Page 20 - Mathematics Coursebook

2 Sequences, expressions and formulae

A famous mathematician called Key words
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Leonardo Pisano was born around
1170, in Pisa in Italy. Later, he was Make sure you learn and
known as Fibonacci. understand these key words:
Fibonacci wrote several books. In sequence
one of them, he included a number term
pattern that he discovered in 1202. consecutive terms
"e number pattern was named term-to-term rule

a#er him. infinite sequence

1 1 2 3 5 8 13 21 34 … … finite sequence
function
Can you see the pattern? function machine

To $nd the next number in the input
pattern, you add the previous two output
numbers. mapping diagram
So 1 + 1 = 2 Fibonacci (1170–1250). map

1 + 2 = 3 unknown
equation
2 + 3 = 5 solution
3 + 5 = 8 expression
5 + 8 = 13 and so on. variable
"e numbers in the Fibonacci sequence are called the Fibonacci formula (formulae)

substitute
numbers. derive

"e Fibonacci numbers o#en appear in nature. For example, the

numbers of petals on !owers are o#en Fibonacci numbers.

"e numbers of spirals in seed heads or pinecones are o#en Fibonacci numbers, as well.

A sun!ower can have A pinecone can have

34 spirals turning clockwise 8 spirals turning clockwise
and 21 spirals turning and 13 spirals turning
anticlockwise. anticlockwise.
In this unit you will learn more about number patterns.

2 Sequences, expressions and formulae 19