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Math Help - Algebra

  1. #1
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    Exclamation Algebra

    1.Use Gauss Theorem to prove that an angle of 20 degree is not contructible.

    2.Use Gauss Theorem to decide whether or not an angle of 6 degree is constructible.


    Thanks very much guys.....
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by suedenation
    [COLOR=Green]1.Use Gauss Theorem to prove that an angle of 20 degree is not contructible.
    Gauss theorem states that an n-gon is constructible \mbox{iff} n=2^k.p_1,\dots, p_r,
    where k \in \mathbb{Z_+} and p_1,\dots, p_r are distinct Fermat primes (note r can be 0).

    If an angle of 20 degrees were constructible so would a 360/20=18 sided
    polygon.

    The first three Fermat primes are 3,\ 5,\ 17, clearly 5 and 17
    do not divide 18, so for the 18-gon to be constructible
    18 would have to be a power of 2, or 6 (as it is 18/3) would
    have to be a power of 2. They are not so the 18-gon is not
    constructible and so an angle of 20 degrees is not constructible.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by suedenation
    or not an angle of 6 degree is constructible
    The 6 degree angle is constructible \mbox{iff}
    the 360/6=60 sided polygon is constructible.

    60=4.3.5=2^2.3.5

    so the 60-gon is constructible and so the 6 degree
    angle is constructible.

    RonL
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