:Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :qwertydawom, ready? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yep :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net MODE #lecture -o Ch4r :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :k, go for it :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :ok :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Well, today, I would like to introduce you to an interesting topic (imho), which is : graph theory. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Obviously, since we are not here for a math course, this will just be elementary stuff, but still precise and a good introduction for further researches in this field. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :First of all, I'll have to define the terminology used in graph theory. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Hopefully, most of the graph theoretic terminology is so intuitive that it is not hard to remember. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, first of all, what's a "graph"? :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :a vertices connected by lines :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :*set of :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :A set of points represented graphically? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :A graph is a pair G = (V, E) of sets satisfying E included in [V]^2. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :satisfying E included in [V]^2... Say what? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :As a conclusion, the elements of E are 2-elements subsets of V. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture : satisfying E included in [V]^2... Say what? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :--> :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :by [A]^m, I denote the set of all m-elements subsets of A :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, we may always assume that V n E = empty_set. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The elements of V are the Vertices (aka nodes, or points). :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :And E represents the Edges of the graph G. :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :ACTION doesn't get it -_- :Elda_Winslacks!loulou@bu-6D350C37.w86-215.abo.wanadoo.fr JOIN :#lecture :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Uh yeah same here.. :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :honestly qwerty, although i do get it, such a mathematical definition is though for people without proper formation :OperServ!services@rest0re.org PRIVMSG #lecture :ACTION gets it!  :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Indeed, like SysSpider and varu|zZz mentioned, to represent a graph, we usually draw a dot for each vertex and join two of these dots by a line if the corresponding two vertices form an edge. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Well, SysSpider, in a previous lecture, I covered set theory, so... :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :that doesn't mean everyone attended it ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :I know, but as a prerequisite, you should at least look (quickly) at the previous lectures. ;) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :it's fair :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Anyway, if this is too hard, let's postpone it for one week. :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture ::o :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Tonight, I'll just cover the most basic stuff :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and, next week, I'll go more deeply (but still being dealing with elementary stuff) into it. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, graph theory was firstly (and mainly created because of that actually) used in economy. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Indeed, it allows, for example, to find the shortest path to go from one city to another. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, let's show how it works. :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :120 : angle of the shortest path between three points. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The length of the shortest road between three cities is obtained like this : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :you draw three points A, B and C in the plane :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and now, the aim is to find a fourth point (let's call it D) which is placed such that : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :m(CDB) = m(BDA) = m(ADC) = 120° :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :where m(stuff) denotes the measure of the angle "stuff" :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :(in degrees) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, come on, take a piece of paper, a pen, and start drawing ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :let me know when you get it :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :10 years and 4 failed calculus courses later... :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :erm.. :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :allow me to ask for some.. clarification :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :what exactly is it that you want us to do? :P :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :I mean, alright, points A, B, and C. Randomly drawn. :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :oh we're supposed to do something? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :draw three points :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :the traveler salesman problem? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yes :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :P = NP? ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well, a special case of it ;) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :yep :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :it was my passion for like 2 years :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :eh.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :lol :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :haha, no, I am not going to prove (or disprove) P = NP tonight :p :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and, I don't want to hear : :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :i can guess it xD :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :P = NP <==> P - NP = 0 <==> P(1 - N) = 0 <==> P = 0 or N = 1, q.e.d. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :;) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :that was my first thought as well lol :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :haha :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, did you get the case n=3 points? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Can this be done for any three points? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yes :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :it is true if each of the angles of the triangle ABC is less than 120°, to be precise. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :(only if) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :less? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :argh :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :ehh :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :wait.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Oh ah.. nvm. xD :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, got it? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :... :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :ok :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :I believe this will REALLY help you : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :http://www.utdanacenter.org/mathtoolkit/downloads/geoassess/geo_2_steiners.pdf :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :take 5 mins. to look at it :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :then, tell me when you're done :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :for those who think they got the case n=3, have a look at : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :http://www.delphiforfun.org/Programs/traveling_salesman.htm :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :now, if you think this is still too "childish" for you : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :http://en.wikipedia.org/wiki/Traveling_salesman :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, by now, as soon as you're done with reading and/or understanding, let me know :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :I miss my triangle.