history of mathematics - National STEM Centre

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Chapter 5 Arab mathematics Introduction In this unit, the term 'Arab' refers to a civilisation containing many ethnic, religious and linguistic groups that flourished between the 9th and 15th centuries AD. The Arab civilisation included 'non-Arab' lands, such as present-day Iran, Turkey, Afghanistan and Pakistan, all of which now have distinctive Islamic cultures. The mathematicians whose work is described in this unit all worked in Arabic. The unit consists of just one chapter which summarises some of the achievements of these 'Arab' mathematicians. This unit is designed to take about 10 hours of your learning time. About half of this time will be outside the classroom. There are summaries and further practice exercises in Chapter 12. Mathematical knowledge assumed • how to solve quadratic equations. 53
5 Arab mathematics You should think of the role of the Arab mathematicians as having two components, which are complementary: • the translation and subsequent handing on of Greek and Indian mathematics texts, such as Apollonius's Conies • their own original contributions, made by embracing and developing both eastern and western mathematics. This chapter falls into four parts. In the first part you learn about the evolution of the Hindu-Arabic number system, and see in Activity 5.1 how the facility with fractions of a whole was used to help implement the Islamic rules of inheritance. In the second part, Activities 5.2 and 5.3, you will learn how the Arab mathematicians took what was known about trigonometry and developed it further. In Activities 5.4 to 5.7 you will study some of the variety of problems, originating from Indian and Chinese texts, on which the Arab mathematicians worked. Then you go on to learn how the Arab mathematicians developed a geometric approach, inspired by Greek geometry, to the algorithmic solution of equations. 5.1 Inheritance problems 5.2 The trigonometry of chords 1 5.3 Compiling trigonometric tables !: 5.4 The chess-board and other problems , 5 5 Amicable numbers 5 6 Homer's method 5.7 The rule eof of "double false I I 5 8 fe Solutions of t quadratic equations 1 5.9 1 Solving cubic ;1 equations '1 5. 10 Graphical deductions Although the chapter has been designed to be read and worked in sequence, the four parts are independent, and if you prefer you may study them in some other order. .x:,^ :h>;;,:, :c;;:,;.•:. :s:^>::»^M.M ;,;;;;;.: ,:^:Z^.:i, , ,: .«
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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
Page 8 and 9: The Babylonians Chapter 1 Introduct
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.
Page 39 and 40: 34 The Greeks Activity 3.4 g Now us
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Page 43 and 44: 38 The Greeks Activity 3.7 therefor
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Page 47 and 48: 42 More Greek mathematics 4.1 Some
Page 49 and 50: The Greeks Q.E.D. stands for 'quod
Page 51 and 52: Figure 4.3 46 The Greeks • treat
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Page 61 and 62: The Arabs Western Arabic, or Gobar,
Page 63 and 64: The Arabs Activity 5.2 Figure 5.3a
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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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134 Searching for the abstract If y
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138 Searching for the abstract Extr
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144 Searching for the abstract math
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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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