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Questions tagged [art]

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

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Is there a general formula for the areas of 4 regions in a square (given 4 exterior points)?

Without loss of generality, assume we have a unit square.  If two non-parallel lines intersect within this square, there will be four points on the boundary of the square. The lines and the boundary ...
Gregg H's user avatar
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2 votes
1 answer
319 views

Group Theory in Non-European/Subaltern Cultures?

I'm doing undergraduate research on the history of Abstract Algebra (specifically permutation groups) and the notion of symmetric groups in indigenous artwork has come up several times. Is anyone ...
zomzoms's user avatar
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9 votes
1 answer
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Le poisson modulo un

I found this image and you can see a cut fish and the words "Le poisson modulo un", meaning "the fish modulo $1$". I wanted to ask what this means, if it is a joke or a metaphor. ...
Lonaldin's user avatar
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3 votes
3 answers
211 views

Finding a Closed Form for a Grade School Art Project [duplicate]

Hello Math StackExchange! When I was in grade school, our math class did an art project where we drew many straight lines to make what appears to be a curve on the outside (pictures attached). I've ...
Jenny Pianist's user avatar
2 votes
1 answer
167 views

Orbifold signature and fundamental tile of Escher's Circle Limit IV

In Conway, Burgel and Goodman-Strauss' book The symmetries of things, Chapter 17, the following picture by Escher was analysed using orbifold notation. It's a hyperbolic pattern in the Poincare disk. ...
Keplerto's user avatar
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10 votes
2 answers
220 views

A periodic layout for the Petersen graph

The Petersen graph is a well-known graph with genus $1$, which means it can be drawn without crossings on a torus. Here is one possible embedding of this type. Topologically, we can think of a torus ...
Misha Lavrov's user avatar
2 votes
0 answers
156 views

Algorithms for drawing hyperbolic tilings

I was looking at hyperbolic tilings on the Poincare disc model like these the other day, and I wondered how I might make my own. I have a basic understanding of what hyperbolic space is and how it ...
zenzicubic's user avatar
2 votes
0 answers
225 views

Software for interactively drawing on a torus

This is possibly not the best place to put this, but I am looking for a software where you can draw on a plane diagram of a torus (unit square with identifications) and it automatically maps the ...
Andrea B.'s user avatar
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2 votes
0 answers
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What is the mathematical description of vanishing line in art?

In drawing tutorials on how to give a drawing the '3d -effect', the concept of vanishing line is brought up. I don't exactly understand it, but it seems so that all parallel lines on the object that ...
Babu's user avatar
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0 votes
1 answer
201 views

Escher's circle limit: Fishes in the Beltrami Poincare disc

As you stare at this, try to imagine yourself as one of the fish. You are exactly the same size and shape as every other fish, and you can swim in a straight line forever without ever seeing any ...
Babu's user avatar
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4 votes
2 answers
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Artist needing to determine geometric angle for sculpture based on platonic solid

Dear Mathematicians I need your help for a new sculpture! I will attach images but first imagine 2 hexagons - where one is rotated 30 deg. They are separated by 12 equilateral triangles. I need to ...
Pete Moorhouse's user avatar
3 votes
1 answer
190 views

How can I calculate $\rho_\alpha(z)$?

I am trying to design a group of complex functions $\rho_\alpha$ that have a type of symmetry that might look nice if it exists. This is what "symmetry" I want to try. $$\alpha=a+bi\space\...
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1 vote
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How can I parametrize curves to move in $\{R,G,B\}$ space which give me pretty and interestingly varying colors for my fractal plots?

A few weeks ago I started doing some Graphical User Interface programming in QT as a part of updating my skills. The first graphical application was a color wave effect explorer which I needed some ...
mathreadler's user avatar
3 votes
1 answer
104 views

How can I approximate $t\to \sin(t)$ function for art purposes using computationally cheap alternatives?

Background : The other day I felt like updating my knowledge with GUI programming so I made a small application that rendered a multivalued periodic function $\mathbb R^3 \to \mathbb [0 ,255]^3$. The ...
mathreadler's user avatar
28 votes
1 answer
1k views

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 ...
Narasimham's user avatar
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0 answers
88 views

Advice: "Stained Glass Optimization and Coloring"

I hope everything is going well for everyone reading this at the moment. I am hoping someone here could offer some guidance and advice for a problem I am looking into. Problem I would like to be able ...
FilteredFrames's user avatar
3 votes
0 answers
59 views

Finding mathematical objects

I am very interested in mathematical art/object such as Moebius strip, Klein bottle, etc. and I am searching a place/website where we can buy such things. Does anyone know where I can find something ...
user avatar
0 votes
4 answers
158 views

How do I make spirograh diagrams using software?

