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It is currently 19 Jul 2012 14:42
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infus3
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Post subject: Triangular numbers equation (reversing an equation) Posted: 24 Jan 2009 18:09 |
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Joined: 17 Oct 2007 08:10 Posts: 31 Location: South Carolina
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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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aluigi
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Post subject: Re: Triangular numbers equation (reversing an equation) Posted: 24 Jan 2009 23:44 |
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Joined: 13 Aug 2007 21:44 Posts: 4068 Location: http://aluigi.org
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ih ih ih this remembers me the old times at school loosing the day with these ehmmmm "things" :)
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infus3
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Post subject: Re: Triangular numbers equation (reversing an equation) Posted: 25 Jan 2009 21:24 |
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Joined: 17 Oct 2007 08:10 Posts: 31 Location: South Carolina
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yeah i think i might have figured it oout though. or i found another equation that will work
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Sethioz
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Post subject: Re: Triangular numbers equation (reversing an equation) Posted: 26 Jan 2009 14:40 |
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Joined: 24 Sep 2007 02:12 Posts: 1114 Location: http://sethioz.co.uk
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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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quandary
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Post subject: Re: Triangular numbers equation (reversing an equation) Posted: 01 May 2009 00:57 |
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Joined: 01 May 2009 00:43 Posts: 4
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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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