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Math Help - Rectangular Prisms

  1. #1
    Newbie
    Joined
    May 2006
    Posts
    5

    Rectangular Prisms

    / = Division
    = = Equals
    *= Multiplication

    Earlier in the year, we did Rectangular Prisms. First, we just counted the Faces, Vertices, and Edges. Of course, we did it with other objects, but I have a simple question about rectangular prisms.

    Now, while counting up all of these Faces, Vertices, and Edges, I came across a pattern!

    It seemed like the following equation kept showing up, no matter what the object looked like (as long as it was still a rectangular prism, of course):
    (V/2)*3=E
    and vise-versa, being
    (E/3)*2=V

    Some objects I drew up had the follwing results, which all seemed to follow my equation:
    Object 1
    (Basic Cube)
    F=6
    V=8
    E=12
    Object 2
    F=8
    V=12
    E=18
    Object 3
    F=12
    V=20
    E=30

    And there's the whole F+V=E+2 thing
    But does anybody know of any relationship from
    F->V or
    F->E

    It's nothering me, because I am just so curious about whether there is some connection there? Thanks in advance to any replies!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Yuripro84
    / = Division
    = = Equals
    *= Multiplication

    Earlier in the year, we did Rectangular Prisms. First, we just counted the Faces, Vertices, and Edges. Of course, we did it with other objects, but I have a simple question about rectangular prisms.

    Now, while counting up all of these Faces, Vertices, and Edges, I came across a pattern!

    It seemed like the following equation kept showing up, no matter what the object looked like (as long as it was still a rectangular prism, of course):
    (V/2)*3=E
    and vise-versa, being
    (E/3)*2=V

    Some objects I drew up had the follwing results, which all seemed to follow my equation:
    Object 1
    (Basic Cube)
    F=6
    V=8
    E=12
    Object 2
    F=8
    V=12
    E=18
    Object 3
    F=12
    V=20
    E=30

    And there's the whole F+V=E+2 thing
    But does anybody know of any relationship from
    F->V or
    F->E

    It's nothering me, because I am just so curious about whether there is some connection there? Thanks in advance to any replies!
    I will not go into any research or what. I will just rely on your findings here.
    So, let us say your findings are correct, then,

    (V/2)*3=E
    and vise-versa, being
    (E/3)*2=V

    Both of which simplify to
    3V = 2E ------------------(1)

    And,
    F+V = E+2 ---------------(2)

    You want to know the relation of F and V, or F and E.

    From the Equations (1) and (2) we can find these relations.

    For the F and V:
    EXpress the E in terms of V in Eq.(2).
    So, from (1),
    E = 3V/2
    Substitute that into (2),
    F +V = (3V/2) +2
    Blah, blah, blah...
    F = (V/2) +2 -----------------(3). There you are.

    Try getting the relation of F and E that way.
    You should get
    F = (E/3) +2 ---------------(4)

    That is it.
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  3. #3
    Newbie
    Joined
    May 2006
    Posts
    5
    Thanks man, those worked for all of my examples, I didn't think it was possible
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