How_To_Be_Good_At_Math

NUMBERS • SEQUENCES AND SHAPES 17

The Fibonacci sequence

One of the most interesting sequences in maths is the Fibonacci sequence, named

after a 13th-century Italian mathematician. The first two terms of the sequence are 1.

Then we add the two previous terms together to get the next term.

REAL WORLD MATHS

Pentagonal numbers

The sides of these five-sided shapes,

called pentagons, are made up of

equally spaced dots. If we start with

one dot, and then count the dots in

each pentagon, we see this

sequence: 1, 5, 12, 22, 35, ...

These numbers are called

pentagonal numbers.

Each pentagon has

five sides with equal

numbers of dots

Each pentagon shares one

corner, called a vertex,

with the other pentagons

1 dot 5 dots 12 dots 22 dots 35 dots

Add the

previous two

terms to find

the next term

We often find

Fibonacci spirals,

like this shell,

in nature

We can use the number sequence to

make a pattern of boxes like this

Sequence

starts at 1

1 1 2 3 5 8 13 21 34 ...

1+1 1+2 2+3 3+5 5+8 8+13 13+

When we connect

the boxes’ opposite

corners, we draw

a spiral shape

34

21

13

8

5

3

(^11 )
016_017_Sequences_and_Shapes.indd 17 29/02/2016 14: