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Math Help - reverse solving of formula

  1. #1
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    reverse solving of formula

    Hi folks. I am trying to draw a regular hexagon given a diameter (being the diameter of a circle drawn around the hexagon).

    I basically have this formula where a = the length along the 6 sides of the hexagon:

    d = a + 2 * cos60 * a (this is right, right?)

    So what I am trying to figure out is how to solve for a. I got this far but my old brain is having a hard time with it:

    d - a - 2 * cos60 * a = 0,
    d - 2 * cos60 * a = a,

    now I think I am supposed to divide the left side by a again but that wouldn't make sense since then I am also dividing the right side by a which would give me 1. Thanks for any pointers.

    J
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  2. #2
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    like a dork I just realized cos60 = 0.5. I'll give that another go now.
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  3. #3
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    could it really be that simple?

    d = a + 2 * cos60 * a,
    d = a + 2 * 0.5 * a,
    d = 2a,
    d / 2 = a

    No way!!! Is this right? Can someone confirm this because it seems to good to be true. Maybe Occham's Razor is right.
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  4. #4
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    Quote Originally Posted by jwopitz View Post
    could it really be that simple?

    d = a + 2 * cos60 * a,
    No, this is NOT right. Where did you get it?

    d = a + 2 * 0.5 * a,
    d = 2a,
    d / 2 = a

    No way!!! Is this right? Can someone confirm this because it seems to good to be true. Maybe Occham's Razor is right.
    No, that's not right. The correct answer is even simpler: Drawing lines from the vertices of the hexagon to the center divides it into 6 equilateral triangles: d= a. That's a well known property or a regular hexagon.
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  5. #5
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    I got the formula d = a + 2 * cos60 * a by saying that a regular hexagon has 6 sides whose lengths are = a. If you bisect the hexagon with a line you are left with a trapezoid where the longer side is = d and the 3 other sides are = a. The two acute angles are 60 each and the two obtuse angles are 120 each. This yields the above formula.

    I am a bit confused by your response as I came to the same conclusion regarding the 6 equilateral triangles however you contradict your own statement by say d = a. Drawing straight lines through the opposite vertices of the hexagon would yield two sides of two triangles to be parallel and continuous. Given that 2r = d for circles then 2a = d for a hexagon. Maybe it was a typo.

    Doing some simple checking on my original formula, it indeed works along with the d = 2a formula. Just a round about way of getting to the same solution. Thanks for the help.
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