Which side of the fence do you sit on?
Unless you are very geeky, please do not read this posting. I do not want to be responsible for wasting your time. Please come back to this blog in a coupla days and God promise, Mother promise, normalcy will return. Also, NO MORE GEEKY COMMENTS ON MY BLOG. Please :)
In the comments section of my last post, Viral and Golu are arguing about whether negative numbers can be a part of a Pythagorean triplet. And since I was the one who started this whole thing in the first place, here are my tuppence.
Viral's POV mainly comes from the idea that the Pythagorean triplet concept came from Pythagoras and was w.r.t right angled triangles. However, in today's world, with math making time go backwards, Golu's idea of negative numbers in a Pythagorean triplet is not too far-fetched.
Now that I think about it, which side you are on in this argument might say a lot about you. Given that you are geeky enough to understand the argument that is.
If you think that negative numbers can be part of a Pythagorean triplet your fundamental instinct is mathematical.
If you think that the fundamental idea of the Pythagorean triplet comes from the historical caricature of a Greek guy in a toga drawing triangles in the sand, then you would say that your fundamental instinct is artsy.
Oh and just in case you have no idea what I am talking about, then too your fundamental instinct is artsy. :)
What say? :D
This will be my last geeky posting for a bit. The number of people who have started to call me a geek has alarmingly gone up. Damage control must be done. :)
In the comments section of my last post, Viral and Golu are arguing about whether negative numbers can be a part of a Pythagorean triplet. And since I was the one who started this whole thing in the first place, here are my tuppence.
Viral's POV mainly comes from the idea that the Pythagorean triplet concept came from Pythagoras and was w.r.t right angled triangles. However, in today's world, with math making time go backwards, Golu's idea of negative numbers in a Pythagorean triplet is not too far-fetched.
Now that I think about it, which side you are on in this argument might say a lot about you. Given that you are geeky enough to understand the argument that is.
If you think that negative numbers can be part of a Pythagorean triplet your fundamental instinct is mathematical.
If you think that the fundamental idea of the Pythagorean triplet comes from the historical caricature of a Greek guy in a toga drawing triangles in the sand, then you would say that your fundamental instinct is artsy.
Oh and just in case you have no idea what I am talking about, then too your fundamental instinct is artsy. :)
What say? :D
This will be my last geeky posting for a bit. The number of people who have started to call me a geek has alarmingly gone up. Damage control must be done. :)
posted by Karthik at 7:08 AM
10 Comments:
Wanted to post a reply and ended up doing this.
i agree with golu.. -ve nos. can be a part of a Pythagorean triplet.
even though lots of stuff started with geometry as the background problem, its a totally different ball game in maths rite now.
well Duh as you pointed out, viral's funda is probably intuitive. But then that is all fuckall stuff that we have just learnt uptil undergrad. There is crap like matrix exponentials, complex logarithms, negative time (as you mentioned).
However, I just googled (would have expected you to do it) and probably Viral is right. http://mathworld.wolfram.com/PythagoreanTriple.html
This is quite interesting because I would have expected people to make a more general form of the pythagorean triplets and extend it to complex numbers in general, let alone negative numbers.
Anyway the thing...is Viral was correct => Duh was correct.
What's more, I just checked bolli's blog (bolli pls allow comments bey) and was abt to refute him on his statement
"And there is reason why it is not extended to integers (or more correctly to any set larger that the natural number set - including whole numbers)"
FUCKKKKKKK, the bloddy pythagorean triplet is defined only for integers. What a loser he was! Seriously. I can understand him not talking abt complex or negative numbers, but atleast extend things to the damn positive real line. Why what is so religious abt integers. Waise he has been screwed by many mathematicians
http://members.fortunecity.com/jonhays/chronology.htm
Bolli one pseud geek funda..what do u mean 'larger set'. Do you know the set of even natural numbers has the same cardinality as the natural numbers. So please to use such terms carefully when writing abt technicalities :D
btw duh by mentioning pythagorean triplets having only integers, you have redundancy in your definition
boss kya lamba comment that yeh
Golu, now I know why they rated me average.
There are people like YOU out there!
Kram
Duh... if you keep posting such geeky stuff... i swear to lucifer i m gonna start a blog 'duh-is-a-bloody-geek' and post its link in all the pornographic sites!
and now we have to post comments to bolli's posts on this blog?? man... this sucks! :)
Abey Golu you just corroborated what I said. Except for one thing. I used the word "larger" in thet spoken context which is incorrect I agree. Anyways, the positive real line is not denumerable, or as you put it does not have the same cardinality as natural numbers. Hence that would atleast be larger. :)
Secondly, I thought I also tried to explain why the things are for positive integers, then there can be "properties of the system". Try proving/disproving the question I put up about ordered Pyhtagorean triplets. General real triplets are as trivial as the theorem itself. Given any number, you can find infinite Pythagorean triplets, even in an ordered set scenario. Not the case even with unordered positive integer triplets. Hence.
And yes, comments enabled, much against my own will. But I want to see what this can lead to.
im sorry but for this chain i shall reply here...aage se ill post in ur thingie...
so i understand that u r saying integers are pseud and all....so hence define pythagoran triplets for them. I believe that it is more realistic to define them for the set of rationals atleast. And the thing which is pseud is the pythagoran theorem and not the triplets. First of all this isnt between u and me :D its between pythagoras and me :D.
"General real triplets are as trivial as the theorem itself". NOOOO thats what im driving at. Do you realise the intuition this guy had to come up with the theorem. As someone pointed out earlier...he did it by just drawing triangles made of squares or crap like that. He probably didnt have trig fundaes and stuff. I think the theorem in itself is very powerful and by NO MEANS trivial. Again we are taught in school that sin and cosine are ratios of sides of a triangle. But for a person who deals purely in geometric fundaes and has NO idea of the trignometric definitions, to come up with something like this is stud. What im trying to drive is that there is nothing sacred about the triplets, it is only the theorem which is useful. Fuck integers, who said that they are really 'nice' to deal with. I can say I want even integers and such crap.
And bolli, one more reason why we have to deal with non integer triplets is like the pseud funda that ppl approximated sqrt(2) by using the pythagoran triplets thingie
Bloody geek golu stop this triplet non sense. And Bolli, go choke up on some thesaurus and die...... muhahahaha
OK..first thing I would like to refute golu on his attack on bolli on larger set thing ..if A is a subset of B, but B is not a subset of A then B is a larger set..fuck cardinality..hence the set of natural numbers is larger than set of even numbers..
Next thing is the pythagorean triplet thing..I guess its more fun to define for natural numbers and then see what properties they satisfy..if u define it for all the numbers then given any "a,b" u can get a "c" such that (a,b,c) is a pythagorean triplet...then it kind of loses its beauty..there is nuthing special abt these numbers then..just my thought..
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