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My Exploration of the Beauty in Mathematics
Introduction
"What is beauty?” Is beauty only in the eye of the beholder, or are there some absolute values? Beauty is a mystery! "I know not what beauty is, but I know that it touches many things", Dürer .
It is difficult to define beauty; but there is much impressive testimony to the importance of the emotions that beauty calls forth.
Richard Jefferies wrote:
“The hours when we are absorbed by beauty are the only hours when we really live…… These are the only hours that absorb the soul and fill it with beauty. This is real life, and all else is illusion, or mere endurance.”
If we study the beauty of nature, art, or architecture we will discover a common
principle running throughout. This common principle is the universal recognition
of pleasant proportion. We all have a natural understanding of good proportion
much in the same way as we know how to divide a line in half or erect a
perpendicular. We easily agree that an object of art has good or bad proportion,
or that this face looks too long, or too short and out of proportion. This
magical connecting thread of proportion, known since antiquity, is none other
than the Golden Proportion, a phenomenon related to beauty.
The following pages illustrate just a few facets of the mystery and magic of
this proportion. The understanding of this concept will enable the reader to
take a first step on a journey of discovery into an unexpected dimension of
beauty which affects our lives at every turn. It is one of the building blocks
of beauty that when applied to art, architecture, music, dental work…..,
produces success.
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