Mondrian was inspired by the harmony of nature and numbers, particularly the proportion known as the Golden Ratio and the associated Fibonacci Numbers.

2. THE GOLDEN RATIO AND FIBONACCI NUMBERS

The ratio, 1 : 1.618, is also known as Phi, an Ancient Greek letter.

Roughly speaking, the Golden Ratio is 1 : 1.5 and a bit more!

As well as a line, we often see the Golden Ratio as a rectangle. Whatever the size,

the ratio is always the same. You could draw a large rectangle of 1m x 1.618m,

or a small rectangle of 10mm x 16.18mm, and the ratio always stays the same.

The Golden Ratio is a proportion that has been used for thousands of years in geometry,

art and architecture, because it is believed it is the most pleasing to the eye.

The Parthenon, by Itkinos and Callicrates, Athens, Greece (5th century BC)

Here you can see the Golden Rectangle placed over the Parthenon. Can you also see more squares and rectangles inside the big rectangle?

The big rectangle is divided at the Golden Ratio horizontally, creating a square and a rectangle. Then that rectangle is divided at the Golden Ratio vertically, creating a square and a rectangle. Then that rectangle... and so on. And they all have the Golden Ratio.

You can see that the different parts of the Parthenon are designed in those squares

and rectangles.

You can create the Golden Ratio easily using Fibonacci numbers.

In 1202, the Italian mathematician Fibonacci used a 6th-century Indian number sequence

to see how many rabbits he would have at the end of a year, if he started with one pair.

This is the sequence of numbers. Can you see what he did?

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21...

Each number is the sum of the preceding two numbers. You could go on forever!

He thought he would have 144 rabbits, but it was all just for maths fun, as he would have always need the right number of baby boy and girl rabbits for his sequence to actually work!

Fun fact: Fibonacci also introduced the Indian-Arabic number system, 0-9, to the West.

Otherwise, we might still be using Roman numerals!

If you draw the Fibonacci number sequence out in squares, you will get rectangles that are around the Golden Ratio, like the Greeks used in the Parthenon, Mondrian used for his art, Yves Saint Laurent used for his dress, and a fancy-dress company used in my dress!

At Fibonacci's numbers 233 and 377 is the precise Golden Ratio, 1 : 1.618!

3. THE GOLDEN RATIO IN ART, OBJECTS AND HUMANS

The Golden Ratio of 1 : 1.618 is important because it is a Mathematical proportion that has been used for thousands of years in geometry, art and architecture.

It is used because it is believed to be most beautiful and restful proportion for us to see.

Amazingly, you can even see it in humans! Here are some examples:

Mona Lisa, by Leonardo da Vinci, Italy (1503)

The violin is designed according to the Golden Ratio, and the scroll even contains the Fibonacci Spiral! You can make the spiral by drawing an arc across each square.

The Great Wave, by Hokusai, (1829)

National Gallery, London (1838). Remind you of anything? The Parthenon!

Eiffel Tower, by Stephen Sauvestre, Paris (1887)

An octave on a piano keyboard is in the Golden Ratio, and consists of the first six

Fibonacci numbers, 1, 2, 3, 5, 8, 13!

The Aston Martin, James Bond's car (1965 onwards), is in the dream Golden Ratio.

And so is Sonic the Hedgehog, a computer game character, Japan (1991 onwards)!

Some people think we like certain faces when they are in the Golden Ratio. Is that why the supermodel Kate Moss is so successful?

But even if you aren't a supermodel, your hand to elbow is still in the Golden Ratio.

And your hand to fingers – and your fist, which also has a Fibonacci spiral!

Maybe your whole body is the Golden Ratio of 1 : 1.618...

And some say the Apple logo is designed to the Golden Ratio too!

And that's not all...

4. THE FIBONACCI SPIRAL AND NUMBERS IN NATURE

Amazingly, the spiral that the Fibonacci sequence and Golden Ratio creates is also seen in Nature, as are the Fibonacci numbers themselves.

Here are some examples:

Many flowers favour 3, 5, 8, or 13 petals - all Fibonacci numbers.

Seeds are often in a spiral of Fibonacci numbers, because those numbers are the

best way to pack more seeds into the space and to get to the sunlight. Pine cones

and pineapples are often a Fibonacci 8 spirals seen one way, 13 the other. How many

do sunflower seeds have?

Sometimes the spirals are amazing...

Sometimes cute...

And sometimes hands down scary!

GOLDEN RATIO ACTIVITIES

ACTIVITY! Can you see what these Fibonacci items are?

ACTIVITY! The first Fibonacci numbers are 1, 2, 5, 8, 13.

How many more can you find in 1 minute?

ACTIVITY! Try to count the spirals in pineapples, pine cones and sunflowers,

and see if you find Fibonacci numbers!

ACTIVITY! Make your own Golden Rectangle, using some Fibonacci numbers. Here's how:

ACTIVITY! Spot more Golden Ratios, Fibonacci numbers and spirals in art, objects,

and Nature.

ACTIVITY! Use numbers and geometry to create your own art.

ANSWERS 1 egg 2 rose 3 pine cone 4 hurricane 5 galaxy 6 nautilus shell 7 Africa 8 ram's horn 9 Calla lily