Talk:Combinatorics
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With sites like this who needs classrooms? This site does a better job explaining things than most teachers do.
- The maths articles are generally very good (I can say this because I've not contributed to them). Just wait til the whole 'pedia is like this! Pcb21 10:15 1 Jun 2003 (UTC)
I think that there is lots of overlap between the contents of this page and of permutations and combinations. Maybe we should just reference people there (for some sections) and just breifly outline?
--Lincsimp 09:21, 10 June 2006 (UTC)
Contents |
[edit] Closed formula for Fibonacci number
should be:
f(n) = (phi)^(n+2)/sqrt(5) - (phi - 1)^(n+2)/sqrt(5)
{ this short program try to verify closed formula for } { Fibonacci number and his recurrence expression }
uses crt;
var
fib, a, b, n : longint; x, fi : real;
begin
clrscr;
{ axioms for given Fibonacci numbers : }
a := 1; { fib(0) = 1 }
b := 2; { fib(1) = 2 }
{ the Golden mean : }
fi := (1 + sqrt(5)) /2;
{ checking of recurrence expression and expresion in closed form : }
for n := 2 to 15 do
begin
fib := a + b; { fib( n ) = fib( n - 1) + fib( n - 2 ) }
x := ( exp( (n+2) * ln( fi)) -
exp( (n+2) * ln( fi - 1)) )/ sqrt(5); { closed formula }
writeln( 'fib( ',n : 5, ' ) = ', fib : 7, ' .... ',x:8:1);
{ shift for next number : }
a := b;
b := fib;
end;
end.
- I haven't run the program, but I have verified with pencil and paper that the formula in the article is right and this one is wrong. - Jwwalker
[edit] External link
An anonymous user keeps adding a bogus external link to an incoherent web page. The user should explain the reason for the link on this page first. Until then, please everyone help me control this matter.
- reply 1 user 80.181.108.117
Anyone can ascertain that the link "http://www.giacomo.lorenzoni.name/solprobcombengl/" exist and work fine. To this respect I recommend you to use a computer that works well surely. For the rest, I hope that you won't continue with low accusations.
- reply Mhym 15:19, 24 December 2005 (UTC)
This is an incoherent list of bogus mathematics irrelevant to the encyclopedia page. It is also written in an extremely flawed English. I will remove it once again and ask you to never again edit this page. Please stop promoting this page at the expense of the Wikipedia users.
- reply 2 212.171.42.221
The animosity, the insulting language, the use of every type of accusation, and above all the absence of precise mathematical reasonings; show dark motives of your action. I hope that an authority prevents you to continue.
- reply Mhym 15:26, 25 December 2005 (UTC)
OK, let's agree to make "external links" only to published articles. If you have evidence that your article is published - please present the evidence. If not - plesae do no bother encyclopedia users with this nonsense.
- reply 3 80.181.108.80
Your rule "ExternalLinks only to published articles" is unfair and contrary to the ideal more essential of Wikipedia: all have the right to know and to judge what others want to make well-known. With which right you continue so stubbornly to make the censor?
- reply Mhym 16:16, 26 December 2005 (UTC)
The most important rule is to have the information correct. This link is unreadble and incomprehensible. Without a publication in a reputable journal the reader cannot make his/her own judgement. I will keep removing it until I am proved wrong (on this Talk page).
- reply 4 212.171.42.92
Use a computer that works well surely (see reply 1). Please not to insist in the care of things that you do not want or cannot understand.
- end of reply 4 212.171.42.92
I made a little research into this and discovered that this is indeed a link to a self-published book: http://books.lulu.com/content/148685 This work is unrefereed yet for sale. The author should STOP using Wikipedia for personal advertisement purposes. Vandalism is always punished on this web site. Mhym 06:02, 28 December 2005 (UTC)
- reply 5 212.171.43.11
see reply 2
- end reply 5 212.171.43.11
- reply 6 212.171.42.114
Requested unprotection: the page has been protected in consequence of false and trivial accusations against ExternalLink "http://www.giacomo.lorenzoni.name/solprobcombengl/".
- end reply 6
I think that external links for this article should be general discussions of combinatorics or major subfields thereof. I don't think that the solution of a particular problem, even if it is correct and well-written, would be appropriate. By the way, my opinion is that Wikipedia should never allow anonymous edits of anything. - Jwwalker 20:52, 29 December 2005 (UTC)
- reply 7
I think that the ExternalLinks "http://www.giacomo.lorenzoni.name/solprobcombengl/" provide a information original and pertinent to Combinatorics. I have not prejudices against the anonymity.
