagoras and Euclid
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amherst, N.Y.
Prometheus Books
2010
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Sequel to: How mathematics happened, the first 50,000 years. 2007. Includes bibliographical references and index |
| Physical Description: | 248 S. graph. Darst. |
| ISBN: | 9781591027737 |
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Record in the Search Index
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| adam_text | Titel: The Babylonian theorem
Autor: Rudman, Peter Strom
Jahr: 2010
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
Db2 146 77
VAT8512 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
6 CONTENTS
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 (7t) 119
RMP PROBLEMS 48 AND 50 120
OB PROBLEM TEXT YBC 7302 122
A SCRIBE FROM SUSA CALCULATES n (ca. 2000 BCE) 123
ARCHIMEDES CALCULATES n (ca. 200 BCE) 126
KEPLER CALCULATES THE AREA OF A CIRCLE (ca. 1600) 131
EVERYBODY CALCULATES THE AREA OF A CIRCLE 132
(ca. 2000)
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
A MODERN ELEMENTARY ALGEBRA PROBLEM 156
OB PROBLEM TEXT VAT 8389 158
Contents 1
Chapter 11. PYRAMID VOLUME 161
HOW THEY KNEW V(pyramid)/V(prism) =1/3 162
EUCLID PROVES y(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 1-1 197
EUCLID 1-22 199
EUCLID 1-37 202
EUCLID 1-47: THE PYTHAGOREAN THEOREM 204
EUCLID 11-22 206
EUCLID 11-14: THE BABYLONIAN THEOREM 207
APPENDIX A. ANSWSERS TO FUN QUESTIONS 213
APPENDIX B. DERIVATION OF EQUATION (I 1.2) 227
APPENDIX C. PROOF ^ IS AN
IRRATIONAL NUMBER 231
NOTES 233
REFERENCES 239
INDEX 245
|
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| isbn | 9781591027737 |
| language | English |
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| physical | 248 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Prometheus Books |
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| spelling | Rudman, Peter Strom 1929- Verfasser (DE-588)140642641 aut The Babylonian theorem the mathematical journey to Pythagoras and Euclid Peter S. Rudman Amherst, N.Y. Prometheus Books 2010 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Sequel to: How mathematics happened, the first 50,000 years. 2007. Includes bibliographical references and index Pythagoras Euclid Geschichte Mathematik Mathematics, Babylonian Mathematics, Ancient Mathematics Egypt History HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020299445&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rudman, Peter Strom 1929- The Babylonian theorem the mathematical journey to Pythagoras and Euclid Pythagoras Euclid Geschichte Mathematik Mathematics, Babylonian Mathematics, Ancient Mathematics Egypt History |
| title | The Babylonian theorem the mathematical journey to Pythagoras and Euclid |
| title_auth | The Babylonian theorem the mathematical journey to Pythagoras and Euclid |
| title_exact_search | The Babylonian theorem the mathematical journey to Pythagoras and Euclid |
| title_full | The Babylonian theorem the mathematical journey to Pythagoras and Euclid Peter S. Rudman |
| title_fullStr | The Babylonian theorem the mathematical journey to Pythagoras and Euclid Peter S. Rudman |
| title_full_unstemmed | The Babylonian theorem the mathematical journey to Pythagoras and Euclid Peter S. Rudman |
| title_short | The Babylonian theorem |
| title_sort | the babylonian theorem the mathematical journey to pythagoras and euclid |
| title_sub | the mathematical journey to Pythagoras and Euclid |
| topic | Pythagoras Euclid Geschichte Mathematik Mathematics, Babylonian Mathematics, Ancient Mathematics Egypt History |
| topic_facet | Pythagoras Euclid Geschichte Mathematik Mathematics, Babylonian Mathematics, Ancient Mathematics Egypt History |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020299445&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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