Does a line have 1 dimension or 2? Explanation….

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If you create a line in say CorelDraw you need to give the line a height e.g thickness. Does this mean a line must therefore have 2 dimensions?

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We say that a line has one dimension.

A line only has one dimension in its pure, mathematical form. Since we use mathematics to define what a line is in the first place, this means that it is the quintessential one-dimensional object. However, practically speaking, lines have two dimensions whenever we draw them.

You can think of it this way. We all know what a circle is. The defining characteristic of a circle is that it is perfectly, absolutely round. But if you draw a circle on a piece of paper, it will never be perfectly round. In fact, if you use a computer to draw it, it won’t be perfectly round either, because there are only so many pixels and on super-zoom it will look pixelated instead of like the smooth curve of our theoretical circles. Besides, the atoms that make up the line you’ve drawn are not in perfect curves.

These mathematical objects are therefore never realized as perfectly in the real world as they are in our equations and our minds. So a line is a one-dimensional object… but every time you draw one, it has two dimensions.

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13 comments

  1. It depends how thick the line is. If the line is a chain of atoms, only one atom thick, then it would only have one dimension.

  2. In math, a traditional straight line has one dimension. If you have a curved or thick line I suppose it would be two.

  3. Mathematically a line is one dimensional, and has a thickness of zero. Since it’s impossible to see something that thin, CorelDraw adds thickness to make it a visible 2D object.

  4. the theoretical definition of a line a 1 dimentional…however, to make it visible, as is the case with CorelDraw, you have to give it some semblance of width, thereby making it 2D.

  5. i dont know what CorelDraw is..but if you mean any line in general..i’m pretty sure its only 1 dimensional..i think its flat shapes that are 2 dimensional ^^

  6. yes. think about it. draw a line on a piece of paper with a marker. the line has width (the size if the marker tip) and length (however long you drew it) good luck!

  7. A line has 1 dimension because there is only 1 possible direction that points can be found.

    A dot has zero dimensions. There are zero directions that points can be found. Similarly, a plane has 2 dimensions, a cube has 3 dimensions, and a living world has 4 dimensions (3 + time).

  8. Good question.

    The answer is… yes and then again … no.

    In practice- yes, in theory – no

    In the same way a ‘point’ (or in this case a pixel) ideally has 0 dimensions an ideal ‘line’ has only 1. However when we try and represent either of these things graphically the result has a finite height and length, albeit in incredibly small units so ends up being a 2 dimensional object.

    So in answer a line has only 1 dimension but we can only represent it by using 2.

    Umm I hope that makes sense!

    Alex

    By the way here’s a quote from Euclid who wrote about this in 300BC and whose work is still valid (and taught) today.

    “1. A point is that of which there is no part.
    2. And a line is a length without breadth.
    3. And the extremities of a line are points.
    4. A straight-line is (any) one which lies evenly with points on itself.
    5. And a surface is that which has length and breadth only.”

    Euclid – Elements Book 1

  9. In mathemetics, a line is defined as having no thickness. So it takes one coordinate to specifiy any point on the line–one dimension.

    Any real line will have thickness. And even thickness on the paper. Most everything in the real world is three dimensional.

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