# Thread: How wide is a line?

1. ## How wide is a line?

Okay, we're always told a line is just a line without width or volume, but theoretically speaking, every line is 1 unit of its measurement wide and full, like for example, a 10 meter line is 1 meter wide and full, because and .
Does this make sense or am I just confused again?

2. A line has length but no volume, but a the symbol of a line can weigh a up to 5 pounds and taste like strawberries.

3. Originally Posted by LordLatch
A line has length but no volume, but a the symbol of a line can weigh a up to 5 pounds and taste like strawberries.
Correct, as far as I can remember 9th grade geometry--the concept of a "line" defines an object whose size could be measured using only one spatial dimension, except I was taught that a "line" by definition has an infinite length. (A "line segment" has a measurable, finite length but no measurable width or depth, and a "ray" is infinitely long but has one defined start/end point which can be plotted on an X/Y grid.)

So, "the width of a line is 0 of the units used to measure its length" would be closer to accurate than "1 unit of its measurement", although 0 doesn't quite seem right, either. (The answer would be more like "the same kind of answer you get if you divide something by zero".)

4. i answered a question incorrectly in a high school maths test when i replied "the answer depends on the width of the dividing line". the question was how many points of division does a circle have to be divided in half. apparently the correct answer was infinite.

5. More specifically, a line has no area nor no volume.

Likewise a point has no length, area, volume or other dimension.

6. Originally Posted by Utisz
More specifically, a line has no area nor no volume.

Likewise a point has no length, area, volume or other dimension.
then they could not exist except theoretically, and would therefore be better expressed as the result of the subtraction of at least one division of infinite from infinite. i.e. the containing boundaries of two or more objects

or something like that

7. Originally Posted by Sol4rplexus
Okay, we're always told a line is just a line without width or volume, but theoretically speaking, every line is 1 unit of its measurement wide and full, like for example, a 10 meter line is 1 meter wide and full, because and .
Does this make sense or am I just confused again?
Yeah. You're confused. Where did you come up with the idea a line was the the width of it's unit of measure?

It's not just wrong, it's flawed.

It's wrong because lines have no width, as others have addressed. By definition they have no width. Consequently, it's curious that you've come up with this idea that they not only have a width, but that they have the width you've suggested.

It's flawed because the method you use to measure the width is internally arbitrary. Under your system, if I measure my line in inches, and I measure off 12 inches, then I'd have 12 square inches. But if I note that I could measure that same distance using feet, then I'd end up with 1 square foot. But one square foot is 144 square inches, so now my measurement is exactly 144 square inches, and simultaneously 12 square inches.

The flaw in your reasoning is adding area and volume to lines in the first place. They don't have those measure. They don't exist in those terms. If you must have a width to your line, conceptually, the go with the real width: lines are one point wide. They are made up of infinitely many colinear points, and are one point wide, one point tall.

Points have no length, width or height, only position.

Length is the measure between two points. Measure has no dimensions beyond itself. Distance has no width or height, though height and width are measures of distance. Your measuring device may have width. Likewise, the mark you make to indicate a line has width, but the line itself, is dimensionless in that direction.

Area is tallying the space between lines in a single plane. Surface area is the area that you would have if the surface were a single plane.

Volume is the measure of space between defined edges in 3-dimensional space--provided that the three dimensions are measure height, width and depth. If your three dimensions are timbre, tone, and duration, then volume isn't the right measure--it doesn't even have the same meaning in the context where those are measured dimensions (sound).

8. Lines are concepts, not actual physical things that inhabit our three dimensional world. That's what tripped you up.

9. All of math is about useful abstractions, as I see it. The width of a line as zero is one such abstraction.

10. Originally Posted by mhc
ti.e. the containing boundaries of two or more objects

or something like that
Actually, yeah, it's probably more helpful to think of points, lines, and planes as boundaries between objects rather than types of objects.

A point has exactly one definite value relative to any imaginable number of axes. A line has a sequential range of definite values relative to two or more axes. A plane has two sequential ranges of definite values relative to three or more axes.

A "point" basically describes the boundary between a line segment and something else--either between Line Segment A and Line Segment B, or between Line Segment A and empty space. If it's a horizontal line segment ending at the point [x=5, y=5] on a two-dimensional grid, then anything at [x=6, y=5] would clearly be part of that line segment, while anything located at [x=4, y=5] or even [x=4.9, y=5], not to mention anything at [x=5, y=6] and so forth, would not be part of the same line segment by definition. You're describing the exact point in space where Line Segment A ceases to exist.

If the point has height, width, or depth, then it can't serve its function properly--is the space occupied by the point itself part of Line Segment A, or not? If you have to say "maybe" or "I don't know" then you're failing to do what you set out to do by locating a point--that being to determine exactly where two-dimensional space stops being a part of Line Segment A and becomes something else. Ergo, points by definition cannot occupy any space, and accordingly have no spatial dimensions--they are, in effect, infinitely small.

A line basically does the same thing for planes (or "plane segments", I guess, but I can't remember whether that's an actual math term or not) in a 3-dimensional space. Anything "up" the X, Y, or Z axis from the line is Plane A, while anything "down" the same axis from the line is not Plane A.

To simplify my convoluted mess of an explanation here, just think of how line segments are formed by the intersection of multiple sides of a polyhedron--the line segment is a description of the range of points at which going any distance in one direction places you within a certain two-dimensional shape but going any distance in any other direction would place you outside of that two-dimensional shape. "Maybe" and "I don't know" aren't acceptable answers--where, exactly the fuck, does this transition occur?

Logically, the line/line segment can only occupy space in exactly one dimension--otherwise it's not possible for it to serve its function as a boundary.

[SIDE NOTE: It's probably clear by this point that I'm not a math teacher--I've just been binge-reading a Neal Stephenson novel where people talk about geometry a lot. LOL.]

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