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 ...
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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 ...
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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. ...
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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 ...
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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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\...
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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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 ...
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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:
1 vote
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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"
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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 ...
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1 vote
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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 ...
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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 ...
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 ...
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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 ...
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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 ...
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 ...
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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 ...
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1 vote
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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://...
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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 ...
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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 ...
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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 ...
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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!
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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 ...
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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 ...
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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 ...
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