Results 1 to 2 of 2

Math Help - maximum number of circles in a rectangle?

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    4

    maximum number of circles in a rectangle?

    I just posted this in the geometry section before realizing this is probably a better fit...

    I'm putting together a project where we're buying some rather expensive plastic sheets and making circles out of it.

    We need to make roughly 18" diameter circles (actually, because of the router width and some errors, it works out to 18 1/4" or 18.125" per circle).

    We've got a few choices of width/length sheets. I'm not sure how many we can get per sheet, obviously the more the merrier.

    I know there's packing theories out there, etc, but haven't been able to adapt any of them for our purpose. I tried hexagonal packing etc, but have been failing miserably.

    I was told the most we can squeeze on a 48" x 120" sheet is 14 circles, I'm pretty sure that's correct. If we only needed 18" we may be able to fit 17 circles, but, that little bit makes a big difference.

    The other two sizes we can choose from are 60" x 120" and 96" x 240" (the bigger the sheet, the more expensive obviously).

    Can anyone point me in the direction of an algorithm or something to calculate the number of circles we can fit? I've searched for a program online and found nothing...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2012
    From
    Uzbekistan
    Posts
    1

    Re: maximum number of circles in a rectangle?

    Quote Originally Posted by barwick11 View Post
    I was told the most we can squeeze on a 48" x 120" sheet is 14 circles, I'm pretty sure that's correct. If we only needed 18" we may be able to fit 17 circles, but, that little bit makes a big difference.
    48" x 120" sheet can fit 16 18'' diameter or 15 18 1/4'' diameter circles at least.
    maximum number of circles in a rectangle?-bx.jpg
    Attached Thumbnails Attached Thumbnails maximum number of circles in a rectangle?-bx.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximum area of rectangle
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 10th 2010, 06:38 AM
  2. Arrangement of circles in a rectangle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 29th 2009, 11:55 PM
  3. Finding maximum volume of a rectangle
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 19th 2009, 05:21 PM
  4. Surrounding circles with rectangle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 16th 2009, 12:06 PM
  5. Maximum Area of a Rectangle
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 4th 2008, 11:06 PM

Search Tags


/mathhelpforum @mathhelpforum