Download Figurate Numbers

Fibonacci Numbers
Stage 4
Year 7
Press Ctrl-A
©2009 – Not to be sold/Free to use
1
Fibonacci Numbers
Discovered by Leonardo Fibonacci in
the year 1202
The sequence of Fibonacci numbers
starts with 0 and 1.
The other terms in the sequence are found
by adding the previous two terms.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34. . .
0+11+1 1+22+33+55+813+8
13+21
The Video
42
2
Fibonacci’s Tiles
A tiling with squares whose sides are
successive Fibonacci numbers in length
42
3
Fibonacci’s Spiral
A Fibonacci spiral, created by drawing
arcs connecting the opposite corners
of squares in the Fibonacci tiling
42
4
Fibonacci’s Flowers
The majority of flowers
have a Fibonacci number as
their number of petals.
Some species include:
1. Lilies, irises and clover
have 3 petals.
2. Buttercups and some delphiniums have 5 petals.
3. Other kinds of delphiniums have 8 petals.
4. Marigolds have 13 petals.
5. Some asters have 21 petals.
6. Daisies have 34, 55 or even 89 petals.
Did you know that four leaf clover are rare
because 4 is not a Fibonacci number?
42
5
Fibonacci’s Rabbits
Mum & Dad
Each pair of rabbits can produce
another pair of rabbits in each of
the next two generations.
42
6
Fibonacci’s Golden Ratio
An approximation for the Golden Ratio can
be found by dividing consecutive ratios
34 ≈ 1.619
Golden Ratio ≈
21
Leonardo da Vinci was
interested in the
proportions in the human
body
42
7
Fibonacci’s Golden Body
Ratio
Floor to Navel - 97
Height - 159
1 : 1.639
Elbow to Fingertips 41
Underarm to Fingertips 63
1 : 1.537
Width of Head - 16
Length of Head – 25
1 : 1.563
Hairline to Bottom of
Nose - 13
Hairline to Chin - 21
1 : 1.615
Fingertip to 1st Knuckle
- 4.2
Length of Finger - 7.1
1 : 1.690
1st Knuckle to 2nd
Knuckle - 2.5
Fingertip to 1st Knuckle 4.2
1 : 1.680
The table shows measurements (in centimetres)
of my body and the ratio they are in.
All of the ratios are reasonably close
to the golden ratio, 1:1.168.
42
8