history of mathematics - National STEM Centre

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14 Answers Activity 2.1, page 13 1 a The table on the front tablet runs from 1,2,..., 14 on the left and 9, 18, ..., 126 on the right. The reverse side runs from 15 to 23 on the left and 135, in nines to 207 on the right. b It is the nine times table. 2 The numbers from 1 to 23 are made by using the symbols Y ar|d "^ standing for 1 to 10. The number 63 appears to be made by using the symbol Y followed by a space, and then f f Y- The number system therefore is based on base 60, with a space between the numbers in the 60s place and the units place. 3 698 4 The Old Sumerians used a system based on 10 and 60 using symbols, instead of place value, to represent larger numbers. The Babylonians adapted this to a system using only two symbols, and relative position to indicate what the symbols meant. However, there was still ambiguity in the Babylonians' system. Activity 2.2, page 14 1 It is the 25 times table. The numbers to the left are 1 to 15, and those to the right are 25, 50, ..., 375. 2 The right-hand number on the first line is "^ py^, while the right-hand side of the penultimate line is f^
14 Answers 3 0;6,40 and 0;2,13,20 4 The only fractions in the decimal system which convert to terminating decimals are those with denominators which have prime factors consisting only of combinations of 2s and 5s; that is, the divisors of 10. 5 a Similarly, in the sexagesimal system, the fractions which terminate when converted to sexagesimals are those with denominators consisting of combinations of 2, 3, and 5, the prime factors of 60. b More fractions have sexagesimals which terminate in the sexagesimal system. 6 6£ = 6;9,22,30, 83^ = 83;0,50 7 | = 0;8,34,17,8,34,17,.... This lies between 0; 8,34,18 and 0; 8,34,16,59. Activity 2.6, page 19 1 The addition sign is >—
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Nuffield Advanced Mathematics Histo
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Contents Introduction 7 Unit 1 The
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Introduction This book, about the h
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The Babylonians Chapter 1 Introduct
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Introduction to the Babylonians On
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Figure 1.2 Stele inscribed with Ham
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Token V Figure 1.5 7 Introduction t
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There are no practice exercises for
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A sexagesimal number system is a sy
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ff m yfr < n Figure 2.5 «« Activi
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Activity 2.5 Babylonian fractions 2
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Activity 2.6 Babylonian arithmetic
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Figure 2.10 Activity 2.9 2 Babyloni
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Type Quadratic Table 2.1 x +ax = b
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Activity 2.12 Geometry Figure 2.13a
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Practice exercises for this chapter
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3 An introduction to Euclid fthese
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The Greeks Activity 3.3 B Figure 3.
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34 The Greeks Activity 3.4 g Now us
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36 The Greeks inscribes another wit
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38 The Greeks Activity 3.7 therefor
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The Greeks Interpret postulate 3 in
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42 More Greek mathematics 4.1 Some
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The Greeks Q.E.D. stands for 'quod
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Figure 4.3 46 The Greeks • treat
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Figure 4.6 48 The Greeks together w
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The Greeks Activity 4.8 The cone Th
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The Greeks Practice exercises for t
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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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Descartes Activity 6.1 Head about D
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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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Page 129 and 130: 10.1 Visualising negative numbers 1
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Page 157 and 158: 752 12 Summaries and exercises Two
Page 159 and 160: 754 12 Summaries and exercises 5 Ar
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Page 163 and 164: 158 Hints Activity 2.3, page 15 2 F
Page 165 and 166: 13 Hints Activity 7.3, page 89 1 Wr
Page 167: outcome 1 step to the right Figure
Page 171 and 172: 14 Answers 3 If AD intersects the l
Page 173 and 174: 74 Answers 2 Suppose that you can f
Page 175 and 176: 14 Answers 4 If he had a daughter t
Page 177 and 178: 14 Answers Activity 6.5, page 79 1
Page 179 and 180: 14 Answers 6 The equation z 2 + az
Page 181 and 182: 14 Answers b This meets the ellipse
Page 183 and 184: 14 Answers To get an interpretation
Page 185 and 186: 14 Answers of multiplication by neg
Page 187 and 188: 14 Answers b The required number is
Page 189 and 190: 14 Answers operator has the effect
Page 191 and 192: 14 Answers A i- B 5 E %2 5)-25 = 39
Page 193 and 194: Index Ptolemy 49, 55, 58 Pythagoras
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