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General triangle rules and formulas?

  1. Aug 10, 2004 #1
    Hi guys I'm looking for a website where I can review basic triangle rules such as the formulas for right triangles... I would look at a geometry book but I dont have one. Its been a long time and I need some reviewing to do.

    I also wanted to ask if anyone knew about the group of triangles such as one with sides measuring 4,5,3.... , 24,25, 7 etc? This are the typical SAT triangles.. and I know there is a patter but I dont know what it is.

    Thanks.
     
  2. jcsd
  3. Aug 10, 2004 #2
    Given integers, a and b, the entire pattern is generated by

    [tex] X=a^2-b^2, Y=2ab, Z=a^2+b^2, where X^2 +Y^2 = Z^2. [/tex]

    You can check this by multiplication and by reading Modern Algebra by Birkhoff and MacLane.
     
    Last edited: Aug 10, 2004
  4. Aug 10, 2004 #3

    Math Is Hard

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  5. Aug 10, 2004 #4

    Gokul43201

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    Also, given any odd interger 'n', [tex]\frac {n^2 + 1}{2}, ~\frac {n^2 - 1}{2} [/tex] complete a triple.

    Thus, for 3, you have 4=(9-1)/2 and 5 =(9+1)/2
    for 5, you have 12 = (25-1)/2, 13 = (25+1)/2
    then there's 7, 24, 25 and 9, 40, 41 and so on..
     
  6. Aug 10, 2004 #5

    Math Is Hard

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    but what's going on at n = 1?
    a zero length side on a triangle can't be possible. :confused:


    or maybe we're not talking strictly about triangles?
     
    Last edited: Aug 10, 2004
  7. Aug 11, 2004 #6
    So what statement is true?.. i'm lost now
     
  8. Aug 11, 2004 #7

    arildno

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    You've got a "degenarate" case here:
    Two "sides" of length 1, one "side" with length 0; that is a straight line segment of length 1 traversed in opposite directions when going around your "triangle" (ending up on your starting point)
     
  9. Aug 11, 2004 #8
    this is getting confusing now =-/
     
  10. Aug 11, 2004 #9

    Math Is Hard

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    I think our triangle just collapses to line segment when n = 1, that's all.
    But correct me if I am wrong, arildno.
     
  11. Aug 11, 2004 #10

    arildno

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    That's what I meant, Math is hard ("degeneracy" is a word often used in similar cases).
     
  12. Aug 11, 2004 #11

    NSX

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    Negative numbers anyone?

    hehe
     
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