Math Puzzle: calculating the dimensions of variable rectangles in a fixed square - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T13:24:02Z http://mathoverflow.net/feeds/question/35620 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/35620/math-puzzle-calculating-the-dimensions-of-variable-rectangles-in-a-fixed-square Math Puzzle: calculating the dimensions of variable rectangles in a fixed square Peter K 2010-08-15T02:27:19Z 2010-08-15T05:10:58Z <p>I've got the following problem, </p> <p>I've got a fixed size square and within there are a fixed number of rectangles to be contained within it. I want the rectangles to cover the maximum amount of space within the square. The size of the rectangles is determined by a weighting. The higher the value of an individual weight of a rectangle, the bigger its surface area. </p> <p>Assuming I have a predetermined weighting for all 9 rectangles, how do I derive at the coordinates (for their position in the square) and their dimensions (width and length).</p> <p>this has had me puzzled, hope someone can help me out...thanks!!</p> http://mathoverflow.net/questions/35620/math-puzzle-calculating-the-dimensions-of-variable-rectangles-in-a-fixed-square/35635#35635 Answer by Gerhard Paseman for Math Puzzle: calculating the dimensions of variable rectangles in a fixed square Gerhard Paseman 2010-08-15T05:10:58Z 2010-08-15T05:10:58Z <p>With no more constraints than this, a simple tiling arises by making all the lengths the same as the side of the square, and the widths proportional to the weights. </p> <p>In other cases, there are existing algorithms (for example, cUtting board out of logs) that employ such heuristics. Care to tell us more?</p> <p>Gerhard "Ask Me About System Design" Paseman, 2010.08.14</p>