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Thread: Octagon math

  1. #1
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    Octagon math

    Had a friend ask me if there was a formula for calculating the length of a side of a 4" octagon- (4" side to side, not point to point).

    Told him I didn't know but I would draw it in my CAD program and that would get him close enough. So I sent him this drawing but now I'M wondering if there is a way to calculate it. I used to be pretty good with geometry but that is now a fer piece back.

    Anybody know? (I fear it's going to be simple and I'll have a DOH! moment)

    Octagon.jpg
    Attached Files Attached Files
    Last edited by Dave Zellers; 10-30-2020 at 9:27 PM.

  2. #2
    Take the diameter of the circle that the octagon is inscribed in and multiply it by 0.383. That's the length of each side. If you start with the length of a side just work the equation backwards to find the diameter.

    The more interesting one is the hexagon because each side is equal to the radius.

    Mike
    Last edited by Mike Henderson; 10-30-2020 at 10:29 PM.
    Go into the world and do well. But more importantly, go into the world and do good.

  3. #3
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    Like most math questions these days there's an on-line calculator for that. For example: https://www.calculatorsoup.com/calcu...ne/polygon.php
    Set to calculate everything for a given inradius, units=inches, set inradius=2, sides=8, pick the number of significant figures. Click Calculate.

    The math isn't all that hard but the calculator is quick (and fun to play with)

    JKJ

  4. #4
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    Quote Originally Posted by John K Jordan View Post
    Like most math questions these days there's an on-line calculator for that.
    JKJ
    Yes- Thanks! I couldn't get it out of my head and I found this one-

    https://www.omnicalculator.com/math/octagon

    Great stuff.

  5. #5
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    Quote Originally Posted by Mike Henderson View Post
    Take the diameter of the circle that the octagon is inscribed in and multiply it by 0.383. That's the length of each side. If you start with the length of a side just work the equation backwards to find the diameter.
    DANG man, talk about nailing the answer to the question! Very cool. The second part about hexagons is absolutely cooler.

    I love geometry. Thanks!

  6. #6
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  7. #7
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    Quote Originally Posted by Bill Dufour View Post
    Very cool site- thanks! Wow- the stuff that is out there...

  8. #8
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    For Algerba students and parents I recommend.

    https://www.purplemath.com/

  9. #9
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    Well, it's pretty simple. If it's 4" across, it's 2" center to side. There are 8 sides, so the included angle of a wedge that includes one side is 360o / 8 = 45o. So, half of a wedge is right triangle with one side 2" and adjacent angle of 22.5o (half the included angle). The side's length is thus 2 * 2" * sin(22.5).

  10. #10
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    x 0.4142 Gets you pretty close. ( that's the 4" side to side measurement x 0.4142)
    Last edited by Mark Hennebury; 11-04-2020 at 11:59 AM.

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