1 A spiral winds in a continuous curve

A spiral winds in a continuous curve round a point. 2

Some spirals are man made. Others are found in natural things such as plants

This type of spiral is called an Archimedean spiral after the Greek mathematician Archimedes.

Archimedes was a mathematician who lived in Greece from 287 BC to 212 BC.

Archimedes drew a special spiral by pulling the legs of a pair of compasses

Circles that are one inside the other and have the same centre are called

How much of the square is yellow? 1 whole 1 2 1 4 1

Copy these numbers and continue the pattern. 1 1 2 1 4 1 1

These spirals are called Baravelle spirals are made with triangles 69

Draw a square with sides 16 cm long? What is the area of the

Mark the midpoint of each side of the square 71

Joint the midpoints to make a new square Colour the bottom right triangle. 72

Mark the midpoint of each side of the new square. 74

Join the midpoints to make a new square. Colour the triangle underneath the new

Continue to draw new squares and colour triangles until the square is too small

Knitted wall hanging made from Baravelle spirals 79

Leonardo of Pisa (1170 – 1250 AD) was an Italian mathematician. He is sometimes

There is a special sequence of numbers called the Fibonacci sequence because Fibonacci wrote

Fibonacci numbers can be found in many places, for example the number of petals

The numbers in the Fibonacci sequence can be used to form a spiral. This

Slides: 114

Download presentation

A spiral winds in a continuous curve round a point. 2

Some spirals are man made. Others are found in natural things such as plants and animals. 6

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 39

Archimedes was a mathematician who lived in Greece from 287 BC to 212 BC. 40

Greece 41

Archimedes drew a special spiral by pulling the legs of a pair of compasses apart while turning the compasses. 42

Circles that are one inside the other and have the same centre are called 43 concentric circles.

How much of the square is yellow? 1 whole 1 2 1 4 1 8 1 16 1 32 67

Copy these numbers and continue the pattern. 1 1 2 1 4 1 1 8 16 1 1 1 32 64 128 1 256 Write down a rule that explains how to find the next number. 68

These spirals are called Baravelle spirals are made with triangles 69

Draw a square with sides 16 cm long? What is the area of the square? 70

Mark the midpoint of each side of the square 71

Joint the midpoints to make a new square Colour the bottom right triangle. 72

Mark the midpoint of each side of the new square. 74

Join the midpoints to make a new square. Colour the triangle underneath the new square. 75

Continue to draw new squares and colour triangles until the square is too small to divide again. 77

Knitted wall hanging made from Baravelle spirals 79

Leonardo of Pisa (1170 – 1250 AD) was an Italian mathematician. He is sometimes called Fibonacci is famous for helping to spread the Hindu Arabic numbers in Europe. These numbers replaced the Roman number system. 85

Italy 86

There is a special sequence of numbers called the Fibonacci sequence because Fibonacci wrote about this sequence. 0 , 1 , 2 , 3 , 5 , 8 , 13 , 21 … 87

Fibonacci numbers can be found in many places, for example the number of petals on a flower is often a Fibonacci number. 2 1 3 13 5 88 21

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 89

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114