The Golden Mean

Ratios and proportion in Art and Design

Commonality

• What have the following got in common?– The Parthenon– Mondrian’s paintings– the arrangement of teeth– the population growth of rabbits– Courbusier’s architecture

INCE earliest history, man has continued to develop his sense of proportion in the shaping of his world.

With the development of mathematics (the measuring of objects and space), early design began the arrangement of objects in harmonious relationship to each other and the space they occupied.

1 1.618

1

1.618

Plan of the Parthenon

Courbusier

The calipers are arranged so that the ratio of the larger to the smaller is exactly 1.618:1.00. This is the Golden mean

Mondrian

Kees van Prooijen a three dimensional GM

The height to width ratio is again based on the golden mean

Da Vinci’s La Giaconda

Human anatomy has strong connections to the Golden Mean.

To construct the Golden Mean take a one by one square, repeat it. Create a two by two square on one edge. Then the three by three, etc.

The whole set follows what is called a Fibonacci series

Tracing out the natural curve creates the nautilus shell shape

In the Nautilus shell the ratio of each segment to the next is;1.618:1 Again the golden Mean.

Rabbits multiplying create the Golden Mean Ratio

The spirals in this plant follow precisely the golden mean curve. This occurs because they are arranged at 360/1.618 degrees to each other

• Try tracing spirals in this pine cone. There are both clock-wise and anticlock-wise spirals available

• Eight clock-wise spirals in the pine cone.

• There are 13 anti-clockwise spirals in a pine cone

• 13/8 is an approximation to the Golden section

Dynamic Symmetry

In the twentieth century two people played primary roles in the revival of the golden section as a design element.

One was Jay Hambridge, and author and art instructor, whose book, Elements of Dynamic Symmetry' was first published in 1920.

The other was Le Corbusier, an authentic genius of twentieth century design, who developed our first clearly identifiable design system called the Modulor.

Fashion

The golden mean gauge shows that the dominant landmarks are in the golden proportion

Even “perfect” teeth tend to the ratio of the golden mean.

The four front teeth, from central incisor to premolar are the most significant part of the smile and they are in the Golden Proportion to each other.

When written freehandwe tend to design letters so that the intersections are in the ratio of the Golden Mean. To a greater or lesser degree of accuracy.Using examples of your freehand typography designs estimate the ratio.

The size of the top loop is in proportion to the bottom loop.