The diagonal of the √4 swings to make a √5 rectangle. Diagram 1 & 2

The √5 is an irrational rectangle with the proportions 1:2.236…

The √5 subdivides evenly into 5 equal rectangles each of which cane subdivided in the same 5 equal rectangles… Diagram 3

For example let’s look at Michelangelo’s ‘Fall of Man’ from the ceiling of the Sistine Chapel… Diagram 4

With primary diagonals, reciprocals and subdivisions… Diagram 5

And then… Diagram 6

You can see other examples here.

The √5 also has other special topological properties and we’ll look at them soon…

The science of design, or of line-drawing, if you like to use this term, is the source and very essence of painting, sculpture, architecture… Sometimes… it seems to me that… all the works of the human brain and hand are either design itself or a branch of that art. -Michelangelo