Talk:Hyperplane

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"Not to be confused with Hypersonic aircraft." -- I didn't intend this as a joke, but if people think it's too dumb, take it out.

No, I think people could come here looking for hypersonic aircraft. It might even be a good idea to move it to the top as a "dab" to point people to the right article immediately. StuRat 03:36, 22 September 2005 (UTC)
I found that pretty funny, but it may nevertheless be useful to someone.. -Simon80 03:25, 31 July 2006 (UTC)
It's a good joke and useful to boot. Zaslav 06:19, 10 November 2006 (UTC)

Contents

[edit] k-hyperplane

No one calls a point or line as 0-1-dimmensional hyperplane, it does not have any sense, you have nice term k-dimensional affine subspace!!!

Even if some use this term it should be stoped, and no reason to mention it here.

So I remove it again

Tosha 04:55, 6 Mar 2004 (UTC)

BTW I would remove realm since again no one use it, and not clear why anybody would need this in principle.

Tosha 04:59, 6 Mar 2004 (UTC)

  • we always include alternately used terms for something, regardless of whether anyone needs it or not
  • if a term or definition is used, it should not be removed, but if it is agreed that the term is in bad usage, it should be explained why it is not good to use the definition or term, and not widescale removed

Dysprosia 05:04, 6 Mar 2004 (UTC)

[edit] k-hyperplane again

Ok, sure, but are you sure that this term is used anywhere except this article? (I do geometry and I did not see anyone who use it).

Even if it is used by few guys, it should be marked as extremally reare so no one will have an idea to use it again.

I will be indeed very surprised if it is used... (can you give me a name of book which use k-hyperplane?)


Tosha 05:22, 6 Mar 2004 (UTC)

Example:

  • Jamison, R.E., 'Finding little hyperplanes in bigger ones'. In Linear algebra and its applications, Volume 35, (February 1981), pp: 11-19.

A k-hyperplane is just a logical abbreviation to refer to a k-dimensional hyperplane. Such an abbreviation is bound to be useful in some contexts.

A.N. Yzelman 10:39, 20 March 2007 (UTC)

[edit] Added too technical tag

I added the to technical tag to the article because I've read it several times and never came away with any kind of understanding of what a hyperplane is. I finally got a friend to explain it to me and its such a basic topic this article could do a much better job of being accessible to someone with only algebra under their belt. I'm not qualified to edit the article, unfortunately, but I know something's wrong when I see it. Triddle 05:10, 16 September 2005 (UTC)

I reworded it to put the simple part up front, and removed the technical tag. If you still think it's too technical, put the tag back on. StuRat 03:27, 22 September 2005 (UTC)
I think the article is missing a good example to drive the point home; I'm not 100% sure what this killer example would be but my friend got it into my head by using the RGB color space as an example. Plot out all the combinations of R, G, and B, then split the entire thing right along the middle of B. You formed a two dimensional hyperplane on the three dimensional color space. I'm not a mathwiz though, not even close. All that I know is that when I read that article I can't make heads or tails about what a hyperplane is but I get my friend's 3D color space explanation. Triddle 05:46, 22 September 2005 (UTC)
I don't think everyone should be able to understand all of the article, but should get the "basic concept", contained in the first paragraph. Do you get that part ? Would some pics help ? Maybe one to illustrate the 1-dimensional case, another for 2-dimensions, and another for 3-dimensions ? StuRat 14:50, 22 September 2005 (UTC)
Moving the paragraphs around sure did help a lot. The first paragraph is simple and I understand it but I think thats because I already understand it now. If I was still 'green' to this concept I'm not sure that would really do the trick. I think a picture would be great; maybe some concrete examples of what one can do with a hyperplane for us kinesthetic learners. Thanks for taking the time to address my concerns. =) Triddle 15:53, 22 September 2005 (UTC)
You're welcome. Does the diagram I added help ? StuRat 18:32, 22 September 2005 (UTC)

[edit] My edit, and kinds of hyperplane

I removed a lot of stuff. Part of it was repetition; saying once that a hyperplane divides the space in two half-spaces is enough. And note that just saying "a hyperplane divides a space in two" is incorrect, any surface divides a space in two. So, one has to be more careful with wording.

I removed the ascii art picture. It is clear enough I think what a line with a point on it is. And the picture is not pretty. A hyperplane cannot be visualized, so all one can do is carefully explain what it is by analogy; so that's done well in the article.

I think it is incorrect to say that a hyperplane is a projective subspace. It is only an affine subspace, which can be linear in certain cases.

And in general, an affine subspace is not linear as the article stated.

In conclussion, the article had a bunch of incorrect and confusing information. Now it is shorter, and I hope clearer. Oleg Alexandrov (talk) 07:39, 17 December 2005 (UTC)

You are mistaken to reject projective hyperplanes. A hyperplane can be a projective hyperplane, which is a hyperplane in a projective space, or a linear hyperplane, which is a hyperplane in a linear space (vector space), or an affine hyperplane, which is a hyperplane in an affine space. In all cases, it is a projective/linear/affine subspace whose dimension is 1 less than that of the whole space. All three kinds of hyperplane appear in the current mathematical research literature. The article should have all three. I will check when I have time, to make sure that is correct. Zaslav 05:53, 10 November 2006 (UTC)

[edit] Technical or nontechnical?

I think the beginning of an article should be accessible to as many readers as possible. Persons seeking more advanced or technical knowledge (though not highly specialized details) should also find it here, as they do in similar articles. Edits made since my last contributions more than a year ago have removed the advanced content. I ask contributors not to dumb down the article. Thank you. Zaslav 06:18, 10 November 2006 (UTC)

[edit] Examples of uses of hyperplanes

It may be a good idea to have examples of uses of hyperplanes. For instance hyperplanes are used in the perceptron neuron model, to seperate patterns. —The preceding unsigned comment was added by FrederikHertzum (talk • contribs) 14:41, 16 April 2007 (UTC).