Talk:Mathematics of paper folding

To-do list for mathematical origami
I know that this talk page is not very Wiki-fied; I'm not terribly knowledgeable about how it all is supposed to look.

The biggest need on this page is for expansion. There's a lot more material about the mathematics of origami out there. Someone definitely needs to write an article about flat foldability and Kawasaki's proof.

A little detail is that names should not be preceded by title ("Dr."). That just isn't the convention; I have never seen a Wikipedia article that did that.

Some of the articles at the bottom of the page (esp. the ones about Britney Gallivan) need to have cross-references in the body of the article (e.g. superscript 1, superscript 2, etc.).

It looks like this article covers several topics (e.g. rigid origami) which could be split off into separate articles. Flat-foldability needs a separate article (Origami treats it as if it needs a separate article). I linked these.

Perhaps this article should be organized around branches of mathematics that touch on origami. Moreover, more attention should be given to the effects of mathematical investigation on the art of origami. --Whiteknox 01:31, 17 November 2006 (UTC)

I too have seen the extent of origami mathematics, especially in Peter Engel's book Origami from Angelfish to Zen. Unfortunately I am not the one to ask about the mathematics of origami either. There are several algorithms for paperfolding as well in Robert J. Lang's book Origami Design Secrets. If only we had someone correctly explain some of the concepts listed in these resources...--Origamikid (talk) 19:28, 10 February 2008 (UTC)

Perhaps this article could go more in depth in the connections origami has with real world applications, and display some of the more basic algorithms that are found in the subject such as the division of paper formula. Also, this article should explain how mathematics are applied to the designing of origami models. —Preceding unsigned comment added by 76.251.40.133 (talk) 02:40, 20 May 2008 (UTC)

Who is Harry Peretest Ickels? Can someone verify and if necessary remove his mention? —Preceding unsigned comment added by 85.28.103.124 (talk) 21:37, 5 June 2008 (UTC)

For the folded Toilet Paper roll- Substituting the 0.04mm thickness and 12 folds we get: L = 351km - NOT the 1.2km claimed by the girl in America

Assuming L = ((Pi*t)/6)*(2^n + 4)*(2^n -1))

.....or am I missing something here. —Preceding unsigned comment added by 81.155.79.113 (talk) 15:06, 11 January 2009 (UTC)

Please ignore that last one - I was a factor of 1,000 out, my bad, hangs head in shame..... km not cm. —Preceding unsigned comment added by 81.155.79.113 (talk) 15:31, 11 January 2009 (UTC)

Haga's theorems
Let the point Q' be the point between Q and C from the picture. The leget QQ' has a factor of third order in x. Isn't that interesting? There are others different rational values that it's shown here.

EulerIntegral —Preceding unsigned comment added by 187.59.190.172 (talk) 16:25, 15 January 2011 (UTC)

Flat-Foldability
I checked out the reference for the four conditions of flat-foldability. In the video it seems Robert Lang gives these conditions as universal for ALL origami crease patterns; he says nothing about flat-foldability. I found a slightly different set of conditions given here www.sccs.swarthmore.edu/users/05/jschnei3/origami.pdf It is possible that I do not understand exactly what flat-foldable means, so if someone could clear this up that would be great. —Preceding unsigned comment added by 141.140.129.59 (talk) 02:16, 23 February 2011 (UTC)


 * Flat foldability is exactly what it says - the model can be folded flat. Those conditions can easily be broken if the model doesn't have to be flat. For instance one could have one valley and any number of mountain folds if the folds don''t have to bend flat. Dmcq (talk) 22:16, 23 February 2011 (UTC)

The image for mountain/valley counting shows a vertex in the middle that does not follow the rule. — Preceding unsigned comment added by Allethrin (talk • contribs) 20:37, 23 February 2011 (UTC)


 * You're quite right - and it isn't flat foldable. Somebody made a silly mistake doing that diagram. I think I know what they were trying for so I'll correct it. In fact all three diagrams should be fixed. That's a nuisance, I won't be able to get round to fixing it till probably Friday. In fact I see the creator has now been blocked for harassing people and that I reverted a load of their stuff to Origami last year because they copied a big chunk from a book verbatim. And I believe I looked at these pictures and thought to myself at least they did something useful. My mistake. Ah well I guess at least it will be fixed and have a picture eventually - I hope not too many people have copied them. Dmcq (talk) 22:13, 23 February 2011 (UTC)

I've replace that image with one that works okay. Dmcq (talk) 15:42, 25 February 2011 (UTC)

Missing sections
I think what is basically missing now in this article is not the maths bits but things like some history and references to current organisations and interest in the area. Dmcq (talk) 15:19, 10 January 2012 (UTC)

Haga's theorems use a unit square?
I think the section on Haga's theorems assumes a unit square. Would it be appropriate to make this explicit? --Doradus (talk) 12:40, 26 March 2012 (UTC)
 * It starts off with 'The side of a square can be divided at an arbitrary rational fraction in a variety of ways.' Dmcq (talk) 13:34, 26 March 2012 (UTC)
 * Was that intended as an answer to my question? I'm not sure whether that's a "yes" or "no"...  --Doradus (talk) 16:53, 23 July 2012 (UTC)
 * There is no need to say unit square, the fraction refers to the side. Dmcq (talk) 19:24, 23 July 2012 (UTC)
 * Ah I see what you mean. I think you're right.  --Doradus (talk) 20:10, 24 July 2012 (UTC)

Heading diagram
I can't really se the point of the diagram in the lead. It starts off with figures that already have measurements and it does simple division.It doesn't even say how to divide by three. Unless there's some objection soon I'll just remove it. It seems to have practically nothing to do with the mathematics of origami. Dmcq (talk) 09:28, 18 October 2014 (UTC)
 * Agreed. --JBL (talk) 13:49, 18 October 2014 (UTC)

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T. Sundara Row
Little is known about this author of Geometric exercises in paper folding. His surname is probably a different Anglicization of Rao, a common surname in South India. He is certainly of Indian origin, and the first edition of the book published by Addison-Wesley in Madras gives his affiliation as "Deputy Collector", which seems to imply that he was a civil servant. The dedication of the book to Henry Stokes also suggest this. But there is no evidence to suggest that he was a professional mathematician. Thus, I have removed the phrase "mathematician" in the sentence that introduces him. — Stringy Acidtalk 16:31, 9 July 2019 (UTC)

decideability
https://arxiv.org/abs/1712.07474 seems to claim that the theory of the Huzita-Hatori-Justin axioms is undecidable. I haven't read the paper yet, so parking the link here for now. 24.130.116.119 (talk) 01:06, 23 May 2023 (UTC)