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, did you have a look at this chapter about the Steiner's point? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :humz.. the quickest way would be to print a dot and 3 lines each 120 degrees with the dot, then just shove the paper around and rotate till it fits. >_> :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Till it meets the requirements noted earlier. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Where is my geometry triangle.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :I read it alright :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :but I can't even answer the first problem in scaffold questions :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :mmk :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well, look at the solution :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and then you'll try to solve the second problem by yourself :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :oh, you said the 'scaffolding questions'.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :in this case, don't worry :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :as long as you managed to understand how to draw the point D :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and noticed that it is indeed the shortest point (I mean, intuitively) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :then it's alright! ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, are you all done with reading? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Ok, I'll go on. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Now that we've seen the case with 3 points, guess what we are going to study? :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :cases with n points? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :not that quickly :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :simply : n=4. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, we have a quadrilateral ABCD. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Ouch, long word.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :haha :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :you mean a plane right? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :? :adrian!adrian@bu-EEDF8135.cpe.net.cable.rogers.com PRIVMSG #lecture :you dont know what a quadrilateral is? :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :Daedalus, he means a four-sided shape :P :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :quadrilateral : polygon with 4 sides and four vertices :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :a polygon with 4 sides :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :that :adrian!adrian@bu-EEDF8135.cpe.net.cable.rogers.com PRIVMSG #lecture :thats grade 3 geometry lol :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :yeah, a plane. xD :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :err no? :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :a plane is an infinite surface :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :For me it is.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :mmm :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :where do you come from? (if I may ask) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :netherlands :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :The netherlands. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*points to IP* :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :okay :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :And i'm in the "highest" class of education :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :but I'm still feeling stupid. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and how do you say so in Dutch? (if I'm not wrong with the language :-/) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :vierkant. (fourside) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :viereck in german I thought. *-) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :from what I know, a vierkant (or kwadraat) is just a square :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :meaning that the 4 sides are equal :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :and the 4 angles :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :each 90 degrees. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :yeah that's right.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :but a plane is a vlak. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :what I'm talking about is a : vierhoek :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :ah. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :now, it's talking? :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :yeah continue.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :okay ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, we take a point E in the center of the quadrilateral. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :With E and two of the points we look for the triangles whose angles are less than 120°, so we are back to our previous case. ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :You have to adjust E little by little. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :ok? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :yes.. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :alright, now I will let you all finish to read all the links I mentioned. ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :the lecture will be continued in (more or less) 10 mins. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :for those who have already read it all, consider it as a little free time! ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net TOPIC #lecture :Lecture going on. - Read! :p - 10 mins. until we go on. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :That computer beats me by far. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :The TSP program :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :2000 miles.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :i wasn't too far off this time th :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*tho :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Just pick the points that are closest to each other each time. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture ::D :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :We got the same result for 20 cities. :D :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :hehe :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :but that has little to do with the actual math behind the program.. >_> :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yes lol :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, let's go on. ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net TOPIC #lecture :Lecture going on. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Let us now study the "Traveling salesman problem". :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :How to minimize the path of our salesman going from city to city. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :?* :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :easy, from the starting dot, calculate the distance of each next city, then pick the one that's closest. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*dot == city :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :This problem seems pretty easy, eh? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :it seems? :| It isn't? :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :nope :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :it's NP :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Damn :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :hey my method works okay as well. >_> :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Well, it becomes extremely complicated when the number of cities increases. