The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course, I do not here speak of that beauty which strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts and which a pure intelligence can grasp. This it is which gives body, a structure so to speak, to the iridescent appearances which flatter our senses, and without this support the beauty of these fugitive dreams would be only imperfect, because it would be vague and always fleeting. Jules Henri Poincare
If a poet sees beauty in a rainbow ... so does the physicist in the laws governing its manifestation. The surface beauty of the rainbow ... is appreciated by all men: it is given. But the buried beauty, uncovered by the industrious researches of the physicist, is understood only by the scientifically literate. It is acquired: education is essential. H. E. Huntley: The Divine Proportion

You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of the mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us. Heisenberg: communication to Einstein

When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong. Richard Buckminster Fuller

Accuracy is, in every case, advantageous to beauty, and just reasoning to delicate sentiment. In vain would we exalt one by depreciating the other. David Hume: An Enquiry Concerning Human Understanding

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. - -Albert Einstein

The great tragedy of science: the slaying of a beautiful hypothesis by an ugly fact. Thomas Huxley

Sweet is the lore which Nature brings; Our meddling intellect Mis-shapes the beauteous form of things:- We murder to dissect. Enough of Science... William Wordsworth: The Tables Turned - An Evening upon the Same Subject

Though we travel the world over to find the beautiful, we must carry it with us or we find it not. - Ralph Waldo Emerson

Everything has beauty, but not everyone sees it. Confucius

Date:	2003-04-08 02:57
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http://www.goldenmeangauge.co.uk/golden.htm

"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 .
If we study the beauty of nature, teeth, or art 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 non other than the Golden Proportion, a phenomenon related to beauty.
The following notes 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 we can easily apply to our dental work, confident of success.