Amazing traces of a Babylonian origin in Greek mathematics
著者
書誌事項
Amazing traces of a Babylonian origin in Greek mathematics
World Scientific, c2007
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author's intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian “metric algebra,” a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets.The book's use of “metric algebra diagrams” in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract “lettered diagrams” in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author's comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics.
目次
- Elements II and Babylonian Metric Algebra
- El.I.47 and the Old Babylonian Diagonal Rule
- Lemma El. X.28/29, Plimpton 322, and Babylonian igi-igi.bi Problems
- Lemma El. X.32/33 and an Old Babylonian Geometric Progression
- Elements X and Babylonian Metric Algebra
- Elements IV and Old Babylonian Figures within Figures
- El. VI.30, XIII.1-12, and Regular Polygons in Babylonian Mathematics
- El. XIII.13-18 and Regular Polyhedrons in Babylonian Mathematics
- Elements XII and Pyramids and Cones in Babylonian Mathematics
- El. I.43-44, El. VI.24-29, Data 57-59, 84-86, and Metric Algebra
- Euclid's Lost Book On Divisions and Babylonian Striped Figures
- Hippocrates' Lunes and Babylonian Figures with Curved Boundaries
- Traces of Babylonian Metric Algebra in the Arithmetica of Diophantus
- Heron's and Brahmagupta's Area Rules
- Theon of Smyrna's Side and Diagonal Numbers and Ascending Infinite Chains of Birectangles
- Greek and Babylonian Square Side Approximations
- Theodorus of Cyrene's Irrationality Proof and Descending Infinite Chains of Birectangles
- The Pseudo-Heronic Geometrica
- A Chain of Trapezoids with Fixed Diagonals
- A Catalog of Babylonian Geometric Figures.
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