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Questions tagged [origami]

In modern usage, the word "origami" is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal of is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques.

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What's a minimal origami construction realizing a cube root?

The constructible numbers are those that can be achieved as lengths of line segments via compass and straightedge, starting with a segment of length $1$. The origami (constructible) numbers are those ...
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3-colored Icosahedron out of 90 Sonobe units

I'm new to Modular-Origami. Currently I'm trying to build a Icosahedron out of 90 Sonobe units. I want to make it three-colored. But I'm having trouble building it so that there are no 2 colors next ...
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Can origami math solve polynomial equations of degree greater than 3?

I heard that straight edge + compass can solve up to quadratic equations. I've also heard the Origami/Paper-folding can solve cubic equations. But can it solve higher-degree polynomial equations (e.g. ...
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How well-studied is origami field theory?

It's well known that angle trisection cannot be done with straightedge and compass alone, as Theorem 1. If $z \in \mathbb C$ is constructible with straightedge and compass from $\mathbb Q$, then $$...
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Analysis with origami.

I use this place for the first time. I usually had many questions in sci.math. Hello teacher~ There is a rectangular(P1) paper. Fold one of the four points of P1 so that it is on one of the two sides ...
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Is there an exact solution for tan(36) using origami from a unit square?

This question is more for chagrins and curiosity than anything else: Is there a way to use origami to construct the tangent of 36 degrees (~0.7265425)? I've come up with the image below, which is ...
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Using (rigid) Origami moves only, what is the maximum volume that can be enclosed by a square piece of paper?

Motivation: This is inspired by this question. The Question: What is the maximum volume that can be enclosed by folding a square piece of paper (with side length $\ell$) using only (rigid) ...
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The Mathematics of Coca Cola's Ribbon Wrapper.

I'm sorry if this is too vague a question or is otherwise deemed poor quality. The Background: I've just seen an advert for the (new?) Coca Cola festive ribbon wrapper. Here's a picture: A ...
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Paper Folding to produce an equilateral triangle

A rectangular strip of paper edge $AC$ is first folded in half making fold crease through mid-point $M$ and again bent folded along a new line through $C$ adjusted such that corner $A$ falls on ...
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Available Literature about Mathematical Origami [closed]

I'm interested in math and origami and I was wondering about where I would find the available literature on stuff like tessellations. Sorry if this is a kind of vague question...
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Can a Origami shape be mathematically defined? [closed]

Given any origami shape, Can It be mathematically defined say any function or equation that can satisfy all points of the origami shape ? If so, How such functions for any origami can be derived with ...
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Pop-up cards Turing complete?

I remember once having found an interesting paper demonstrating the pop-up card to be Turing complete. (In a similar fashion as ruler and compass being able to solve quadratic equations and origami ...
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Sequence of folds for finding intersection of two circles, given centers/radii

I know that any ratio that can be constructed by use of a straightedge and compass (and some which cannot) can be constructed by folding paper. I am not certain whether or not the same is true of ...
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Cuboids around folded paper

There is no backstory to this question; I just thought of it. Take a piece of origami paper, a square with area 1. Then fold the paper in any way possible without cutting. There is no limit to the ...
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Origami Axiom 4 is Redundant? (Huzita–Hatori)

I have some question regarding Huzita–Hatori axioms. Axiom 4 states that given a line and a point, we can make a fold passing through the point perpendicular to the line. Axiom 5 states that given ...
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The common tangent of two tilted parabolas

I very recently asked a question here about finding the tangent to a tilted parabola but this was only part of a larger question I had. I figured that I would be able to solve it myself with answers ...
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Regular pentagon from a square paper

I found this page with instructions to create a pentagon from a square paper: Fold the square in half to create a rectangle Mark half in the right side: Mark half in the down side: Fold from the ...
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Ratio of folded isosceles triangle area

Take an isosceles triangle with legs length $1$ and base angle $\theta$. Take the apex and move it to a leg vertex. Describe the ratio of the new folded shape's area to its previous as a function of $\...
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How many “tiles” for a flexagon with $n$ sides?

For a flexagon with $n $ sides, how many tiles does it have? A tile is when the components are stuck together and not folded, The number of tiles are the number of triangles you can see on one ...
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Shortest triangle strip knot

Join rigid equilateral triangles at the edges to make a strip of rectangles. What is the minimal number of triangles needed to make a knot? The triangles should not intersect. Same question -- ...
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Origami: What shapes are impossible?

Let's say we had a collection of pieces of rectangular paper of any size to choose from. Using one sheet only of any chosen size, what three-dimensional (or two-dimensional) shapes are impossible to ...
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Simplest algorithm for edge coloring of a dodecahedron?

I have an origami model of a dodecahedron I am assembling. There are 30 edges with 3 colors of 10 each. I could use a diagram that gives a possible 3 color edge coloring. However, is there some sort ...
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Mathematics of real-life folded objects.

What is the name of the field of mathematics which can be used to describe folded objects like blankets, aprons, and paper origami. I'm looking along the lines of a tuple with custom entriesor sth ...
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Proof of folding to trisect a right angle

If first you fold a normal (letter or A4) piece of paper in half: and then you fold one corner to meet the halfway line: Then you've trisected the right angle at bottom left - but how does one prove ...
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How to fold a paper into a flat model and when we pull on a side it goes 3D

I saw a pretty interesting origami in this video : https://youtu.be/0Z-eWYhtEhY?t=3092 but I can't figure out how to fold it. Can you help? Thanks.
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Is there a mathematical way to fold a $20 dollar bill for compactness?

I had a strange thought. I used to carry a pill fob on my keys with an emergency $20 bill in it, before the whole thing got stolen. I always had some trouble fitting the bill inside the fob and ...
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Huzita Axiom 6 - Computing the Origami Trisection of an Angle

The Galois theory proof of the improssiblity of angle trisection rests on studying the triple angle formula $\cos 3\theta = 4 \cos^3 \theta - 3 \cos \theta$. Ruler and compass numbers can only be ...
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How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
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List all regular n-gons with up to 80 sides that can be origami constructible.

I know an origami constructible regular n-gons are those with $n=2^a3^bρ≥3$ sides where ρ is a product of distinct Pierpoint primes (i.e prime of the form $2^u3^v+1$). So, the Pierpont primes (p) I ...
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Solving Cubic Equations Using Origami

I have to write a research paper on a mathematical topic for my class; I chose the above topic. I understand that a parabola can be formed using a focus and directrix, both created by origami folds, ...
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Why do folded concentric circles and rectangles form a hyperbolic paraboloid?

Here is a "self-forming" origami that I made from folding concentric circles - it would also happen if I folded concentric rectangles. How can the fold shapes such a saddle-like geometry?
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Solving Cubic Equations (With Origami)

I am working on a project about Mathematics and Origami. I am working on a section about how origami can be used to solve cubic equations. This is the source I am looking at: http://origami.ousaan.com/...
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Mathematics and Origami

I am reading through this paper about the math behind origami: http://www.math.washington.edu/~morrow/336_09/papers/Sheri.pdf However, I am getting confused with definitions 3.3 and 3.4. I am not sure ...
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Math and Origami

I am working on a project for class about the mathematics behind origami and write now I am looking into what is and is not constructible. I've gotten to the definition of origami constructible points ...