What is the relationship between lines and shapes?

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What a great question. The best place to start is to give a definition of a line. The simplest defintion of a line, according to geometry is: a line is defined by two points. Actually a line is more complicated than that, because there can be many points in a line.

A shape is much harder to define, because they are so many different shapes. Some of these shapes are easier to define, like a circle. For instance, a circle has uniform radius from a center point. Other shapes are very irregular and very difficult to define. For example, how do you define a lightning bolt? A good definition for shape, according to gemoetry is: a shape has two or more point, a line being the simplest.

In light of these points, a line is the most basic shape, but shapes can be extremely complex. Several lines can create shapes, such as a square or a triangle. From this perspective, shapes can be seen a the amalgamation of many lines.

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