Luigi Auriemma

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 Post subject: Triangular numbers equation (reversing an equation)
PostPosted: 24 Jan 2009 18:09 

Joined: 17 Oct 2007 08:10
Posts: 31
Location: South Carolina
Hello, I figured out an equation to find a triangular number, and now I want to reverse it so I can enter the triangular number and find the the line it is on.

I need some help with the following equation:


n * (( n / 2 ) + 0.5) = TN

Thus:

15 * (( 7.5 ) + 0.5 ) = 120

I would like to be able to have TN and solve for n. I couldn't figure out a way to reverse the equation or isolate n.

Can anyone help me with this please?


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 Post subject: Re: Triangular numbers equation (reversing an equation)
PostPosted: 24 Jan 2009 23:44 

Joined: 13 Aug 2007 21:44
Posts: 4068
Location: http://aluigi.org
ih ih ih this remembers me the old times at school loosing the day with these ehmmmm "things" :)


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 Post subject: Re: Triangular numbers equation (reversing an equation)
PostPosted: 25 Jan 2009 21:24 

Joined: 17 Oct 2007 08:10
Posts: 31
Location: South Carolina
yeah i think i might have figured it oout though. or i found another equation that will work


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 Post subject: Re: Triangular numbers equation (reversing an equation)
PostPosted: 26 Jan 2009 14:40 

Joined: 24 Sep 2007 02:12
Posts: 1114
Location: http://sethioz.co.uk
just in case i ask/suggest. have you tried wikipedia and google ? I'm very sure there's reversed equation for that. im not good with equations, so if i would see the right one (reversed) without the name that says "reversed triangular numbers equation" then i doubt i would reconize it..so i can't help you by searching..well i did few quick searches and found tons of equations (including this one here).


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 Post subject: Re: Triangular numbers equation (reversing an equation)
PostPosted: 01 May 2009 00:57 

Joined: 01 May 2009 00:43
Posts: 4
Well, if you would have written it a bit better, you would have gotten the answer...

x(x+1)/2 = TN = (x^2+x)/2

<==>

x(x+1) = 2 * TN

<==>

x(x+1) + 0.25 = 2 * TN + 0.25

<==>

(x+0.5)*(x+0.5) = 2 * TN + 0.25

<==>

(x+0.5)^2 = 2 * TN + 0.25

<==>

(x+0.5) = +/- sqrt(2*TN + 0.25)

<==>

x = -0.5 +/- sqrt(2*TN + 0.25)

And that's it, you don't even need a calculator...


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