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2 A spiral winds in a continuous curve round a point.
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6 Some spirals are man made. Others are found in natural things such as plants and animals.
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39 This type of spiral is called an Archimedean spiral after the Greek mathematician Archimedes. In an Archimedean spiral the gap between the curves of the spiral stays the same.
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40 Archimedes was a mathematician who lived in Greece from 287 BC to 212 BC.
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41 Greece
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42 Archimedes drew a special spiral by pulling the legs of a pair of compasses apart while turning the compasses.
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43 Circles that are one inside the other and have the same centre are called concentric circles.
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67 How much of the square is yellow? 1 whole 1212 1414 1818 1 16 1 32
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68 Copy these numbers and continue the pattern. 1 2 1 1 4 Write down a rule that explains how to find the next number. 1 8 1 16 1 32 1 64 1 128 1 256
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69 These spirals are called Baravelle spirals. Baravelle spirals are made with triangles
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70 Draw a square with sides 16 cm long? What is the area of the square?
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71 Mark the midpoint of each side of the square
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72 Joint the midpoints to make a new square Colour the bottom right triangle.
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74 Mark the midpoint of each side of the new square.
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75 Join the midpoints to make a new square. Colour the triangle underneath the new square.
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77 Continue to draw new squares and colour triangles until the square is too small to divide again.
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79 Knitted wall hanging made from Baravelle spirals
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85 Leonardo of Pisa (1170 – 1250 AD) was an Italian mathematician. He is sometimes called Fibonacci. Fibonacci is famous for helping to spread the Hindu Arabic numbers in Europe. These numbers replaced the Roman number system.
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86 Italy
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87 There is a special sequence of numbers called the Fibonacci sequence because Fibonacci wrote about this sequence. 0, 1, 1, 2, 3, 5,5, 8,13,21 …
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88 Fibonacci numbers can be found in many places, for example the number of petals on a flower is often a Fibonacci number. 1 5 3 2 21 13 8
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89 The numbers in the Fibonacci sequence can be used to form a spiral. This spiral can be found in natural things and is sometimes called the golden spiral. Chameleon's tail Nautilus Shell
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