- end reply 7
[edit] Grammar and intro
I'll say that you all have taken on a monumental task in explaining combinatorics, and I wish you much luck and skill. That said and wished, I'd like to point out a couple of things that seem to 'stick out' as in need of improvement.
[article quote] An example of a combinatorial question is the following: What is the number of possible orderings of a deck of 52 playing cards? That number equals 52! (fifty-two factorial). It may seem surprising that this number (80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000) is so big.
Anyone who has been introduced to factorials will hardly be surprised that 52! is so big. Thus, a reader might logically sense that this article will be addressed to people with little mathematical knowledge. But this article will probably lose all readers that know little of basic math. Beginners cannot be expected to know much about sequences and series, so in that respect, this article will require some seriously skilled and clever presentation to get the ideas across to the unknowledgable.
[article quote] He applied similar formulae for permutations with and without repetitions using the Arabic alphabet for illustrative purposes. He also does some work on combinatorial reasoning.
This is pretty bad English. A dead person 'does' nothing. The answer of course is that 'He also did or performed or pioneered something back then.'
There is some good material in this article but remember that the article leaves behind all beginners by the end of the introduction, so it might be best to not let the article suggest that beginners will be able to follow. I have no intention of editing the hard work of others here, but am happy enough to try to help by making suggestions. Peace.
- Hi, I recommend you read Wikipedia:Talk_page_guidelines before you post again in Talk. I've taken the liberty to add a header to your section. In regards to your comments, I like the intro which mentions 52! as being a big number. It starts the article off in an interesting way, instead of plowing right into the maths. It makes the article more appealing to beginners. Nothing wrong with that. As far as the bad grammar goes, next time feel free to just make an edit. There's no point in bringing it up in Talk when its an obvious fix. --JRavn talk 21:56, 18 August 2006 (UTC)
[edit] Algebraic Geometry
Perhaps mentioning the work of Rota connecting algebraic geometry to combinatorics would enrich this entry. I don't know anything about it, in fact I ended up checking this entry to find out about this.
[edit] Stomachion section
The following text was added by User:Gryspnik a few days ago. While apparently correct (the links work, and seem to back up what's said), it was very out of place where it was put, so I've moved it here for later, better incoporation into the article. JesseW, the juggling janitor 18:59, 23 September 2006 (UTC)
- Recently there was discovered that the work of Archimedes "Stomachion", believed to be lost, was the first work of Combinatorics ever written. A palimpsest discovered a few years ago, contains most of this lost work and involves finding the number of ways that the problem posed in the Stomachion can be solved. This game consists of 14 irregular strips of paper that can be placed in many different ways in order to form a square. There is additional information on this in the following links:
You are right Jesse, I moved this info in the history section of combinatronics were it actually belongs. Thanks for that note.
[edit] Formula Question
The formula for Combination with repetition seems somehow strange to me. It consists of three expressions whereas the last two seem odd. Inside the parenthesis they both have the same upper part (n+r-1) but different lower parts (r and n-1). Therefore, either r = n-1 or r = (n-(n-1) = 1) should hold, which I do not believe is always true. I already know the first expression (with r at the bottom) and think that it is correct – how about the second one? —The preceding unsigned comment was added by 141.51.122.97 (talk • contribs) .
- The expressions are all equivalent. In general,
,- because choosing p items (to keep) out of p+q items is equivalent to choosing q items (to throw away) out of p+q items. Either decision amounts to partitioning the set of p+q items into two blocks, one with p items and one with q items. For the formula for combinations with repetition, p=r and q=n-1. Michael Slone (talk) 04:40, 18 October 2006 (UTC)
[edit] Consistent Examples
I think the article might read better if we used the same example for each of four different methods, such as how many trigrams you can make from the first four letters of the alphabet. For permutations with repetition, it's 64; for permutations without repetition, it's 24; for combinations without repetition, it's 4; and for combinations with repetition, it's 20. A list of each of the sets of trigrams in questions might also be helpful, if it doesn't take up too much space. Thoughts? 64.12.116.139 05:32, 23 October 2006 (UTC)
[edit] That number at the top
Could someone write out its name, as well as the numbers? It's not that important, but it might be cool. --Santasassassin 15:15, 13 December 2006 (UTC)
