Topology

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Exz
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Topology

Post by Exz »

Hi folk, I'm new here. I am interested in various ideas that I shall hopefully post about, but I am kicking off with the four colour theorem. I can't see a forum about topology. If this belongs in a different forum, then please let me know.
The four colour theorem, that any map only requires four colours, was supposedly solved by a computer, with there being precisely 1,936 such maps. I have worked out that there are three types of map, each of which can have one slight variation which also requires four colours, and that two of these principal maps can have infinite variations. There are thus infinite maps requiring four colours.
How would I post diagrams thereof?
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Alec Smart
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Re: Topology

Post by Alec Smart »

Exz wrote:There are thus infinite maps requiring four colours.
How would I post diagrams thereof?
That's a hell of a lot of diagrams, I think you may be being a little over ambitious.
Smart by name and Alec by nature.
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Exz
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Re: Topology

Post by Exz »

Hmm... indeed! I don't need to post infinite diagrams, the variations are recursive. But it would be a lot simpler to be able to post diagrams, rather than describe them in words! There must be a way that I can post a .pdf or something, isn't there?
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Alec Smart
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Re: Topology

Post by Alec Smart »

Exz wrote:There must be a way that I can post a .pdf or something, isn't there?
I just keep clicking on things until I get the desired effect. I have to admit that it's not the ideal way to achieve the result you're after, it's a bit time consuming and there are often embarrassing incidents along the way but I usually get there in the end. I hope this advice is of some help to you.
Smart by name and Alec by nature.
Belinda
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Re: Topology

Post by Belinda »

Can't it be simply and explicitly written in language? I am guessing that it means that in any layout ,( at least any layout on a plane surface) , the constituents are indicated by hues. Four hues only are enough so that no constituent part merges visually with any other constituent part. Does the theory work in three or more dimensions?

I say "hues" rather than "colours" because tones or shades of the same hue are probably not what is meant by the theory.
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Exz
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Re: Topology

Post by Exz »

Yes, it means any map on a plane, 2d surface. I have thought about higher dimensions, and I *think* that any 3d or higher body would require infinite colours. If you look up 'four colour theorem' on Wikipedia, you will see that it is generally accepted that the problem was solved by a computer (the first mathematical problem to be solved by a computer), and that there are finite maps which require four colours, 1,936 specifically. I have *definitely* found that there are infinite such maps. It would be a lot easier if I could post diagrams somehow. I have just knocked up a .pdf, in the hope of posting it somewhere. Can anyone tell me if I can post a .pdf here? Or will I have to somehow set up a website?

-- Updated December 24th, 2015, 4:09 am to add the following --

From my first post, I meant there are two maps which can have a slight variation, not all three. And two maps can have infinite variations, but not the same two!

-- Updated December 24th, 2015, 1:13 pm to add the following --

Hello Again,
Trying to discuss anything here is very frustrating. It takes an age for things to appear. Why is this?
I am now using the 'Talk Page' on Wikipedia, the four colour theorem page, but I've still to work out how to get them to reply to me!
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Exz
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Re: Topology

Post by Exz »

OK, apparently the people who know these things are aware that there are infinite maps requiring four colours. It's just not mentioned anywhere!

-- Updated February 18th, 2016, 1:58 pm to add the following --

Hmm... I have been *trying* to work out whether my ideas/discoveries re: the 'four colour theorem' hold significance. I still think they do. It did not take what used to be a super-computer (or nowadays any old computer) a lot of computrons to work out. Well, apparently it did, and they keep on about this, so how come I worked it out myself?

Please someone have a look at the 'talk' pages on 'four colour theorem' on wikipedia, and try and explain to me why I am being rubbished...
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Sy Borg
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Re: Topology

Post by Sy Borg »

Exz, Alec rubbishes anything that he finds too esoteric. Belinda responded respectfully.

I've bumped the topic for you. It's not as per the rules but just this once.
The greatness of a nation and its moral progress can be judged by the way its animals are treated—Gandhi.
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Exz
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Re: Topology

Post by Exz »

OK, cheers...
Greta, or anyone, apparently I'm not yet *allowed* (??) to post a URL, but could anyone who's ever looked at the four-colour-thingy, or been good at topology, have a look at the Wikipedia site, and its talk pages, and explain to me why the authors of the above are rubbishing my suggestion that the problem can be solved without throwing a computer at it? Please? I don't get it. Am I just being thick? I don't think so, but that seems to be the Wikipedia contributors' implication...
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