# 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.

34 questions
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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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### 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/...