Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060712 01:48:33
for a challengehello everybody ... in fact i dont know how to start ImPo$$!BLe = NoTH!nG Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ... #2 20060713 08:07:45
Re: for a challengeviews : 16 ImPo$$!BLe = NoTH!nG Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ... #3 20060713 10:06:55
Re: for a challengeYou could start with Add Two Numbers and the Answer is Always 1089 "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #4 20060713 10:16:22
Re: for a challengeYou could always use my historical proof that i^{i} = e^{π}/2 ∈ R. I did it for a talent show and won, so I guess it could be used as good mathematical magic. It was a great day for mathematics. If you would like me to write out the problem, just ask. #5 20060713 10:39:22
Re: for a challengeZhylliolom, I get , where n is an integer. Could I see your work?Interesting question though, I have to say. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20060713 14:14:45
Re: for a challengeHopefully we all know Euler's formula: For this problem, let 0 ≤ θ ≤ 2π. Now ask yourself, for what value of θ will e^{i}θ = i? Why yes, it's π/2! So now we know that e^{i}π/2 = i. Now let's take it to the next level: Now if we remove the restriction 0 ≤ θ ≤ 2π, then we get the general solution where n ∈ Z. I'm not sure why you have just n and not 2n, Ricky. Odd values of n in your solution would give Now take a simple case of some 0 ≤ θ ≤ 2π that could give e^{i}θ = i. 3π/2 is our value. Then So, given the same interval 0 ≤ θ ≤ 2π, (i)^{i} ≠ i^{i}, so I will conclude that your n should be 2n. Last edited by Zhylliolom (20060714 08:07:19) #7 20060713 23:37:09
Re: for a challengesin(3pi/2) doesn't equal 1, does it... "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20060714 00:14:32
Re: for a challengeHey you guys are discussing something too difficult here! X'(yXβ)=0 #9 20060714 05:16:52
Re: for a challengethank you alot guys ImPo$$!BLe = NoTH!nG Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ... #10 20060816 19:55:30
Re: for a challengeOr you could just try looking in the Exercises forum. We're adding some every now and then, so check back regularly! Last edited by Devantè (20090215 10:18:30) 