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The smallest figure that tiles the hyperbolic plane (H2) is the "237" triangle, whose angles are π/2, π/3, π/7. What is the smallest tile in H3? — Tamfang ( talk) 01:14, 26 January 2008 (UTC)
Just curious about interesting maths. Those of you who are most passionate about math should be able to put forth your favorite(s). What is, in your opinion, the most beautiful, interesting, or elegant mathematical thing that you have found? HYENASTE 03:18, 26 January 2008 (UTC)
Mine is this " Genetic complementary learning autonomously generates fuzzy rule." I am still learning on Wikipedia how it all comes together. My first step is understanding Stochastic matrix. I just want to understand Stochastic matrix as fast as possible, so I can grasp some cool formulas published regarding GCL. :) -- Obsolete.fax ( talk) 07:44, 26 January 2008 (UTC)
Mine is Immerman-Szelepcsényi theorem. It is a genuinely suprising result and the proof is in some sense an elaborate mathematical joke. I also like Gödel's incompleteness theorems for similar reasons. Third mention is the proof that Hex (board game) is won by the first player to move. What I want to say - mathematical beauty is not related much to the importance underlying problems or to the simplicity of the result. It works more like jokes. You hear a story and in the end you get an additional surprising information, that completely changes the way you view the story. Take a look at the last link, the "Strategy" paragraph - anybody can understand it. Thorbadil ( talk) 11:52, 26 January 2008 (UTC)
Nice challenge! My favorite is the formula
It is not quite trivial, it has a some symmetry, and it is useful for converting between gamma distribution and poisson distribution. It is applicable when computing the probability that the best soccer team won, given only information on the outcome of a particular match. The beauty is entirely in the eyes of the beholder. Bo Jacoby ( talk) 12:11, 26 January 2008 (UTC).
My favorite would a result in probability theory regarding supermartingales. Which basically says that if you are in an unfavorable game (where you will loose money on the average) then there is no betting strategy that will make the game fair or favorable. There are strategies to make the game "less unfair" but it will still be unfair. Furthermore, the optimum betting strategy, in any game, is actually the bold strategy in which you bet all or nothing. These results might sound obvious, but what is interesting is that they have been mathematically proven. A Real Kaiser ( talk) 05:35, 27 January 2008 (UTC)
as amatter of fact ,i asked this before but i got no answer.i just want here to say it could be something,it could be important after study it.you can also go to my talk and see the pdf file that contains this discussion. the purpose of this theory is an attempt to show that real numbers can be generated or counted randomly and intensively .
Consider we express the tow positive real numbers ,A&B as,
A=Σam[(10)^(n-m)] B=Σbm[(10)^(n-m)] Where,( n,m=0,1.2,……) am,bm,positive integer Now if, am+bm=pm+10,pm<10 pm,positive integer Then we define the relationship R, ARB={pm*(10)^(n)}+{(pm+1)*(10)^(n-1)+..... Obviously, R; looks like adding backwards.e.g, 341R283=525 =(3+2)=5,(4+8)=12,(1+1+3)=5 Lets now pick up arbitrarily the infinite sequence
S0=Σn\(10)^(n),+Σn\(10)^(n+1) + Σn\(10)^(n+2)+.....
Where n=1to9 ,10to99,100to999 ,...etc.respectively
i.e, S0=0.123456789101112131415161718192021222324.... n ,is apositive integer. In order to generate or count* the real numbers within the interval,e.g. (0,1),
We define ,F;
F:N→IR
Where ,
F(n)=SnR0.1
Where, Sn, the set of sequences
S1=s0 R 0.1
S2=s1 R 0.1
etc.
hypothesis
There are an infinite sequences,s1,s2 that we can make S1RS2 Close enough to any real number.
now in order to solve the equation xR0.1 =1,x got to approach 1.9999....but how to solve xRx =1?obviousely,R,is an equevalence relation on positive real numbers set,natural numbers set and positive rational number set.
