Results 1 to 5 of 5

Math Help - Filling an area

  1. #1
    Newbie
    Joined
    May 2014
    From
    United States
    Posts
    3

    Filling an area

    I'm trying to fill an area with objects, but I can't seem to wrap my brain around the problem well enough to find a solution. Here is the problem:

    I need to fill a trapezoidal area with rows of rectangular objects, laid end-to-end lengthwise. The rows need to be separated by a distance "D". If the rectangular objects have a length "L" and a width "W", and I need to use exactly "N" number of objects, how do I determine the maximum distance "D" to space the rows out?

    Thanks in advance.
    Last edited by Kaldric; May 30th 2014 at 02:43 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,791
    Thanks
    693

    Re: Filling an area

    You need more information, like the height of the trapezoid and the length of the bases. Is the height h and the bases b_1,b_2?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2014
    From
    United States
    Posts
    3

    Re: Filling an area

    I have measurements of all parts, but I want to keep the formula generic because I actually have two trapezoids to fill. For now, I just want to use h, b1 and b2 for the basic dimensions of the trapezoid.

    I'm pretty sure that gives me enough information to solve the problem, but I could be wrong.
    Last edited by Kaldric; May 30th 2014 at 04:15 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,791
    Thanks
    693

    Re: Filling an area

    \dfrac{h}{W+D} gives the number of rows you will have. Assuming b_1 is the longer base and b_2 is the shorter one, then the maximum number of rectangles you can have in a single row is given by \left\lfloor \dfrac{\dfrac{h-W}{h}b_1 + \dfrac{W}{h}b_2}{L} \right\rfloor. If N is less than that, then D = h-W. If N is greater than that, then you need another row. Assuming all rows have equal spacing, then place the second row so that a third row will not fit, but maximizes the space between itself and the first row already placed. Keep going until all rectangles are placed.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2014
    From
    United States
    Posts
    3

    Re: Filling an area

    I don't think that's quite what I'm looking for. It might help if I introduce another variable. Let's call the number of rows "R". Now D=(h-R*W)/(R-1), where R-1 represents the number of spaces.

    Does that make sense?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Filling an array
    Posted in the Math Challenge Problems Forum
    Replies: 2
    Last Post: August 27th 2013, 05:52 AM
  2. Pipe Filling
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 28th 2011, 09:03 AM
  3. Space Filling Curves
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: August 11th 2010, 07:28 AM
  4. help filling this table!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 24th 2010, 08:03 AM
  5. Filling in table
    Posted in the Algebra Forum
    Replies: 16
    Last Post: October 5th 2009, 11:57 AM

Search Tags


/mathhelpforum @mathhelpforum