Recent content by GroupTheory1

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    Triangle Approximation Derivation

    Almost but not quite. I cannot figure out where the sin^2(B) factor comes from.
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    Triangle Approximation Derivation

    The law of cosines says that b^2 - a^2 = c^2 - 2ac * cos(B), so, b - a = -2ac * cos(B) / (b+a) + c^2 / (b+a). If one says that a ~ b because c << a, then the above becomes b - a ~ -c * cos(B) + c^2 / (2a), which is close but does not match and is way off for B approaching zero...
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    Triangle Approximation Derivation

    Homework Statement Here is a drawing with all the needed variables: http://i.imgur.com/192GI.jpgHomework Equations The Attempt at a Solution I have been trying to figure out how this approximation is derived for some time now and have no progress to show for it. Any help in figuring out the...
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    Element Orders For Group Of Order 30

    Thanks for helping me think through this!
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    Element Orders For Group Of Order 30

    True. I should have said that there are at least two elements of order 15 (there are eight actually). Now, does that mean that every group of order 30 will have at least eight elements of order 15? I think it does, since the group of order 15 is cyclic -- not so sure if that order is preserved...
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    Element Orders For Group Of Order 30

    Homework Statement Given a a group of order 30 w/ a non-normal Sylow 5-subgroup, the problem is to count the number of elements of orders 5, 3, 2, and 1. Homework Equations The Attempt at a Solution I understand the Sylow theorems and can use them to show that there must be 24...