209.8.244.39 ( talk) 12:31, 26 January 2008 (UTC)husseinshimaljasimdini
Dear Meni Rosenfeld,Black carrot is right.that is exactly what i meant. Husseinshimaljasimdini ( talk) 12:37, 28 January 2008 (UTC)husseinshimaljasimdini-baghdad-iraq
by reviewing the general mapping,R,where,ARB={pm*(10)^(n)}+{(pm+1)*(10)^(n-1)+..... it seems that binary operation is irrelevant.my main consern here is,can this relation with the set of sequences obove be applied to generate or count uniformly the irrational numbers set independently of considering cardinals concept or cauchy sequences?also can this relation be generalized to solve equations like xR1=10? OR xRx=(-1)?or xR1=(-1)? 210.5.236.35 ( talk) 14:04, 28 January 2008 (UTC)husseinshimaljasimdini. also i mean here, can the mathemetical constructure of R,be fixed to be an equlevance relation involves negative numbers? 210.5.236.35 ( talk) 14:14, 28 January 2008 (UTC)Husseinshimaljasimdini
Thank you very much Black carrot for your advice.as amatter of fact the department of mathematics in my college has ran out of experts, specially after the war and when i asked them the were making fun of me because iam physicist,thats why i am annoying you guys here whith my questions. 85.17.231.25 ( talk) 09:06, 30 January 2008 (UTC)husseinshimaljasimdini
yes black carrot.but the part of countablity conserns me.you know very well that ,G,is countable set if the sub sets that form ,G,are countable,now by reviwing the general concepts of countable set, we know that,K,is countable,if there exists an injective function F:K→N,either,K, is empty or there exists a surjective function,F:N→K.in the example that i gave above ,dont you think that ,F:N→(0,1),where,F=(SnR0.1),is asurjective?i also think F:(0,1)→N,is aninjective .(N,is the natural numbers set).if such function exists,does this make the positive irrational numbers set countable?because we know it is not. 88.116.163.226 ( talk) 12:31, 31 January 2008 (UTC)husseinshimaljasimdini
I am a highschool senior, and I am looking at attending college with a CS major. I looked over the course requirements, and I saw that I will have to take Calculus I, II, and III. I was wondering, what on earth would you use calculus for while writing computer programs?
Thanks.
J.delanoy
gabs
adds
23:50, 26 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 25 | << Dec | January | Feb >> | January 27 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The smallest figure that tiles the hyperbolic plane (H2) is the "237" triangle, whose angles are π/2, π/3, π/7. What is the smallest tile in H3? — Tamfang ( talk) 01:14, 26 January 2008 (UTC)
Just curious about interesting maths. Those of you who are most passionate about math should be able to put forth your favorite(s). What is, in your opinion, the most beautiful, interesting, or elegant mathematical thing that you have found? HYENASTE 03:18, 26 January 2008 (UTC)
Mine is this " Genetic complementary learning autonomously generates fuzzy rule." I am still learning on Wikipedia how it all comes together. My first step is understanding Stochastic matrix. I just want to understand Stochastic matrix as fast as possible, so I can grasp some cool formulas published regarding GCL. :) -- Obsolete.fax ( talk) 07:44, 26 January 2008 (UTC)
Mine is Immerman-Szelepcsényi theorem. It is a genuinely suprising result and the proof is in some sense an elaborate mathematical joke. I also like Gödel's incompleteness theorems for similar reasons. Third mention is the proof that Hex (board game) is won by the first player to move. What I want to say - mathematical beauty is not related much to the importance underlying problems or to the simplicity of the result. It works more like jokes. You hear a story and in the end you get an additional surprising information, that completely changes the way you view the story. Take a look at the last link, the "Strategy" paragraph - anybody can understand it. Thorbadil ( talk) 11:52, 26 January 2008 (UTC)
Nice challenge! My favorite is the formula
It is not quite trivial, it has a some symmetry, and it is useful for converting between gamma distribution and poisson distribution. It is applicable when computing the probability that the best soccer team won, given only information on the outcome of a particular match. The beauty is entirely in the eyes of the beholder. Bo Jacoby ( talk) 12:11, 26 January 2008 (UTC).
