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Amazing Traces of a Babylonian Origin in Greek Mathematics

by Jöran Friberg World Scientific
Pub Date:
04/2007
ISBN:
9789812704528
Format:
Hbk 496 pages
Price:
AU$269.00 NZ$275.65
Product Status: Available in Approx 14 days
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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.

Contents:


Elements II and Babylonian Metric Algebra


El.I.47 and the Old Babylonian Diagonal Rule


Lemma El. X.28/29 la, 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, Ptolemy's, and Brahmagupta's Area and Diagonal 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

Jöran Friberg (Chalmers University of Technology, Gothenburg, Sweden)