Talk:Quintic equation
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- This page is kind of messy. Eyu100
- I agree. In my opinion an encyclopedia article should not contain a cartoon, especially one that is only loosely connected with the subject. Thinking that something is funny is POV anyway. Also I am disturbed by the repeated mentioning of computer algebra systems. I know they are powerful. I know they may very well be mentioned somewhere in the article. But the way they are in right now simply breaks the flow of the text and obscures the core idea I wish to learn from the article. Pure mathematics and practical applications should really be in separate sections. — Pt (T) 22:13, 20 Apr 2005 (UTC)
- I disagree with the statement that an encyclopedia article shouldn't contain a cartoon. In some cases, and not just those about humor or cartoonists, a cartoon is very appropriate. I do agree though that this particular cartoon is only loosely connected with the subject (as a pun, of course, the joke has no substantive contribution to the content of the article). As the contributor of the cartoon, however, I would like to note that this type of cartoon might be seen in a techincal (even encyclopedic) article in certain types of mathematical, scientific, and engineering magazines, and even serious academia need not be completely humorless. Perhaps very few people besides me find the cartoon appropriate (or funny for that matter), in which case it should go, but if this is an issue, there should be some discussion to determine if this is the case. CyborgTosser (Only half the battle) 16:32, 30 May 2005 (UTC)
- I agree. In my opinion an encyclopedia article should not contain a cartoon, especially one that is only loosely connected with the subject. Thinking that something is funny is POV anyway. Also I am disturbed by the repeated mentioning of computer algebra systems. I know they are powerful. I know they may very well be mentioned somewhere in the article. But the way they are in right now simply breaks the flow of the text and obscures the core idea I wish to learn from the article. Pure mathematics and practical applications should really be in separate sections. — Pt (T) 22:13, 20 Apr 2005 (UTC)
did you actually make that cartoon? i just cant get over it (no im serious) good work :)
btw is this the easiest approach? im finding the reduction a bit difficult
Is it true that Galois was the one who proved insolvability for equations of degree higher than 5? I think I saw somewhere that Abel's proof was valid for n>5 too.
I'd dispute that the Brin Radical solution counts as an Algebraic solution. The formula for a Brin Radical includes an infinite sum, and hence is not strictly speeking algebraic (although I'd prefer someone with a bit more knowledge on this to verify this).
From Galois Theory 2nd Edition, I Stewart, Chapman and Hall, ISBN 0-412-34550-1 Therorem 15.7 (p144) If K is a Field of characteristic zero and n >= 5, then the general polynomial of degree n over K is not soluble by radicals. --Pfafrich 18:59, 18 November 2005 (UTC)
I've split the Brin Radical material into a seperate page. I think the previous treatment gave too much emphesis to the Brin Radicals, and downplayed the insovability by radicals which is a very deep and beautiful result, which gavce rise to the foundations of much of modern group theory. --Pfafrich 20:57, 18 November 2005 (UTC)
Shouldn't the general formula be more like:
- ax5 + bx4 + cx3 + dx2 + ex + f = 0
instead of:
- ax5 + bx4 + cx3 + dx + e = 0
Or is this a different type of quintic than the article is talking about? --Psiphiorg 21:07, 18 November 2005 (GMT)
- I think it's the same thing, ie. you get rid of the quadratic term with a substitution of variables like the one for the cubic. Phr 11:52, 25 February 2006 (UTC)
- I think this was my mistake when originally typing in. ax5 + bx4 + cx3 + dx2 + ex + f = 0 is the general form. Phr may be correct in that it can be simplified, but I've not checked this. --Salix alba (talk) 15:47, 25 February 2006 (UTC)
[edit] the degree afte a quintic equation...
What comes after a quintic equation? How do you solve and graph it? And what comes after that? How do you solve polynomials where the highest degree is over 1 million, or progressive? I have been looking around and it seems that every one likes to say they cannot be solved.
[edit] The caption in the image is truncated and therefore misleading.
The caption of the image "Polynomialdeg5.png" appears in my browser as:
Polynomial of degree 5: f(x) = (x+4)(x+2)(x+1)(x-1)(x-3)/20
without the final "+2".
Can the size of the image be adjusted to account for the size of the caption? Or perhaps the caption can be shrunk to fit? —The preceding unsigned comment was added by Ndokos (talk • contribs) 13:38, November 22, 2006 (UTC)
- I have added spaces between the factors and around the plus sign so that the caption can word wrap. How does it look now in your browser?
- --Psiphiorg 00:39, 23 November 2006 (UTC)
- Looks good! Thanks.
- --Ndokos 21:18, 30 November 2006 (UTC)
"this is known as the Abel-Ruffini theorem, first published in 1824, which was one of the first applications of group theory in algebra"
This is untrue, due to a confusion between Abels work which has no mention of groups, with the slightly later work of Galois, who developed finite group theory to prove the inslovability (by the way Galois proof reads more like a sketch of a proof, rather than a proof itself)
