Leonardo da Vinci. In the Renaissance, the golden section achieved near mystical
status – the astronomer Johannes Kepler described it as a mathematical ‘precious
jewel’. Later, Gustav Fechner, a German experimental psychologist, made
thousands of measurements of rectangular shapes (playing cards, books,
windows) and found the most commonly occurring ratio of their sides was close
to Φ.
Le Corbusier was fascinated by the rectangle as a central element in
architectural design and by the golden rectangle in particular. He placed great
emphasis on harmony and order and found this in mathematics. He saw
architecture through the eyes of a mathematician. One of his planks was the
‘modulator’ system, a theory of proportions. In effect this was a way of
generating streams of golden rectangles, shapes he used in his designs. Le
Corbusier was inspired by Leonardo da Vinci who, in turn, had taken careful
notes on the Roman architect Vitruvius, who set store by the proportions found
in the human figure.
Other shapes
There is also a ‘supergolden rectangle’ whose construction has similarities with
the way the golden rectangle is constructed.
This is how we build the supergolden rectangle MQPN. As before, MQSR is a
square whose side is of length 1. Join the diagonal MP and mark the intersection
on RS as the point J. Then make a line JK that’s parallel to RN with K on NP.
We’ll say the length RJ is y and the length MN is x. For any rectangle, RJ/MR =