![]() ![]() How many lines do you see in Figure 1? The answer takes us into a mixture of philosophy and geometry. Cartesian plane illustrating many different lines. In this page the "line" is described in the context of Cartesian geometry in exactly two dimensions. If you draw a "line" on a piece of paper and then crumple the paper, what does this do to the line? The word "point" has been mentioned but not defined. ![]() The minimum possible distance between New York City and Rome follows the curvature of the earth. After all every point on the surface of the earth is always moving.Ī line is the locus of a point that moves from one fixed point to a second fixed point so that the distance traveled is the minimum possible. Some wit might argue that there is no such thing as a fixed point. In astronomy the shortest possible distance between two fixed points might be curved. ![]() This "line" could not be seen under the most powerful microscope.Ī line is the shortest possible distance between two fixed points. It might be better to say that a definition may not be possible (or adequate.)Ī line has length but no breadth. The concept of "line" in geometry is so basic that a definition may not be necessary. "That horse is descended from a great line of thoroughbreds." or The word "line" is open to many different interpretations, as in: ![]()
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