INTRODUCTION TO THE GOLDEN MEAN

… and the Fibonacci Sequence

The Golden Mean

Aristotle defined it as…the desirable middle between two extremes, one of excess and the other of deficiency

In Art,a term used to describe aesthetically pleasing proportioning within a piece.

It is not merely a term -- it is an actual ratio.

So what is the Golden Ratio? The golden ratio is 1 to 1.618034.

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two numbers to get the next)

The GOLDEN RATIO and FIBONACCI NUMBERS sea shell shapes, branching plants, flower

petals and seeds, leaves and petal arrangements all involve the Fibonacci numbers.

The Golden Mean also known as… The Golden Ratio The Golden Section The Golden Rectangle The Golden Number The Golden Spiral The Divine Proportion

Wait… this is Math

The line AB is divided at point M so that the ratio of the two parts, (the smaller MB to the larger AM) is the same as the ratio of the larger part AM to the whole AB.

This is kind of like geometry…

Given a rectangle having sides in the ratio 1:1.6

Dividing the original rectangle into a square and new rectangle results in a new rectangle having sides with a ratio 1:1.6.

This is called a Golden Rectangle

Every other division of the rectangle into squares results in a spiral

This figure is known as a whirling square.

Fibonacci Sequence & the Golden Rectangle

Golden Rectangle Golden Spiral

What is this called again?

Throughout history, the ratio for length to width of rectangles of 1.61 has been considered the most pleasing to the eye.

The Golden Mean and Art

The Parthenon

The exterior dimensions of the Parthenon in Athens, built in about 440BC, form a perfect golden rectangle.

With the Golden Rectangle

The Parthenon

Leonardo Da Vinci’s Mona Lisa

Try drawing a rectangle around her face.

Are the measurements in a golden proportion?

With Divine Proportion

Mona Lisa

Today, where might you want to use the Golden Mean to create an image that is pleasing to the eye?

Modern Day Examples

TWITTER

Apple Logo

iCLOUD Logo

2 hands each of which has ...

5 fingers

3 parts

2 knuckles

Look at your own hand

Grab a ruler from the center of the table

Your turn… finger, hand, arm, foot

It can be found EVERYWHERE!!!!

The Golden Mean in Nature

The spiral is created by the Golden Rectangle divisions.

Nautilus Shell

The Golden Spiral can be seen in the arrangement of seeds on flower heads.

Seeds

Pine cones show the Golden Spirals clearly. Here is a picture of an ordinary pinecone seen from its base where the stalk connects it to the tree.

Pine Cones

On many plants, the number of petals is a Fibonacci number:Buttercups have 5 petals; Lilies and Iris have 3 petals; some Delphiniums have 8; sorne Marigolds have 13 petals; some Asters have 21 and Daisies can be found with 34, 55 or even 89 petals.

Flower Petals

Two days from now…

You will choose a pattern from nature which is created through the phenomenon of the Golden Mean such as the pattern in a Nautilus Shell and create an original design.

The Possibilities are infinite… The pattern of a butterfly wing…. Patterns of sea creatures…… Close ups of patterns from nature….. Leaf arrangements, leaf veins, petal

patterns…. Feather patterns from birds such as one

feather, or the entire tail pattern of a peacock….

Look at animals, bugs, fish, and plants to get ideas…..

Quick Rubric

The design must be original.

The painting must use a pattern found in nature to inspire the design.

The project is to be done in tempura paint.

The design must show technical craftsmanship.

The student must make good use of class time and take proper care of tools and supplies.

THE DESIGN MUST USE THE GOLDEN MEAN