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What does this equation mean to you?

  1. May 9, 2008 #1
    Hi first time on this forum. Ok I was bored and found a way to calculate numbers to the power of 2:

    a b c d e f [tex]\infty[/tex]
    1 2 3 4 5 6 [tex]\infty[/tex]


    b-1=a c-2=a d-3=a e-4=a f-5=a g-6=a

    [tex]b^{2}=a^{2}+a+b \vee b^{2}=a^{2}+2a+1[/tex]



    [tex]c^{2}=a^{2}+2(2a+2) \vee c^{2}=a^{2}+4b[/tex]



    Same for the rest d,e,f,g,...[tex]\infty[/tex]

    What am I getting at? Well I'm at my second year at high scool , and well I still don't have the "software" :-) to find any other mening of this. I don't really know what I made up exept counting powers in my head using what's above.

    Thanks for any input!
     
  2. jcsd
  3. May 9, 2008 #2

    CRGreathouse

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    I don't understand your method. How would it find 2^8, for example?
     
  4. May 9, 2008 #3
    What I meant is that you can raise any number with this equasion but only to the power of ^2
     
  5. May 10, 2008 #4
    What you are doing is finding a relation between two numbers and their second powers (squares of the numbers), not powers of 2 which means 2 muptiplied by itself a certain number of times, 2,4,8,16,32, .... In algebra, there is a way to multiplied b^2 = (a+1)*(a+1) to get the square of b since b = a + 1. You got it right when you got the result a^2 + 2a + 1. Similaly c^2 = (a+2)*(a+2). You wrote c^2 = a^2 + 4b which is correct given your values for a,b and c. But a^2 + 4b = c^2 can Be true for whole values of a,b and c only if [tex]c = a + 2m[/tex] where m is also a whole number (or integer). Try it for different values of a and c. It is correct also if c = a+ 4 and b = 2a + 4. Try it for various values of a and c. You would be making a good start in number theory if you could show that c^2 could equal a^2 + 4b where a, b and c are each integers, if c = a + n where n = 2m (or an even number) but not if n = 2m + 1 (or an odd number).
     
  6. May 10, 2008 #5
    Thanks ramsey2879 for the info, again sorry for my bad math lingo.
     
  7. May 10, 2008 #6

    CRGreathouse

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    Ah, I see. You can square any number. So can you show me how you would square 12 with this method?
     
  8. May 11, 2008 #7
    :
    a=11 b=12
    b^2=121+11+12 or b^2=121+22+1
    144=144 144=144

    a=10 b=11 c=12
    c^2=100+2(20+2) or c^2=100+4(11)
    c^2=100+44 c^2=100+44
    144=144 144=144
     
    Last edited: May 11, 2008
  9. May 11, 2008 #8
    This is simple to show via algebra:

    [tex]c = a + 2[/tex]
    [tex]c^2 = (a+2)*(a+2)[/tex]
    [tex] = a^2 + 4a + 4 = a^2 + 4(a + 1)[/tex]
    [tex] = a^2 + 4b [/tex]

    or if c = a + 2n then
    [tex] c^2 = (a + 2n)(a+2n)[/tex]
    [tex] = a^2 + 4na + 4n^2[/tex]
    [tex] = a^2 + 4b \quad \| b = n(a+n) [/tex]
     
    Last edited: May 11, 2008
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