history of mathematics - National STEM Centre

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Fowls Input None. 0-+D while A + fi+C+L>100 or 189A + 225fi + 245C + 945£»31500. Even so, the Fowls algorithm takes 102 minutes to run on one type of calculator.
13 Hints Activity 7.3, page 89 1 Write MP and MO in the forms MP = MN - NL and MO = MN + NL . Activity 9.8, page 120 3 What is the size of the difference between the areas? Activity 10.1, page 125 2 b Remember that 2 x 3 is the same as 0 + 3 + 3 . Think about -3 + (-3) . How can you can write this in multiplication notation? Does this help you extend further your number line model? You might have difficulty extending this model to include examples such as -4x2 and -4 x -2 . If your model can interpret these types of examples, discuss it with a friend or your teacher. Activity 10.2, page 125 1 You are much more likely to come across subtracted numbers, as opposed to free standing negative numbers, in the modelling of practical problems. Can you see how these might have made them more acceptable? Can you think of some examples where subtracted numbers arise in problems relating to everyday situations? Would free standing negative numbers arise in the same situations in a meaningful way? Activity 10.3, page 126 1 Set out the problem as -5x + 6y + 8z = 290 where x, y and z are the prices of cows, sheep and pigs respectively. Solve these equations for x, y and z. Activity 10.5, page 127 1 The area of the rectangle with sides (a - b) and (c - d) is the same as the area of the large rectangle with sides a and c, provided that you subtract off the area of the L-shaped border. Write this statement as an equation. Activity 10.6, page 128 1 a The first part of the extract explains about the construction of the geometrical figure shown in the diagram. The result of the proposition is actually described in the section of the extract entitled Demonstration. You should concentrate on this part. Try to identify the squares and rectangles referred to in this section and then describe in your own words the relationship between them. Note that the extract refers to squares and rectangles by just two points, those at opposite ends of one of the diagonals of the square or rectangle. Introduce letters to represent the lengths of the sides of the squares, then you should be able to write down an algebraic formula which is equivalent to the result.
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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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Page 117 and 118: 772 The beginnings of calculus 9.1
Page 119 and 120: Figure 9.4 774 Calculus you can wri
Page 121 and 122: Calculus including Descartes, under
Page 123 and 124: 118 Calculus Activity 9.7 Cavalieri
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Page 129 and 130: 10.1 Visualising negative numbers 1
Page 131 and 132: 126 Searching for the abstract For
Page 133 and 134: Searching for the abstract Activity
Page 135 and 136: Searching for the abstract John Wal
Page 137 and 138: Searching for the abstract 31. Hith
Page 139 and 140: 134 Searching for the abstract If y
Page 141 and 142: Searching for the abstract Practice
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Page 147 and 148: Searching for the abstract d Do you
Page 149 and 150: 144 Searching for the abstract math
Page 151 and 152: 146 Searching for the abstract As a
Page 153 and 154: Searching for the abstract How does
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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
Page 161 and 162: 156 12 Summaries and exercises usin
Page 163: 158 Hints Activity 2.3, page 15 2 F
Page 167 and 168: outcome 1 step to the right Figure
Page 169 and 170: 14 Answers 3 0;6,40 and 0;2,13,20 4
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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