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Let us illustrate the problem. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :That's why the exhaustive search takes so long. *-) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :With my car, I say I can take back two of my friend -adrian and bot- to their home. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :I begin with adrian, and then bot, or the contrary. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Then, the day after, I also propose it to Ch4r. :adrian!adrian@bu-EEDF8135.cpe.net.cable.rogers.com PRIVMSG #lecture :what? :adrian!adrian@bu-EEDF8135.cpe.net.cable.rogers.com PRIVMSG #lecture :oh :adrian!adrian@bu-EEDF8135.cpe.net.cable.rogers.com PRIVMSG #lecture :k :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :In the first case, there were two locations, 2 possibilities. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Now that I propose to take Ch4r back too, :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*adrian then bot then Ch4r :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :3! = 6 ;x :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*adrian then Ch4r then bot :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*bot then adrian then Ch4r :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yes Ch4r ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, end the list! :) :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :*bot then Ch4r then adrian :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :*Ch4r then bot then adrian :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :*Ch4r then adrian then bot :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :exactly. :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, we have 3 locations, 6 possibilities. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The explanation (of this 6) : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :3 choices for the 1st location :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :2 for the 2nd one :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and only one for the last one : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :3*2*1 = 3! = 6. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :And then, the week after, Daedalus comes with us. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :yeey :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*adrian then bot then Ch4r then Daedalus :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*adrian then Ch4r then bot then Daedalus :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Save the typing, I think we get this part, is it really important? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :*etc. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :lol :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :nvm. xD :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :4 locations :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :4! = 4*3*2*1 = 24 possibilities (no, I wasn't going to write them all! :P) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :4*3*2= 24 options. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yep :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :120, 720, (4900+140).. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :And now, say I want to take 10 people back.. (it appears that my car is in fact a BIG car.. :P). :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :hahaha :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :10 locations :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :It increases drasticly :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :10*9*...*3*2*1 = 3628800 possibilities .... :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Sweet :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and with 100 people (do I have a plane or what? :P) :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :lol :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :it really goes high.. :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :100! = 0.933*10^(158) possibilities o_O :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :hahaha :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :thank you Ch4r for the exact value :) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :You also got a lot of friends btw. :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :np ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture : You also got a lot of friends btw. --> haha, yes :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :To have an idea of what this incredibly big number represents : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :even with the maximum velocity of the computers nowadays :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :let's say 1 nanosecond to examine one possibility :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :it will need 10^(158) ns to examine them all, that is 10^(149) seconds. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :there are almost 10^7 seconds in a year :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, it will take 10^(142) years :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :the age of the universe is almost 10^(10) years :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, it will take 10^(132) times the age of the universe :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :OMFG! :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :lol :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :nice :varu|zZz!haha@CE63F4D7.FABB7C37.D6FD55A0.IP PRIVMSG #lecture :so essentially, another 10-20 big bangs will happen till all possibilities are explored :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :!= :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::)* :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, well, if I decide to take back the 157 members of BU, hehe.... :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Now, you're probably interested in knowing the solution to this problem, aren't you? :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :I'm very curious, and hoping it doesn't involve really hard math, because i'm kinda bad at it. :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :ACTION nods :P :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Well, the solution giving the optimal path to our salesman is NOT simple. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :During the past centuries, guides were published to help to organize the tour. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :In fact, a general solution for any number of locations or any lengths between the steps is not known at the moment I write this. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Here, I will show you a possible method : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Our salesman wants to go through each dot of the tour, in fact : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :via the shortest path, without going twice at the same place :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :What's the shortest path passing through all these points? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Let us assume the points are the vertices of a parallelepiped in n dimensions. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :We denote the vertices by 000...00, 000...01, 000...10, etc. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, in 2D, with 4 points, the vertices would be : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :00, 01, 10, 11 :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :in 3D, with 8 points : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :000, 001, 011, 010, 110, 111, 101, 100 :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :gray code :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :We organize the lengths of the parallelepiped from the greatest to the smallest, :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and we begin with the vertice 000...00. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :We can do this without loss of generality. