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Geometry in art
By Anonymous on Wednesday, December 29, 1999 - 04:52 pm:

i need to know how geometry is used in art. i know it is used in vanishing points, but i need some more examples and a little more detail. it would be greatly appreciated it you could help me and/or give me some places where i could look this up. thanks

By Neil Morrison (P1462) on Wednesday, January 5, 2000 - 07:34 pm:

The golden ratio (occasionally denoted by the Greek leter Phi [looks like a spinning top]) is used in art to give pleasing shapes and sizes. I think the ratio is 1/(0.618) which means the ratio is about 1.618 (surprising?)

Wait now I remember:

a half of [1 + (sqrt of 5)]

Greeks did lots of things with it. If you want I can give some interesting uses/properties (although not necessarily relevant to art).

By Dan Goodman (Dfmg2) on Thursday, January 6, 2000 - 08:10 pm:

To the original poster: What exactly do you want to know about geometry and art? The thing you mentioned "vanishing points" is part of perspective, which is a mathematical system for drawing three dimensional landscapes as they would look to someone inside the landscape taking a photograph. If you want more information about perspective, say so, otherwise say what you need.

By Anonymous on Thursday, February 3, 2000 - 09:15 am:

How would you create a priceless picture using geomatry? Has this been done before?

By Dan Goodman (Dfmg2) on Thursday, February 3, 2000 - 09:25 pm:

Well, the pictures of Mondrian probably sell for a hell of a lot of money, these are very geometric. Here is an example:

Composition with Yellow Patch

Also, the renaissance painters were the first to use perspective, here is one by Uccello:

Saint George and the Dragon

Of course, none of these artists use mathematics in itself, but as a tool.

By Dan Goodman (Dfmg2) on Thursday, February 3, 2000 - 09:52 pm:

Also worth mentioning, the cubists, here is a Braque:

Woman with a guitar

Or how about M.C.Escher, who used non Euclidean geometry:

Smaller and Smaller

By Charles Wray (M354) on Saturday, February 26, 2000 - 04:13 am:

Neil is very rt in re PHI. t is a component of what the artist's call COMPOSITION, which is not generally mathematically defined but calls for the artist to develop an intuitive sense of good composition by studying other works of art by experienced artists. Artistic compositions also lend themselves to geometrical structures (euclidian) as expressions of relevance or relationship of objects in the pictures fixed frame.

By Charles Wray (M354) on Saturday, February 26, 2000 - 05:19 pm:

Dear Anon--Agfter sending my message last eve I retired to a night of mind-muttering--a hypnogogic free-fall into the structural lattices of ART. I had sucessfully resisted the temptation to leaf thru sundry lexicons seeking an appropriate definition of esthetic "composition" from the hoary-headed word-savants. For further cortical confabulation see D'Arcy Thompson's "On Growth and Form"--contains muriad descriptions of natural geometry, leaf,limb and flower imbued with mathematical magic also crystal lattices, diatoms, and divers bio-symetries: the polar one of the sun-flower bloom, the bi-lateral of the human body the axial symetry of Watson & Cricks helical DNA.
God, in his infinite wisdom, endowed our whole universe with his ineffable mathematics. The true-born artist draws on it with instinctive skill if not formal math. understanding. An example to ponder: the sublime form of a hen's egg has invested many sculptureswith elegance. See sculpture by Arp. Brancusi(modern) also Venuses of Willendorf and Lespugue (18,000-30,000 BC)
An interesting exercise: take a zerox copy of Botticelli's Primeravera, a straight edge and compass and discover the "geometry";and try Picasso's Demoiselles d'Avignon. Pax Vobiscum !