My favorite would a result in probability theory regarding supermartingales. Which basically says that if you are in an unfavorable game (where you will loose money on the average) then there is no betting strategy that will make the game fair or favorable. There are strategies to make the game "less unfair" but it will still be unfair. Furthermore, the optimum betting strategy, in any game, is actually the bold strategy in which you bet all or nothing. These results might sound obvious, but what is interesting is that they have been mathematically proven. A Real Kaiser ( talk) 05:35, 27 January 2008 (UTC)
as amatter of fact ,i asked this before but i got no answer.i just want here to say it could be something,it could be important after study it.you can also go to my talk and see the pdf file that contains this discussion. the purpose of this theory is an attempt to show that real numbers can be generated or counted randomly and intensively .
Consider we express the tow positive real numbers ,A&B as,
A=Σam[(10)^(n-m)] B=Σbm[(10)^(n-m)] Where,( n,m=0,1.2,……) am,bm,positive integer Now if, am+bm=pm+10,pm<10 pm,positive integer Then we define the relationship R, ARB={pm*(10)^(n)}+{(pm+1)*(10)^(n-1)+..... Obviously, R; looks like adding backwards.e.g, 341R283=525 =(3+2)=5,(4+8)=12,(1+1+3)=5 Lets now pick up arbitrarily the infinite sequence
S0=Σn\(10)^(n),+Σn\(10)^(n+1) + Σn\(10)^(n+2)+.....
Where n=1to9 ,10to99,100to999 ,...etc.respectively
i.e, S0=0.123456789101112131415161718192021222324.... n ,is apositive integer. In order to generate or count* the real numbers within the interval,e.g. (0,1),
We define ,F;
F:N→IR
Where ,
F(n)=SnR0.1
Where, Sn, the set of sequences
S1=s0 R 0.1
S2=s1 R 0.1
etc.
hypothesis
There are an infinite sequences,s1,s2 that we can make S1RS2 Close enough to any real number.
now in order to solve the equation xR0.1 =1,x got to approach 1.9999....but how to solve xRx =1?obviousely,R,is an equevalence relation on positive real numbers set,natural numbers set and positive rational number set.
209.8.244.39 ( talk) 12:31, 26 January 2008 (UTC)husseinshimaljasimdini
Dear Meni Rosenfeld,Black carrot is right.that is exactly what i meant. Husseinshimaljasimdini ( talk) 12:37, 28 January 2008 (UTC)husseinshimaljasimdini-baghdad-iraq
by reviewing the general mapping,R,where,ARB={pm*(10)^(n)}+{(pm+1)*(10)^(n-1)+..... it seems that binary operation is irrelevant.my main consern here is,can this relation with the set of sequences obove be applied to generate or count uniformly the irrational numbers set independently of considering cardinals concept or cauchy sequences?also can this relation be generalized to solve equations like xR1=10? OR xRx=(-1)?or xR1=(-1)? 210.5.236.35 ( talk) 14:04, 28 January 2008 (UTC)husseinshimaljasimdini. also i mean here, can the mathemetical constructure of R,be fixed to be an equlevance relation involves negative numbers? 210.5.236.35 ( talk) 14:14, 28 January 2008 (UTC)Husseinshimaljasimdini
Thank you very much Black carrot for your advice.as amatter of fact the department of mathematics in my college has ran out of experts, specially after the war and when i asked them the were making fun of me because iam physicist,thats why i am annoying you guys here whith my questions. 85.17.231.25 ( talk) 09:06, 30 January 2008 (UTC)husseinshimaljasimdini
yes black carrot.but the part of countablity conserns me.you know very well that ,G,is countable set if the sub sets that form ,G,are countable,now by reviwing the general concepts of countable set, we know that,K,is countable,if there exists an injective function F:K→N,either,K, is empty or there exists a surjective function,F:N→K.in the example that i gave above ,dont you think that ,F:N→(0,1),where,F=(SnR0.1),is asurjective?i also think F:(0,1)→N,is aninjective .(N,is the natural numbers set).if such function exists,does this make the positive irrational numbers set countable?because we know it is not. 88.116.163.226 ( talk) 12:31, 31 January 2008 (UTC)husseinshimaljasimdini
I am a highschool senior, and I am looking at attending college with a CS major. I looked over the course requirements, and I saw that I will have to take Calculus I, II, and III. I was wondering, what on earth would you use calculus for while writing computer programs?
Thanks.
J.delanoy
gabs
adds
23:50, 26 January 2008 (UTC)