Questions tagged [art]

Use this tag for questions related to art and mathematics, the applications of mathematics in art, or vice versa.

Mathematics and art are related in a variety of ways. Mathematics can be discerned in music, dance, painting, architecture, sculpture, and textiles but has its strongest relationship with visual arts.

Artists have used mathematics since at least the 4th century BC when Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio $1:\sqrt2$ for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De Divina Proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi and in his paintings. Engraver Albrecht Dürer referred often to mathematics in his work Melencolia I. In modern times, graphic artist M. C. Escher used tessellations and hyperbolic geometry, with the help of mathematician H. S. M. Coxeter, while the De Stijl movement, led by Theo van Doesburg and Piet Mondrian, explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jali pierced stone screens, and muqarnas vaulting.

Mathematics has directly influenced art with conceptual tools such as linear perspective, analysis of symmetry, and mathematical objects such as polyhedra and the Möbius strip. Magnus Wenninger creates colorful stellated polyhedra, originally as models for teaching. Mathematical concepts such as recursion and logical paradox can be seen in paintings by Rene Magritte and engravings by M. C. Escher. Computer art often makes use of fractals such as the Mandelbrot set and other mathematical objects such as cellular automata.

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St. Basil's cathedral, Moscow steeple shape

Onion-shaped dome cathedral architecture seen here appears to include in its lower part a geometry of positive, and in upper (steeple) part negative Gauss curvature. The corresponding elliptic and hyperbolic geodesics transition at an inflection…
Narasimham
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An Illustrated Classification of Knots.

Let me be honest here: I know very little about Knot Theory. I'm sorry. I've a friend though, someone with no training in Mathematics at all but who is a huge fan of knots (for whatever reason), who knows even less than I do about it, apparently.…
Shaun
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Mathematics and the art of linearizing the circle

[I edited the question and put stronger emphasis on "constant curvature" than on "naturalness".] One of the most prominent problems of ancient mathematics was the squaring of the circle: to construct the square with the same area as a given…
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Math and Cubism Theory books?

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…
hhh
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What does this music video teach us about 863?

This delightful animation by Stefan Nadelman depicts "the additive evolution of prime numbers", set to Lost Lander's song "Wonderful World": http://www.youtube.com/watch?v=TZkQ65WAa2Q. (If you haven't watched it, you may want to do so before reading…
Chris Culter
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Suggestions for topics in a public talk about art and mathematics

I've been giving a public talk about Art and Mathematics for a few years now as part of my University's outreach program. Audience members are usually well-educated but may not have much knowledge of math. I've been concentrating on explaining…
Cheerful Parsnip
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Scaling and rotating a square so that it is inscribed in the original square

I have a square with a side length of 100 cm. I then want to rotate a square clockwise by ten degrees so that it is scaled and contained inside the existing square. The image below is what I'm attempting, but with a square, not a triangle. (Image…
jb3330421
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Mirror anamorphosis for Escher's Circle Limit engravings?

You are probably familiar with "mirror anamorphosis," the rendering in a painting of a distorted figure that can be undistorted by viewing in an appropriately tilted or curved mirror. The skull in the Hans Holbein painting (the streak at bottom…
Joseph O'Rourke
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Is there a simple perfect squaring of a 1366 by 768 rectangle?

So, a simple perfect squaring of a rectangle is a tiling of that rectangle by squares whose side lengths are all distinct integers. Additionally, not subset of the squares must form a smaller rectangle. My question is if there is a simple perfect…
PyRulez
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Mathematics and cinema

I wander if anyone of you have some knowledge about relations between abstract algebra and cinema. I'm not searching for movies about mathematics or algebra; I'm searching for some kind of application of algebra in the technical or aesthetic aspect…
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Legitimate papers refuting the significance of the golden ratio in art?

I'm not sure this is the right place to ask about this, but is there any legitimate peer-reviewed paper refuting the significance of the golden ratio in art? I can find numerous websites and blogs scattered around the web on this topic, but I don't…
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How were complex geometric shapes drawn without computers?

How did mathematicians create drawings of complex geometric shapes in the past, without 3d graphics in computers? Here is one example of what I’m talking about, drawn in the 16th century:
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Pythagorean theorem painting

I came across this painting(http://www.galleriarusso.com/works/10586-pythagorean-theorem.html) which clearly shows a dissection proof of the pythagorean theorem. The closest proof I found was #72 on this page. I have two questions. 1) Would someone…
JZachary
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Different mathematical models for Audio? Their dimensions and limitations?

Stephen Hazel suggested some dimensions such as time, pitch, velocity of note down event, current root note of chord, chord type(major/minor/7th/etc), pan of the mix, volume of the mix and holding pedal. Vi Hart has popularized orbifolds with…
hhh
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Where is a good source for serious math (wall-size) posters?

Where is a good source for math wall posters that give glimpses of serious and beautiful mathematics? I'm a faculty member looking to find some wall posters (e.g. 2 ft x 3 ft) to hang in a handful of display cases around our department. I'd like the…
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