A question about graphs
March 2, 2009 1:34 PM   Subscribe

On blank graph paper, what is the mathematically proper name for any random line you see on the page? It wouldn't be "coordinate" since that refers to the line's value. It wouldn't be "grid" since that refers to all of the visible lines. It wouldn't be "axis" since there can be only one in each direction. I'd also be cool with the name for all of the lines (as a set) that are parallel to one another. Thanks!
posted by crapmatic to Science & Nature (14 answers total) 1 user marked this as a favorite
The mathematically proper name for a line is "line" or "line segment" (if it's not infinite).
posted by mr_roboto at 1:43 PM on March 2, 2009 [1 favorite]

horizontal and vertical grid lines
posted by robotot at 1:50 PM on March 2, 2009

I guess you could call each horizontal and vertical line a locus: the vertical lines are loci satisfying X=N for some value N (regardless of where you imagine your coordinate origin to be), and the horizontal lines are loci satisfying Y=N for some value N.
posted by letourneau at 1:53 PM on March 2, 2009

I think we call it a grid or grid line (I work in educational publishing).
posted by fiercecupcake at 1:57 PM on March 2, 2009

I'm going to go with parallel. From the OED entry for grid:

"1. a. An arrangement of parallel bars with openings between them; a grating."

and then for parallel:

"2. Freq. in pl. More generally: a (usually straight) line that runs side by side with and equidistant from another. "

So you could describe a piece of graph paper as having red parallels on a white background, for example.
posted by jedicus at 1:58 PM on March 2, 2009

I'm not sure what you mean by "mathematically proper." I'm not sure there is a strictly mathematical term for them; after all, the x=5 line has no more significance, mathematically than the x=5.5 line, but if you're using integer values as the lines, one happens to appear on the paper and one does not. The printed lines are an aid to understanding but do not necessarily have any mathematical significance in and of themselves, so there's no "mathematical" term for them AFAIK.

Generally, I'd refer to it as a "grid line" which seems to meet all of your objections other than the "mathematically proper" one. Maybe if you gave us the context you're trying to use it in, that might help? (And the sets I'd just call "horizontal grid lines" and "vertical grid lines.")
posted by DevilsAdvocate at 2:01 PM on March 2, 2009 [1 favorite]

Sorry, "mathematically proper" was sloppy on my part. What I mean is a term that is formally appropriate. The responses so far are very helpful -- thanks!
posted by crapmatic at 2:07 PM on March 2, 2009

I would call the sets of parallel lines "longitudinal" and "transverse", where the longitudinal ones run parallel to the longer edge, and the transverse ones run parallel to the shorter edge.
posted by muddgirl at 2:26 PM on March 2, 2009

I'd also be cool with the name for all of the lines (as a set) that are parallel to one another.

A pencil of lines

(you can think of a set of lines that all intersect in a single point as looking kind of like a pencil point; a set of parallel lines can be viewed as intersecting "at infinity")
posted by leahwrenn at 2:26 PM on March 2, 2009

ok, a pencil of lines is not all the lines parallel to, say, the x-axis, but...the set of all such lines is the entire plane, right? because for each real number r, there is a corresponding horizontal line passing through y = r. But if you're talking about a particular (typically finite, but it's not part of the definition) collection of parallel lines, you could talk about a pencil and you wouldn't be wrong.

As a mathematician, if I needed to talk about the horizontal and vertical lines on a piece of graph paper, I would call them gridlines, like DevilsAdvocate mentioned.
posted by leahwrenn at 2:30 PM on March 2, 2009

Graphing software usually refers to them as "grid lines".
posted by halogen at 2:35 PM on March 2, 2009

I might say 'rulings', horizontal and vertical rulings.
posted by jamjam at 3:13 PM on March 2, 2009

Indeed, if the set of all lines is the grid, then each line is individually a grid line and the set of vertical or horizontal lines are the vertical grid lines and the horizontal grid lines. If you want to talk about the actual lines on a piece of paper, then rulings would be fine as well, but grid lines is more general.
posted by ssg at 6:56 PM on March 2, 2009

Mr. Roboto is correct.
posted by gjc at 7:46 PM on March 2, 2009

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