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The Babylonians Chapter 1 Introduction to the Babylonians Chapter 2 Babylonian mathematics Introduction In this unit, you will learn how writing and then mathematics developed in the Babylonian era. Babylon was the major city of one of the world's first civilisations. It was one of the capitals of southern Mesopotamia, formed by the valleys of the Euphrates and Tigris rivers in the area of modern Iraq. The Mesopotamian civilisation flourished for some 3600 years, from 3500 BC until the appearance of the last cuneiform text in AD 75. Mesopotamia was inhabited by the Sumerians from 3500 BC until about 2000 BC, and then by the Babylonians from 2000 BC until AD 75. Many of the features of modern society - complex social organisation, political and religious structures, urban centres, sophisticated productive and economic systems, for example - first developed in the four great river valley civilisations of the time. The other three were around the Nile, the Indus, and the Yellow rivers. Such features depended on development in the two basic human languages: words and numbers. Our writing and mathematics are rooted in Mesopotamia. The unit begins with some background introduction. Chapter 2, which is far more mathematical, is concerned with the ways in which the Babylonians carried out arithmetic and mathematics using a number system based on 60. They were able to find square roots and to solve quadratic equations. This unit is designed to take about 10 hours oi your learning time. About half of this time will be outside the classroom. Read Chapter 1 quickly. Its purpose is to give you a background to Babylonian mathematics. Then go on to Chapter 1, There are summaries and further practice exercises in Chapter 12. Mathematical knowledge assumed • knowledge of quadratic equations would be useful.
Introduction to the Babylonians If you would like more background information, a good reference is Early Mesopotamia by J N Postgate, Routledge, This chapter gives you important background to the society of the Babylonians, and the context in which they developed their mathematics. There are no mathematical activities in this chapter. Read this chapter as background, so that you can understand the achievements described in Chapter 2. The map in Figure 1.1 shows you where the Babylonians lived, around 2000 BC until AD 75. Figure 1.1 Background to the Babylonians The following extracts give a general impression of Mesopotamian life in the second millennium BC. They show you something of a culture whose needs had previously led to the development of writing. Legal dispute about a lost donkey This extract is about a pack-ass which Ilsu-abusu hired from Warad-Enlil and Silli- Istar, his brother, in the town of Simurrum, and then lost.
Page 2 and 3: Nuffield Advanced Mathematics Histo
Page 4 and 5: Contents Introduction 7 Unit 1 The
Page 6 and 7: Introduction This book, about the h
Page 10 and 11: Introduction to the Babylonians On
Page 12 and 13: Figure 1.2 Stele inscribed with Ham
Page 14 and 15: Token V Figure 1.5 7 Introduction t
Page 16 and 17: There are no practice exercises for
Page 18 and 19: A sexagesimal number system is a sy
Page 20 and 21: ff m yfr < n Figure 2.5 «« Activi
Page 22 and 23: Activity 2.5 Babylonian fractions 2
Page 24 and 25: Activity 2.6 Babylonian arithmetic
Page 26 and 27: Figure 2.10 Activity 2.9 2 Babyloni
Page 28 and 29: Type Quadratic Table 2.1 x +ax = b
Page 30 and 31: Activity 2.12 Geometry Figure 2.13a
Page 32: Practice exercises for this chapter
Page 35 and 36: 3 An introduction to Euclid fthese
Page 37 and 38: The Greeks Activity 3.3 B Figure 3.
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5 Arab mathematics You should think
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The Arabs Western Arabic, or Gobar,
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The Arabs Activity 5.2 Figure 5.3a
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7776 Arabs Activity 5.4 This proble
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62 The Arabs Activity 5.6 Horner's
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64 The Arabs Indian text. For over
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D B P N M K Figure 5,9a The Arabs D
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68 The Arabs Figure 5.10 Activity 5
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The Arabs Practice exercises for I
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72 6.1 Read about Descartes The app
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76 Descartes Figure 6.5 Figure 6.5
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Descartes fViete (Vieta in Latin) w
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Descartes The next two sections con
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82 Descartes Activity 6.9 a 3 - b 3
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i——— Figure 6.12 Figure 6.13
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Descartes Practice exercises for th
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Figure 7.2 Descartes Activity 7.1 i
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N- i- L Descartes Thus I have In th
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A Descartes Activity 7.7 Reflecting
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94 Descartes 23 It is true that the
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96 Descartes Figure 7.11 shows a ge
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98 Descartes It is clear that the p
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Descartes ractice exercises lor thi
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102 Descartes Activity 8.1 Activity
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104 Descartes In the next section y
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Descartes Today we call these numbe
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Descartes Activity 8.9 Normals Figu
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Descartes Practice exercises for th
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772 The beginnings of calculus 9.1
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Figure 9.4 774 Calculus you can wri
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Calculus including Descartes, under
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118 Calculus Activity 9.7 Cavalieri
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Figure 9. 7 / 120 Calculus dy 1 Wri
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Calculus JPractiee exercises this c
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10.1 Visualising negative numbers 1
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126 Searching for the abstract For
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Searching for the abstract 31. Hith
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146 Searching for the abstract As a
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752 12 Summaries and exercises Two
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754 12 Summaries and exercises 5 Ar
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156 12 Summaries and exercises usin
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158 Hints Activity 2.3, page 15 2 F
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13 Hints Activity 7.3, page 89 1 Wr
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outcome 1 step to the right Figure
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14 Answers 3 0;6,40 and 0;2,13,20 4
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14 Answers 3 If AD intersects the l
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74 Answers 2 Suppose that you can f
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14 Answers 4 If he had a daughter t
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14 Answers Activity 6.5, page 79 1
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14 Answers 6 The equation z 2 + az
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14 Answers b This meets the ellipse
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14 Answers To get an interpretation
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14 Answers of multiplication by neg
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14 Answers b The required number is
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14 Answers operator has the effect
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14 Answers A i- B 5 E %2 5)-25 = 39
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Index Ptolemy 49, 55, 58 Pythagoras
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