Dimension is a characteristic of all geometric regions, objects, and spaces. The previous sections have probably already made you aware of the concept of dimension. It is roughly the number of directions in which a region or object can be measured. More formally, it is the number of lines required to span a region in space. Examples make dimension much easier to understand.
A point is zero-dimensional. It has no length, width, thickness, or any other physical means of measurement. It only exists as a symbol to identify a single location in space.
A line is one-dimensional. It has the dimension of length. To put it another way, there is only one way that you can move along a line: lengthwise. In a similar vein, there is no way to move within a point. A point is a single location in itself, whereas a line is a collection of points, or locations.
A plane is two-dimensional. It has length and width. (Technically speaking, the property of width is really only length in a different direction). You can move along a plane in two directions, lengthwise and widthwise. You might think that you can actually move along a plane in an infinite number of directions, but actually every direction in which you move can be broken down into a component of length and a component of width.
It should now be easier to understand the more formal definition of dimension:
the number of lines required to span a region in space:
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