Dave Posted March 13, 2003 Share Posted March 13, 2003 i saw something similar to the regular argument used to prove 1=2 the other day, and i thought i'd share it in here since these forums seem a little dead on the maths side sometimes it goes like this: (cos(x))^2 = 1 - (sin(x))^2 then, 1 + cos(x) = 1 + sqrt(1 - (sin(x))^2) squaring, (1+cos(x))^2 = (1+sqrt(1 - (sin(x))^2))^2 now when x = 2*pi/3: (1-1/2)^2 = (1 + sqrt(1-3/4))^2 1/4 = (1+sqrt(1/4))^2 therefore 1=9 i haven't looked at it much, as mainly i find these things tedious, but i thought it was quite neat so here you are. enjoy Link to comment Share on other sites More sharing options...
JaKiri Posted March 14, 2003 Share Posted March 14, 2003 It'll be an incorrect sign on a sqrt. It almost always is. Link to comment Share on other sites More sharing options...
zakfab Posted July 23, 2003 Share Posted July 23, 2003 Maths 'tricks' are stupid, they only work on people who don't understand maths. (cos(x))^2 = 1 - (sin(x))^2 This is correct. Now you have square rooted both sides, and added one. then, 1 + cos(x) = 1 + sqrt(1 - (sin(x))^2) Nope, the lhs is 1 + sqrt(cos(x)^2) The 1 is added to make the lhs positive, as you can't sqrt a negative number (unless you want to go into imaginary numbers). So when the -0.5 is squared it becomes +0.25. Then is square rooted to be +0.5. The one is added and it all works out. 2.25 = 2.25 Link to comment Share on other sites More sharing options...
Dave Posted July 23, 2003 Author Share Posted July 23, 2003 Originally posted by zakfab Maths 'tricks' are stupid, they only work on people who don't understand maths. No they aren't. Sure, some might be quite simple, but it encourages people to actually think about why things are wrong. When I was 16, my maths teacher showed me a bit of 'trick' maths that was interesting because you can't get it to work without explaining why the equation x^3 = 1 has 3 different answers, and this encourages people to continue with mathematical studies - and hence help them understand the mathematics. Link to comment Share on other sites More sharing options...
NavajoEverclear Posted July 24, 2003 Share Posted July 24, 2003 1 does not = 2 or 9. one is one. I have one head, only one, not two, and certainly not 9. If the equation says that (even if i could understand it i dont care to think about it, its summer) then it is a flaw in the mathmatical system, because 1 is one, this is physically backed everywhere. Look at your computer monitor as you read this. You have one computer monitor, go buy 8 more and tell me this is not different. How does 1=9? Tricks are all nice and good, and it maybe funny to show that our system is flawed, but it is that, proof of flaw, not proof of nonsense. Of coarse if you know me i think proof is impossible to proove anyway, but i think most people would agree with my faith that one is one, not 2 or 9. Unless you can explain how (i am open to listening), i'm sticking to that belief. Link to comment Share on other sites More sharing options...
NavajoEverclear Posted July 24, 2003 Share Posted July 24, 2003 excuse for that somewhat offended/offending reply, you probably meant it just as a humorous way showing our flawed system. I shouldn't have been dumb enough to believe you believed it yourself. Unless you can explain it logically (im not really in the mood to read mathmatics equations, but i guess i will try if neccesary) as some concept. Link to comment Share on other sites More sharing options...
zakfab Posted July 24, 2003 Share Posted July 24, 2003 NavajoEverclear: I already showed where the 1 = 9 trick goes wrong. Link to comment Share on other sites More sharing options...
NavajoEverclear Posted July 24, 2003 Share Posted July 24, 2003 so that means there is not a flaw in the system? but you dont even have to figure it out to know that the only two possibilities are error in use of the system or flaw of the system itself. I know one is not the same thing as 9 unless someone show me some complex concept that prooves it so. Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 There isn't. It's a flaw in the use of the system. Link to comment Share on other sites More sharing options...
alt_f13 Posted August 19, 2003 Share Posted August 19, 2003 I once went through two pages of algebra to find out V = V It was a life changing experiance. Link to comment Share on other sites More sharing options...
NSX Posted August 19, 2003 Share Posted August 19, 2003 Originally posted by dave When I was 16, my maths teacher showed me a bit of 'trick' maths that was interesting because you can't get it to work without explaining why the equation x^3 = 1 has 3 different answers, What are the 3 answers? 1 is an answer... What are the other 2? Originally posted by alt_f13 I once went through two pages of algebra to find out V = V It was a life changing experiance. lolz I know what you mean... I thought those were bad, then I learned about proofs Link to comment Share on other sites More sharing options...
Dave Posted August 19, 2003 Author Share Posted August 19, 2003 z^3 = 1 z^3 - 1 = 0 (z - 1) is a factor (z = 1 is a root) (z - 1)(z^2 + Az +1) = 0 equating co-efficients in z^2 gives A = 1 therefore the other roots (by solving the other equation) are (-1 +- sqrt(3)*i) / 2 Link to comment Share on other sites More sharing options...
NSX Posted August 20, 2003 Share Posted August 20, 2003 dave said in post #12 :z^3 = 1 z^3 - 1 = 0 (z - 1) is a factor (z = 1 is a root) (z - 1)(z^2 + Az +1) = 0 equating co-efficients in z^2 gives A = 1 therefore the other roots (by solving the other equation) are (-1 +- sqrt(3)*i) / 2 ah...very clever...cools Thanks dave Link to comment Share on other sites More sharing options...
Peter Dunn Posted August 20, 2003 Share Posted August 20, 2003 I'm going for a sqrt Link to comment Share on other sites More sharing options...
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