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This is a similar question as the art question about music here. I am trying to understand how to formulate different styles of cubism mathematically. Ok, we surely will not end up to one definitions so let me break it to some styles:

  • block minimization style where you try to get the same message as earlier with as few blocks as possible (can be used to exaggerate or blur thing etc)
  • vertex minimization or maximization
  • certain area optimization
  • rotation centers and groups (you define certain points to which you apply the same operation again and again -- and the initial point reoccurs, to find the most appropriate form)

the above styles or perhaps better called methods are not exhaustive so I am looking for some books that would advance the area from mathematical perspective.

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If this question will not be well received here, it seems like there is a chance it will be welcomed on cstheory.SE instead. Perhaps under some reformulation, but still. –  Asaf Karagila Jun 21 '11 at 13:13
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Not an answer, but there is a Journal of Mathematics and the Arts. –  lhf Jun 22 '11 at 1:40
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1 Answer

up vote 9 down vote accepted

This book may be of great interest to you:

Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought,
by Tony Robbin. (The link is to Amazon.com where the book is featured, along with the means to "Look Inside"/preview the book.)

A review of that book is available, in pdf format, in the American Mathematical Society Notices, online: Shadows of Reality: Book review

I also came across this pdf of an article Cubism and the Fourth Dimension, by Elijah Bodish (University of Montana) published in TMME vol6, no.3, start p .527. At the bottom of the post is an example of cubism, and is discussed in the article. (For the OP: if it's nothing you already don't know, sorry about that). I found this to be particularly relevant given the article's opening statement (here, cut short):

When one looks into the subject of geometries that attempt to explain fourth dimensional space, it is inevitable that one encounters references to Cubism. The purpose of this paper is to find what the similarities between this mathematical concept and cubism are.... It is important to see how the two fields are interrelated in order to gain a better understanding of both fields, in this case art and geometry." (Elijah Bodish)

The following are some of the references listed in the paper linked above:

Anderson, Kirsti. The Geometry of an Art. Springer Science and Business Media, New York, New York, 2007.

Cabanne, Pierre. Cubism. Finest S.A./Editions Pierre Terrail, Paris, France, 2001.

Golding, John. Cubism: A History and an Analysis. Harper & Row, Publishers, Inc., St 1968.

Henderson, Linda Dalrymple. The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton University Press, Princeton, New Jersey, 1983.

Ivins Jr., William M. Art & Geometry: A Study in Space Intuitions. HarvardUniversity Press, Cambridge, Massachusetts, 1946.

Robbin, Tony. Shadows of Reality. Yale University Press, New Haven, 2006. Stokstad, Marilyn. Art History. Harry N. Abrams, Inc., New York, New York, 2002.


Exemplar, for your viewing pleasure::

Duchamp: "Nude..."

Marcel Duchamp. “Nude Descending a Staircase #2.” Oil on canvas, 1912. (Cabanne 85).

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+ Ohhh! what is this picture??! Wierd!! :-o –  B. S. Feb 20 '13 at 10:35
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