
Unexpected Links Between Egyptian And Babylonian Mathematics.
Title:
Unexpected Links Between Egyptian And Babylonian Mathematics.
Author:
Friberg, Jöran.
ISBN:
9789812701121
Personal Author:
Physical Description:
1 online resource (308 pages)
Contents:
Preface -- Contents -- Chapter 1 Two Curious Mathematical Cuneiform Texts from Old Babylonian Mari -- 1.1. M. 7857. A Fanciful Interpretation of a Geometric Progression -- 1.1 a. M. 7857. A text with three kinds of counting numbers -- 1.1 b. OB texts with ascending or descending geometric progressions -- 1.1 c. A Late Babylonian text using the trailing part algorithm -- 1.1 d. The sum of a geometric progression in an Old Babylonian text -- 1.1 e. The sum of a geometric progression in a Seleucid text -- 1.1 f. P.Rhind # 79: a parallel to M. 7857 in a hieratic papyrus -- 1.1 g. Summary. The Mesopotamian roots of a Mother Goose riddle -- 1.1. M. 8631. Another Curious Mathematical Text from OB Mari -- 1.1 a. M. 8631. A fanciful interpretation of 30 doublings -- 1.2 b. The Old Babylonian doubling and halving algorithm -- 1.2 c. P.IFAO 88: A parallel to M. 8631 in a Greek-Egyptian papyrus -- 1.2 d. Summary. The Mesopotamian roots of a well known legend -- Chapter 2 Hieratic Mathematical Papyri and Cuneiform Mathematical Texts -- 2.1. Themes in P.Rhind, a Hieratic Mathematical Papyrus Roll -- 2.1 a. P.Rhind, a hieratic mathematical recombination text -- 2.1 b. Theme E: division problems (P.Rhind ## 24-38) -- 2.1 c. Theme F: sharing problems (P.Rhind ## 39-40, 63-65, 68) -- 2.1 d. Theme G: geometry problems (P.Rhind ## 41-46, 48-60) -- 2.1 e. Theme H: baking or brewing numbers (P.Rhind ## 69-78) -- 2.1 f. Theme I: a combined price problem (P.Rhind # 62) -- 2.2. Themes in P.Moscow, a Smaller Hieratic Mathematical Papyrus -- 2.2 a. P.Moscow: Another Egyptian mathematical recombination text -- 2.2 b. P.Moscow # 23: A combined work norm -- 2.2 c. P.Moscow ## 6-7, 17: Metric algebra -- 2.2 d. P.Moscow # 14: The volume of a truncated pyramid -- 2.2 e. P.Moscow # 10: The area of a semicircle(?) -- 2.3. Hieratic Mathematical Papyrus Fragments.
2.3 a. P.Berlin 6619 # 1: Metric algebra -- 2.3 b. P.UC 32160 (= Kahun IV.3) # 1: A cylindrical granary -- 2.3 c. P.UC 32160 # 2: An arithmetic progression with 10 terms -- 2.3 d. P.UC 32161 (= Kahun XLV. 1): A list of large numbers -- 2.4. Conclusion -- New thoughts about the nature of P.Rhind -- Summary: Comparison of hieratic Egyptian and OB mathematics -- Chapter 3 Demotic Mathematical Papyri and Cuneiform Mathematical Texts -- 3.1. Themes in P.Cairo (Ptolemaic, the 3rd C. BCE) -- 3.1 a. P.Cairo, a hieratic mathematical recombination text -- 3.1 b. P.Cairo 8 (DMP ## 24-31). A pole against a wall -- 3.1 c. P.Cairo 1 (DMP ## 2-3). Two closely related division problems -- 3.1 d. P.Cairo 2 (DMP ## 4-6). Completion problems -- 3.1 e. P.Cairo 3 (DMP ## 7, 15-16, 18). A rectangular sail -- 3.1 f. P.Cairo 4 (DMP ## 8-12, 14, 17). Reshaping a rectangular cloth -- 3.1 g. P.Cairo 7 (DMP # 23). Shares in a geometric progression -- 3.1 h. P.Cairo 9 (DMP ## 32-33). Diameter of a circle with given area -- 3.1 i. P.Cairo 10 (DMP ## 34-35). Metric algebra -- 3.1 j . P.Cairo 11 (DMP ## 36, 38). An equilateral triangle in a circle -- 3.1 k. P.Cairo 12 (DMP # 37). A square inscribed in a circle -- 3.1.1. P.Cairo 13-14 (DMP ## 39-40). Pyramids with a square base -- 3.1 m. P.Cairo 15-16 (## "32-33"). Metric algebra -- 3.2. P.British Museum 10399 (Ptolemaic, Later than P.Cairo) -- 3.2 a. P.BM 10399 1 (DMP # 41). A circle-and-chord problem -- 3.2 b. P.BM 10399 2 (DMP ## 42-45). Masts (truncated cones) -- 3.2 c. P.BM 10399 3 (DMP ## 46-51). The reciprocal of 1 + 1/n, etc. -- 3.3. P.British Museum 10520 (Early(?) Roman) -- 3.3 a. P.BM 10520 1 (DMP # 53). The iterated sum of 1 through 10 -- 3.3 b. P.BM 10520 2 (DMP # 54). A multiplication table for 64 -- 3.3 c. P.BM 10520 3 (DMP # 55). A new multiplication rule.
