Are there exceptions for Maekawa's theorem?

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Are there exceptions for Maekawa's theorem?

Postby Brimstone » July 30th, 2019, 10:03 pm

I remembered having read about Maekawa's theorem about flat foldability on an inner vertex being disproved but I could not remember where but finally I found what thread it was, it is this one: viewtopic.php?f=16&t=12181&p=132045

Specifically:

Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.


And latter Razzmatazz was asked to provide evidence:

PauliusOrigami wrote:
Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.

Could you give me a reference (source)?


But Razzmatazz's answer is based on an article that to be read needs to be purchased first:

Razzmatazz wrote:Apparently the proof is in this document: http://dl.acm.org/citation.cfm?id=313852.313918

But it is in the wikipedia article for Kawasaki's theorem here: http://en.wikipedia.org/wiki/Kawasaki%27s_theorem


So does anyone have more information on said exceptions/disproval?
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Re: Are there exceptions for Maekawa's theorem?

Postby Baltorigamist » July 31st, 2019, 1:45 am

I remember finding a presentation online (unfortunately, I can’t remember where) that touched on the (dis)proof of the theorems, giving crease patterns of a couple counterexamples. I have it saved on my computer, however; so maybe I can send it to you. (This assumes that I’m thinking of the right one.)
As far as I can remember, it has something to do with the law of origami that a sheet can’t intersect itself. In essence, two vertices that would ordinarily fold flat on their own may not fold flat together if they’re too close on the paper.
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Re: Are there exceptions for Maekawa's theorem?

Postby Brimstone » July 31st, 2019, 1:11 pm

Thank you Balton, I'll PM you my email address
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