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Math Help - points on a circle...

  1. #1
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    points on a circle...

    ok so here is the question...

    ok so there are 5 points on a circle, and if two points form a segment, how many segments are there. what is the number of line segments.

    this seemed straight forward, i chose my answer to be 7. i made a circle and connected the points careful not to double back, my book says the answer is 10? where did i go wrong?
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  2. #2
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    Re: points on a circle...

    Just list them. Points A, B, C, D, E

    AB, AC, AD, AE - 4
    BC, BD, BE - 7
    CD, CE - 9
    DE - 10

    I'm not sure what it was you were trying to draw.
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  3. #3
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    Re: points on a circle...

    and you know what there is a pattern. ok the problem said there were 5 points. ok so if i subtract 1 from 5 and then add 4+3+2+1 i get the answer? i thought it was a fluke, but then i tried it on another problem and it worked? can you tell me why this is true? whats actually going on here?
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  4. #4
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    Re: points on a circle...

    When was your last trip through Mathematical Induction?
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  5. #5
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    Re: points on a circle...

    gulps-its been a while. my math is a little rusty, yes i know.
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  6. #6
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    Re: points on a circle...

    Quote Originally Posted by slapmaxwell1 View Post
    ok so here is the question...

    ok so there are 5 points on a circle, and if two points form a segment, how many segments are there. what is the number of line segments.

    this seemed straight forward, i chose my answer to be 7. i made a circle and connected the points careful not to double back, my book says the answer is 10? where did i go wrong?
    If you have done elementary combinatorics then {5 \choose 2}=10 should do it.
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  7. #7
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    Re: points on a circle...

    Quote Originally Posted by slapmaxwell1 View Post
    gulps-its been a while. my math is a little rusty, yes i know.
    OK, without any advanced math technics:

    If you have n points than you can draw (n - 1) segments connecting each point with every other point. That means you have

    n \cdot (n-1) segments.

    Since you have drawn every segment twice you have to divide by 2 to get the correct result:

    (n := number of points; s := number of segments)

    s = \dfrac{n \cdot (n-1)}2
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  8. #8
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    Re: points on a circle...

    thanks again....

    Quote Originally Posted by earboth View Post
    OK, without any advanced math technics:

    If you have n points than you can draw (n - 1) segments connecting each point with every other point. That means you have

    n \cdot (n-1) segments.

    Since you have drawn every segment twice you have to divide by 2 to get the correct result:

    (n := number of points; s := number of segments)

    s = \dfrac{n \cdot (n-1)}2
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