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  1. #31
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    Quote Originally Posted by RayG View Post

    Diameter Of A Circle-circle_poly_inside-jpg
    This is I believe the "correct" answer to the original question

    the hole and the space -- which is a virtual circular hole -- meet at a tangent
    the two radii form a chord
    regards from Alberta, Canada

    ian

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  3. #32
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    Quote Originally Posted by ian View Post
    This is I believe the "correct" answer to the original question

    the hole and the space -- which is a virtual circular hole -- meet at a tangent
    the two radii form a chord
    another smart a***... Ray, ueee, and Stuart, you have competition!!

  4. #33
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    Quote Originally Posted by Glenn.Visca View Post
    Wow ... Can you lads do tomorrow's tatts numbers too ?
    Nah we're not psychic, we just like maths. Mind you, how many times do you see the headline "Psychic wins lotto, again"

    Ew
    1915 17"x50" LeBlond heavy duty Lathe, 24" Queen city shaper, 1970's G Vernier FV.3.TO Universal Mill, 1958 Blohm HFS 6 surface grinder, 1942 Rivett 715 Lathe, 14"x40" Antrac Lathe, Startrite H225 Bandsaw, 1949 Hercus Camelback Drill press, 1947 Holbrook C10 Lathe.

  5. #34
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    Quote Originally Posted by Ueee View Post
    Nah we're not psychic, we just like maths. Mind you, how many times do you see the headline "Psychic wins lotto, again"

    Ew

    A few years ago there was review of Super Fund returns for a wide range of super funds.
    The funds with the highest returns were the Super Funds for employees of Super Funds (funny about that)
    The fund with the lowest return was the one for the horse racing industry.

  6. #35
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    Quote Originally Posted by ian View Post
    This is I believe the "correct" answer to the original question
    the hole and the space -- which is a virtual circular hole -- meet at a tangent
    the two radii form a chord
    It's also the solution that converges quickest to the "natural" solution of just dividing the circumference into 2n segments x h wide.

    Here is the third solution, which is the one Ueee and Stuart liked.

    Diameter Of A Circle-circle_solution_3-jpg

    So the three versions.. are

    D= h/sin(pi/2n) h=18mm n=16 holes D = 183.84 mm
    D= h/tan(pi/2n) h=18mm n=16 holes D = 182.76 mm
    D= 2h/sin(pi/n) h=18mm n=16 holes D = 184.53 mm

    D= 2hn/pi h=18mm n=16 holes D = 183.32 mm ( arc length version )


    since sin(pi/2n) converges on pi/2n for large values of n, likewise tan(pi/2n)=pi/2n, and sin(pi/n)=pi/n

    All end up with D=2hn/pi funny that..

    On tattslotto... my son reckons tattslotto is a TAX on people who are bad at maths.. doesn't stop me buying tickets though.

    Ray
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  7. #36
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    Oh ruddy hell!!!....... just when I thought you guys had it all sorted out as to why how when and which way is correct????

  8. #37
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    It just goes to show that there are more than one way to skin a cat... Or what ever you skin down there
    Best Regards:
    BaronJ.

  9. #38
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    Quote Originally Posted by BaronJ View Post
    It just goes to show that there are more than one way to skin a cat... Or what ever you skin down there
    could be all crap too BaronJ

    did you notice they, each method proposed, have different results...so I reckon all of them have the same idea as I...

  10. #39
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    Ueee and Stuart might like their solution, but I think it really only works for small values of n

    when n is moderately large I think RayG's 2nd option looks best -- and is the easiest to set out !

    although when the hole diameter is small and n gets very large there's no real difference between RayG's solution 1 and 2.


    There's a very simple explanation why that is so, would anyone care to say why?
    regards from Alberta, Canada

    ian

  11. #40
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    This might also come in handy for working out circle divisions and increments.

    http://www.blocklayer.com/circle-divider.aspx

    Might even add a second inner circle with option of smaller circles (holes) centered on the inner circle circumference increments?

  12. #41
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    Quote Originally Posted by ian View Post
    Ueee and Stuart might like their solution,
    Thats because its the only one that gives 18mm between the holes(though there is another)

    Quote Originally Posted by ian View Post
    but I think it really only works for small values of n
    How so?

    Quote Originally Posted by ian View Post
    and is the easiest to set out !
    how does that come into it? once your picked your answer the set out is the same.

    Quote Originally Posted by ian View Post
    although when the hole diameter is small and n gets very large there's no real difference between RayG's solution 1 and 2.


    There's a very simple explanation why that is so, would anyone care to say why?
    Sooner or later you end up with an "almost" straight line and(I think) all the while Rays solutions move closer to the U and S solution?

    Given its likely a critical application like form work for a birdbath I think we have it close enough to be "fit for purpose". Though I think I have another answer but the best my maths ability can do is say its "something less than 183.346mm"

    Stuart

    lots of "I think"s. its early and I'm in a hurry... its been fun

  13. #42
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    Quote Originally Posted by Stustoys View Post
    Though I think I have another answer but the best my maths ability can do is say its "something less than 183.346mm"
    Stuart
    Got a diagram?


    Ray

  14. #43
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    Quote Originally Posted by RayG View Post
    Got a diagram?
    No but I'll butcher one of yours.

    Now I'm not even 100% sure this isnt one of your methods.

    Take the OPs drawing to mean 18mm measured on the arch. So the first part is easy. 16*18= pretty much half the circumference. But how do you work out the length of the arch "through the hole" until you know the diameter? Its not an 18mm chord..... to top that off I've changed my mind, it has to be "something MORE than 183.346mm" lol

    Time for calculus?

    Perfection is a pita lol

    Stuart
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  15. #44
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    Hi Stuart,

    The arc length is just arc_length = radius * angle in radians

    So..

    angle = 2pi/2n --> angle = pi/n
    h = r * angle

    D = 2r = 2*h*n/pi for h=18, n=16 D = 183.32

    That's the one I called the "natural solution" earlier.. Of course, you could mix and match hole versus space methods...

    Ray

  16. #45
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    Hi Ray,

    I thought that might be the one... but the bit I'm not getting is.

    Any arch draw through the center of a circle has to be longer than the diameter of the circle.
    So the 16 spaces are 18mm. The 16 archs are "more than 18mm".
    So the diameter has to be more than 32*18/pi... doesn't it?

    Stuart

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