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*vertex :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :yes, vertex, sorry ;) :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :dw, it's the part i got. ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The solution is unique. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :It consists, for the salesman, to go from one vertex to another using the Gray code, like you noticed! ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Adleman managed to build an ADN computer who solve one version of the traveling salesman problem. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The ADN computer needed one week, while a classic computer would have needed years.. :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :but this was just for one problem? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :oh, by the way : ADN = DNA* :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Daedalus, you can have a look at (just the beginning) : http://web.cecs.pdx.edu/~mperkows/temp/June16/dna2.pdf :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :So, now, let's introduce the notion of "polynomial problem" :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :1/ Sorting problem. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Sorting 1000000 objects should take about 1000 times more than sorting 1000 objects. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :In fact, the simplest sorting programs take a time proportional to the square of the number of articles to be sorted. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The theoricians of the complexity were able to show that the quickest possible sorting program would require a number of steps proportional to the number of objects, multiplied by its logarithm. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :(For those who are already confident with this idea of complexity, it means, that, if we have n objects, the simplest algorithm has a complexity of O(n^2) while the 2nd one has a complexity of O(n*ln n)) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :2/ Polynomial problem. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The problems whose solution can be computed in a time at most proportional to a given power of the size of the problem are said to be of polynomial type, or P. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Nowadays, with the computers, they are considered as easy. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :3/ The T.S.P. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Find the shortest path to visit once and only once a set of given cities. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The best exact solutions found are tantamount to make the program examine almost all the possible paths. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The number increases exponentially with the number of cities. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :(see the solution above) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :4/ Non-deterministic problem :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :To solve the problem of the salesman, we can imagine a computer which would be able to browse simultaneously all the possible paths. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :When arrived at a "crossroad", the machine separates into two parts and browses simultaneously the two paths. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Then, this machine could solve the problem in a polynomial time. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :These problems are said to be NP. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :The connection of the components on a circuit is of this type. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :Same goes for the automatic reasoning. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :5/ Practically speaking : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :We have never been able to transform a NP problem into a succession of problems of type P. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :We always proceed with approximative methods which do not guarantee the quality of the answer at all, and which are sometimes really.. sucking. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :This problem to know if, yes or not, P = NP is still open, and if you can prove or disprove it, you can win $1 million as it is one of the seven Millenium problems. (cf. http://www.claymath.org/millennium/) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :And, I will let you meditate on this, as this lecture now comes to its end. :) :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :cool stuff :D :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :good lecture :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :thank you :) :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :no, thank _you_ ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :you're welcome ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :next week, we will go on with this :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :cool :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :so, the pre-requisite will only be this lecture :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :ok :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*sob* :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :*grabs math books* :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :excellent lecture qwerty :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :glad you liked it ;) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :i'd like to say that whoever proves that P = or != NP gets a million dollars ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture : This problem to know if, yes or not, P = NP is still open, and if you can prove or disprove it, you can win $1 million as it is one of the seven Millenium problems. (cf. http://www.claymath.org/millennium/) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::P :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :oops :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :i hadn't noticed :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :hehe :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :np (meaning no problem in this case, eh? ;P) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :yeah ;) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :it's actually quite a problem hehe :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :haha :) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well, see you next week then! (same time, 8PM GMT+0) :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :sure :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :oh, and Daedalus, don't be mistaken, I can't speak Dutch at all! :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PRIVMSG #lecture :/part :SysSpider!SysSpider@B192B06C.491107F.3A4803A3.IP PART #lecture :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :I just know some math vocabulary, and that's it. lol :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Nice, how come? Where are you from? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :from France :Daedalus!Nick@bu-A5719BE5.adsl-surfen.hetnet.nl PRIVMSG #lecture :Too bad of the language, but otherwise one fine country. xD :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture ::) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :well, how come I know a bit Dutch? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :because I am fond of math :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :and, since not all the mathematicians can speak english (most of them do though) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :I need to have a basic math. vocabulary ;) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :in : :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :1/ english - well, that's ok now. (tbh, there are even some precise words that I know in english, but not in french.. haha) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :2/ spanish :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :3/ dutch :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net PRIVMSG #lecture :no, not chinese yet :P :Ch4r!Ch4r@bu-BBA3FD18.hsd1.ca.comcast.net PRIVMSG #lecture :xD