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How can I algebraically divide a length into equal segments while considering the width of the borders?
There are a lot of dimensions that I want to split into
equal length
parts, usually into three parts, and I want to have
equal length
empty space between the segments. However, increasing the length of the space that they take up is not an option, so borders between the segments must subtract from the value of the original length. Since the borders have width, it's not as simple as dividing by 3 to get the length of each segment. Lengths must be in integers, rounding is fine, and the center segment is allowed to be a single unit longer than the rest. Ideally, the border length is
<
10% of the segment length. Looking specifically for an expression, to completely avoid sketching any diagrams.
Correction: "the length is less than OR EQUAL TO 10% of the segment length"
1 Answer
- ?Lv 74 days agoFavorite Answer
If you'ret into n segment lengths, then if you need to allow borders on BOTH ends of each segment, including the ones at the ends, you'll need to allow for n+1 border widths in addition to the n segment lengths. Treating as variables the segment length S and border width W, we derive the expression
nS + (n+1)W
as the original length you're subdividing. You can choose values of W and S according to the particular situation.
If you only need borders between the segments rather than at the beginning and ending--as in the case of using a saw to cut up a board, then replace the n+1 with an n-1 to account for dropping two end borders.
