September 17th, 2018, 07:22 AM  #1 
Member Joined: Feb 2013 From: London, England, UK Posts: 38 Thanks: 1  Formula for n^2 without explicitly performing n*n:
I am reposting this here, because it's being shut down on Maths Stack Exchange. There's some snobby people on there who don't like stuff like this. Thanks!! Formula for n^2 without explicitly performing n*n: $$n^2 = [(1  (1)^n)/2] + [(1 + (1)^n)/2] * [4 * ({n + (1  (1)^n)/2}/2)] + [4 * ({n + (1  (1)^n)/2}/2)] * [({n + (1  (1)^n)/2}/2)  1]$$ That's it. Hopefully, I've not made any errors in it. Here's a simplified version: Let s = (1  (1)^n)/2 ; and t = (1 + (1)^n)/2 Then, expression for n^2 is as follows: n^2 = s + t * 4 * ((n + s)/2) + 4 * ((n + s)/2) * ((n + s)/2  1) 
September 17th, 2018, 09:18 AM  #2 
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 140 
Perhaps they are not snobby. Maybe they just don't see the point. Is this supposed to be more efficient for a computer or calculator? I don't have the requisite expertise to answer that. If this is your claim, then post some data so that the computer gurus on this site can assess the efficiency of your claim. If this is supposed to be more efficient for a human, then I would try $\displaystyle n^2=(nd)(n+d)+d^2$. For a well chosen small value of $\displaystyle d$, you can square $\displaystyle n$ in your head. If it is neither of these, then you should really say what the point is. 
September 17th, 2018, 09:21 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond 
$$n^2=\sum_{k=1}^n(2k1)$$

September 17th, 2018, 09:27 AM  #4 
Member Joined: Feb 2013 From: London, England, UK Posts: 38 Thanks: 1 
@mrtwhs The point isn't that there is no point. But equally, need everything have a point? I'm not making any claims, it's a statement of fact. I don't need a disclaimer because nothing is being claimed. I simply chanced upon this as I was doing other research, thought it might be interesting or useful to someone at some point, so posted it. I personally have no real use for it, but felt, perhaps misguidedly, that it might be of utility to others. 
September 17th, 2018, 09:37 AM  #5  
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 140  Quote:
 
September 17th, 2018, 09:47 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025  Why do you not simply say: simplify right side ?
Last edited by Denis; September 17th, 2018 at 09:51 AM. 
September 17th, 2018, 10:01 AM  #7 
Member Joined: Feb 2013 From: London, England, UK Posts: 38 Thanks: 1 
@mrtwhs Sorry, I wasn't trying to be surly or anything. It's just that a few people on the MSE website basically shut the question down. I can't see that there's a good reason. I'm not saying it's all that useful, just that it might be, in case someone is looking for some such thing at some point in the future. Speaking from personal experience, I often encounter interesting things in maths which seem irrelevant to the matter at hand at a particular juncture of research, but the trick is to write them up semineatly, and then archive the little result, no matter how trifling or seemingly insignificant. Then invariably, some other avenue opens up down the road, at which point the little finding becomes useful and applicable. 
September 17th, 2018, 10:07 AM  #8  
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 140  Quote:
However the top formula gave $\displaystyle 3^2=36$. I think there is a typo in the top formula.  
September 17th, 2018, 10:13 AM  #9 
Senior Member Joined: Aug 2012 Posts: 2,311 Thanks: 706  
September 17th, 2018, 10:18 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025  

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