## The Golden Mean or Golden Section

The 'Golden Mean' is merely a mathematical ratio usually discerned by the painter as the ratio of the larger side of a rectangle as it relates to the shorter. Derived by the ancient Greeks it can be constructed geometrically or expressed as a simple ratio, namely 1:1618... Like "pi", the number 1.618... is an irrational number. Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments. The builders of Paestum used the Golden Mean in their temples. Artists as diverse as Leonardo da Vinci and George Seurat used the ratio when constructing their paintings.

In classical architecture it was thought this particular ratio was the most pleasing to the eye and its extrapolation into a spiral could be found replicated in nature in such diverse things as pine cones and sea shells or the curve of a fern.

I see no particular theological significance in the golden mean, nor do I slavishly design my paintings or canvases to follow its geometry.

Well that noted then how is this 'golden mean' found using a ruler and a compass?

Quite simply.

In Fig 1 we draw a square.

In Fig 2 we divide it into two.

Fig 3 and we use our compass to transfer the diagonal to the base line. Then we form the rectangle that for artists represents the 'golden mean' .

Ok now we know what the 'golden mean' is what do we do with it? How do we employ it to assist our painting? Well, the most obvious is to buy your canvases in the proportion 1:1.618 (or thereabouts). Other than that you will understand why, in the previous lesson, I used my particular diagonal method to define my painting accents and if you look at the diagram below you will see where I superimpose the golden mean over the diagonals. It is almost an identical result. Otherwise one method could be described as robust while the other more precise.

(A full view of this painting can be seen by pressing here. It is also available as a quality giclee print.) To find out how I designed this particular painting format, using the golden mean, you will need to go to the advanced golden mean section of these lessons as the particular details may cause the odd frown or need for some to visit our site refreshment area (open 24 hours). Anyway it does not mention the 'Golden Triangle' (really an isosceles triangle with base angles of 72 degrees and not an unspecified area in SE Asia), and its not for the instinctive painter. It is however, important for those who seek to understand order before they experiment with chaos.

STUDENT ACTIVITY: Repeat and copy my diagrams. Label them.

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