GOLDEN MEAN EXPLAINED AND ADAPTED
Finding a satisfactory format for a square canvas
You will recall my explanation of how the 'golden mean' is constructed
I intend to use this golden rectangle as the basis for the major composition elements in my painting. First I will extend the diagonal of the original square to meet the extended vertical of the right side of the rectangle as shown in Fig 5
From this point of intersection I draw a square that will encompass and center the original square (here shaded) as in Fig 6. Thus I have established the proportions of my smaller square within the larger.
Fig 7 what is the proportion of x to y? Realizing the shaded triangle is a right angled triangle whose hypotenuse is the square root of the sum of the other two sides then ...
Fig 8 Since my canvas is 50" (126cm) square then after finding the center using my diagonals I measure approx 11" (27cm) to the right to find the vertical line and point 'B'. 
Thus we have our square within a square. This, as you can see, is essentially the 'design' standard I used for the paintings shown below.
Fig 9 The 'Golden Rectangle' can be further divided into smaller 'golden rectangles' and arcs of circles added to make a 'Golden Spiral' similar to those you see in pine cones etc.
For the unfinished painting on the right a few more strategic secondary accents were aligned with these secondary golden rectangles.
STUDENT ACTIVITY:Draw your own 'golden spiral' beginning with a unit (ad = 6" or 250mm) and find out the proportions for a 'golden triangle'. Allow 40min.
GO
TO ... improve old photographs
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