You may have heard of the Golden Section, or the phrase "Fibonacci Sequence' before, particularly if you read the "Da Vinci Code".
The Fibonacci sequence is a series of numbers:
0+1=1, 1+1=2 , 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21 etc etc
We can translate these figures into geometric shapes and then it becomes much clear why we are talking Maths in an art topic.
The sides of the squares are the total of each stage. Let's just look at the shapes rearranged a little, and then with a curve drawn round opposite corners. Can you see a spiral in the curve?
This spiral is found throughout nature. Let's apply those numbers, shapes and spirals to some photos.
The centre point of the Fibonacci spiral occupies the point approximately 5/8ths of the distance across the width of the picture. Artists over the centuries have called this the Golden Section or the ideal position to place the focus of the picture. This is not a rule that is bedded in concrete. It merely identifies an ideal position for the focus.
Look at any Internet search engine for ‘Golden Section’ and you will easily get bogged down in calculations and Algebraic symbols.
The two essential things to keep in mind are the facts...
The link to a very clear explanation - from which the examples above were drawn - is here http://photoinf.com/Golden_Mean/Eugene_Ilchenko/GoldenSection.html
Like any rule, there are plenty of exceptions, but if you remember, we are told never to put a horizon line half way up (or down) a picture but to put the horizon line approximately 1/3 of the way. There is very little difference between 5/8 and 2/3.
We don’t have to be precise in our measurements, we just have to hold the idea in our heads when we compose our picture.
Please note these are all copyright - so don't go copying them!
Amalfi Coast - a watercolour by Tom Hill
This is a lovely composition, and you will note that the major elements of the picture are all away from the centre point of the picture where the road comes down to the beach. The light coloured building which has the lightest light of the end wall adjoining the darkest dark of the shadow, is on one of the golden section points. Draw a line vertically down a three eighths section from the left and most of the major features fall within it.
The Wave, Oil Painting by Clyde Aspervig
The crashing wave shows enormous power and the line of the wave foot is not central but approximately on the five eighths line.
The dark area to the left where the wave has still to break makes a meeting with the foam at the golden section point.
Back Place in Rain, Melbourne - Watercolour by Greg Allen
An amazing artwork with a lovely feel to it.
Just look at the lady in the blue coat and orange brolly. She is on the five eighths line from the left and the umbrella is close to that magic golden section point.
Once again there is little detail at the centre.
Evening Walk, Enborne - Watercolour by Jeane Duffey
A very atmospheric painting.
Look where the figure stands - OK not far off central but on the important line three eighths from the bottom of the picture.
There a lot of nice compositional touches here, but like all the images shown, you can look around and see how the artist avoids the dead centre ground and piles on the detail around the edges of the small block in the centre formed around the golden section points.
Don’t get too worried about this area of composition. The rules are not set in concrete, and the picture police will not come calling if you put your main feature in the centre. Sometimes it can’t be avoided.
And like all rules, there are plenty of cases where the rule is proved by the breach of it.