There are these "string math artworks" I believe they are called "spirographs" where people usually take a circle or other geometric shape and put in nails on the shape and then ...
Erock Brox's user avatar
7 votes
1 answer
133 views

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:
Goutham Kancharla's user avatar
1 vote
1 answer
482 views

union of two disjoint topological spaces is a topological space? [closed]

union of two disjoint topological spaces is a topological space? if it is not. when this statement will be right "union of two disjoint topological spaces is a topological space"
Sam Sam's user avatar
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0 votes
1 answer
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fundamental group ( Klein bottle * Projective plane)

How can I compute the fundamental group for (Klein bottle $\#$ Projective plane) since I know the scheme for the projective plane is (cc) and the scheme for Klein bottle $ab(a^{-1})b$? Or in the ...
Sam Sam's user avatar
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1 vote
0 answers
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Proof verification upper bound on the Mondrian Art Problem

I have been doing some thinking on the Mondrian Art Problem and think I may have discovered something. I think I have improved the upper bound for odd numbers from $k$ (for a $k$ by $k$ square) to $(...
Houston's user avatar
  • 326
11 votes
1 answer
197 views

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 ...
Christopher King's user avatar
13 votes
2 answers
2k views

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 ...
Hans-Peter Stricker's user avatar
4 votes
2 answers
700 views

Realistic 3D fractal Christmas tree

I would be interested to see a realistic 3D fractal-generated Christmas tree. The best I could find is the Adobe Stock image below.                   &...
Joseph O'Rourke's user avatar
6 votes
2 answers
163 views

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 ...
JZachary's user avatar
3 votes
1 answer
200 views

Do the loops "Snakes" by M.C. Escher correspond to a regular tilling of the hyperbolic plane?

In M.C. Escher's Snakes, you have three snakes going through some loops. I'm more interested in the loops though. In this image, a ring model of the hyperbolic plane is given. It is given by $w=e^{za}...
Christopher King's user avatar
3 votes
2 answers
380 views

Is this Escher artwork a tessellation of the half-plane model of hyperbolic space?

One Escher's prints look like this. A similar one is this. These look suspiciously like Poincaré half-plane models of the hyperbolic plane (there are pieces of artwork by Escher specifically based on ...
Christopher King's user avatar
4 votes
2 answers
382 views

Do there exists art works representing high math-related topics?

I'm not looking for pieces in which math related object appears with allegoric meanings, but works which aim to to have mathematical objects as principal subjects. Specifically, I was wondering if ...
Andrea Gallese's user avatar
3 votes
0 answers
157 views

Fractal-like shapes - is there a name for these?

So I created some geometric art inspired by string art. I feel like there's a name for this type of shape/image. I'm asking on mathematics.stackexchange because the process of generating the below ...
Alecto Irene Perez's user avatar
0 votes
3 answers
252 views

How can I draw a 10 unit long line? [closed]

Last question I asked like this was a bit overkill so let's try something simpler instead. How can I write an equation of the form <stuff with x>$=0$ that ...
SoniEx2's user avatar
  • 147
6 votes
2 answers
260 views

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 ...
Eric Miles's user avatar
10 votes
1 answer
480 views

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 ...
Valeria Arango's user avatar
4 votes
1 answer
227 views

Finding parameter paths for beautiful fractal animations

So I just got renewed interest in fractals and especially animations with fractals. To make an image or a frame, we usually need to evaluate a fractal for a subset of it's parameters. However for many ...
mathreadler's user avatar
1 vote
0 answers
93 views

What is the root structure of the Diffeomorphism Group?

Being a physicist, I think it'd be cool to have Coxeter plane projections of the root systems of the symmetry groups associated with the fundamental forces hanging on my walls (example for E8: http://...
Eriek's user avatar
  • 311
16 votes
5 answers
3k views

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 ...
Shaun's user avatar
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11 votes
3 answers
4k views

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 ...
jb3330421's user avatar
  • 111
10 votes
0 answers
194 views

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 ...
user256021's user avatar
4 votes
1 answer
336 views

How can I understand is the picture $2D$ or $3D$

I can not understand is this picture 2D or 3D. What is the rule or condition to be a 2D or 3D picture. How can I understand that? Please help me!
Fazla Rabbi Mashrur's user avatar
9 votes
1 answer
433 views

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 ...
Chris Culter's user avatar
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11 votes
1 answer
1k views

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 ...
Joseph O'Rourke's user avatar
5 votes
0 answers
154 views

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 ...
hhh's user avatar
  • 5,517
12 votes
1 answer
822 views

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 ...
hhh's user avatar
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11 votes
6 answers
1k views

Suggestions for topics in a public talk about art and mathematics [closed]

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 ...