1

*

*The Fibonacci Numbers start with 1 and 1.

*The next number represents the sum of the

previous two numbers.

2

*

3

*

If you take any two

consecutive Fibonacci

numbers and divide them,

then the value of that ratio is

approximately 1.6

This is often called the

golden ratio

Small Number Large Number Ratio

3 5 1.666666

5 8 1.6

8 13 1.625

13 21 1.615

4

*

Rectangles (called golden

rectangles) can be drawn using

consecutive Fibonacci numbers as

the dimensions.

This golden rectangle (55 wide by

34 high) can be subdivided into

smaller golden rectangles.

A nice spiral can be drawn in each

golden (“Fibonacci”( rectangle –

no matter what the size.

*

Spirals of a pineapple:

Three arms of 5, 8, and 13

5

Spirals of a pinecone:

5 arms and 8 arms (small ones)

8 arms and 13 arms (large ones)

Scientists speculate that plants grow in

spiral formation (with Fibonacci

numbers) because this arrangement

makes for the perfect spacing for

maximum growth and survival.

Bananas have 3 or 5 flat sides.

*

6

* Lilies and irises = 3 petals

Black-eyed Susan’s = 21 petalsCorn marigolds = 13 petals

Buttercups and wild roses = 5 petals

7

~ Fibonacci spiral found in both snail and sea shells

*

*

A scale has 8 notes

There are 13 notes through its octave

5 black notes, 8 white notes

8

*

Body parts:

1 nose

2 eyes

3 segments in each limb

5 fingers on each hand

9

DNA molecules:

21 angstroms wide

34 angstroms long

(in each full cycle of the double helix)

The ratio of consecutive parts of the

fingers is equal to 1.6

*

The Parthenon ( an ancient temple in

Athens) fits almost precisely into a

golden rectangle.

10

In the United Nations building, the width of

the building compared with the height of

every ten floors is a golden rectangle

*

The Parthenon ( an ancient temple in

Athens) fits almost precisely into a

golden rectangle.

11

Mona Lisa’s beautiful smile appears to change and her eyes seem to follow you as

you move about her. Her proportions have been examined extensively, and Leonardo

seems to have made extensive use of the golden rectangle in its creation.

*

The “Rule of Thirds” in

photography

12

*

• Cigarette packs (89 x 55 mm)

• Matchboxes (55 x 34 mm)

• Business cards (89 x 55 mm)

• Index cards

• Some calculators and cell phones

• Some computer and TV screens

13

*

*Fibonacci: Fingerprint of

God

*Golden Ratio in the Human

Body

*1.618 Phi

14