3.3 d. P.BM 10520 4 (DMP # 56). 2/35 expressed as a sum of parts -- 3.3 e. P.BM 10520 5 (DMP ## 57-61). Operations with fractions -- 3.3 f. P.BM 10520 6 (DMP ## 62-63). The square side rule -- 3.3 g. P.BM 10520 7 (DMP ## 64-65). The quadrilateral area rule -- 3.4. P.British Museum 10794 (Date Uncertain) -- Multiplication tables for 90 and 150 (DMP ## 66-67) -- 3.5. P.Carlsberg 30 (Probably 2nd Century BCE)29 -- 3.5 a. P.Carlsberg 30 # 1 (DMP # 69). The diagonal of a square, etc. -- 3.5 b. P.Carlsberg 30 # 2 (DMP ## 71-72). A system of linear equations -- 3.6. P.Griffith Inst. I. E. 7 (Late Ptolemaic or Early Roman) -- A theme text with linear equations -- 3.7. P.Heidelberg 663 (Ptolemaic, 2nd or 1st C. BCE) -- 3.7 a. P.Heidelberg 663 # 1. A vertically striped trapezoid -- 3.7 b. P.Heidelberg 663 # 2. A horizontally striped trapezoid -- 3.7 c. P.Heidelberg 663. Parallel texts -- 3.8. Conclusion -- The importance of P.Cairo for the history of mathematics -- The other demotic mathematical papyri -- Chapter 4 Greek-Egyptian Mathematical Documents and Cuneiform Mathematical Texts -- 4.1. O.Bodl. ii 1847 (30 BCE), an Ostracon with Schematic Field Plans -- 4.2. P.Oxyrhynchus iii 470 (3rd C. CE). A Water Clock -- 4.3. P. Vindobonensis G. 26740. Five Illustrated Geometric Exercises -- 4.3 a. P.Vindob. G. 26740 # 1. A segment of a circular band -- 4.3 b. P. Vindob. G. 26740 ## 2-4. A circle area found in three ways -- 4.3 c. P.Vindob. G. 26740 # 5. The area of a semicircle -- 4.4. P.Mich. 620. Systems of Linear Equations. Tabular Arrays -- 4.4 a. P.Mich. 620 # 1. A system of linear equations: four unknowns -- 4.4 b. P.Mich. 620 # 2. A system of linear equations: two unknowns -- 4.4 c. P.Mich. 620 # 3. A system of linear equations: three unknowns -- 4.5. P.Akhmîm (7th C. CE). Calculations with Fractions -- 4.5 a. P.Akhmîm. Ten tables of fractions.
4.5 b. P.Akhmîm 1. The capacity measure(?) of a truncated cone -- 4.5 c. P.Akhmîm 2. The capacity measure of a rectangular granary -- 4.5 d. P.Akhmîm 3, 5. Unequal sharing, and division exercises -- 4.5 e. P.Akhmîm 4-10. Examples of counting with fractions -- 4.5 f. P.Akhmîm 9. Prices and market rates -- 4.6. WT.Michael 62 (7th? C. CE). Prices and Market Rates -- 4.7. Problems for Right Triangles and Quadrilaterals -- 4.7 a. P.Genève 259. Problems for the sides of a right triangle -- 4.7 b. P.Chicago litt. 3. Three types of non-symmetric trapezoids -- 4.7 c. P.Cornell 69. Non-symmetric trapezoids, and a birectangle -- 4.8. P.Vindobonensis G. 19996 (1st C. CE?). Stereometric Exercises -- 4.8 a. P.Vindob. G. 19996: Contents -- 4.8 b. P.Vindob. G. 19996 # 10. A pyramid with a triangular base -- 4.8 c. P.Vindob. G. 19996 # 13. A truncated triangular pyramid -- 4.8 d. P.Vindob. G. 19996 # 18. A square pyramid -- 4.8 e. P.Vindob. G. 19996 # 19. A truncated square pyramid -- 4.8 f. P.Vindob. G. 19996 # 24. A truncated circular cone -- 4.8 g. Pyramids and cones in Old Babylonian mathematical texts -- 4.9. Conclusion -- Relations between Greek-Egyptian and Babylonian mathematics -- New Thoughts About the History of Ancient Mathematics -- Index of Texts -- Index of Subjects -- Bibliography.
Abstract:
Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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