![]() In particular, a line segment is not a line. Note that a part of a line is not a line. Any other definition is equally acceptable provided that it is equivalent to these. Three equivalent definitions of line are given below. They are criticized afterwards, see axiomatic approach. Still, the definitions given below are tentative. Fortunately, it is possible to define a line via more elementary notions, and this way is preferred in mathematics. Straight lines are treated by elementary geometry, but the notions of curves and curvature are not elementary, they need more advanced mathematics and more sophisticated definitions. However, this is not a good idea such definitions are useless in mathematics, since they cannot be used when proving theorems. It is tempting to define a line as a curve of zero curvature, where a curve is defined as a geometric object having length but no breadth or depth. To define a line is more complicated than it may seem. In other words, plane geometry is the theory of the two-dimensional Euclidean space, while solid geometry is the theory of the three-dimensional Euclidean space. Plane geometry (called also "planar geometry") is a part of solid geometry that restricts itself to a single plane ("the plane") treated as a geometric universe. Lines are treated both in plane geometry and in solid geometry. 2.1 What is wrong with the definitions given above?.1.1.6 Definition via Cartesian coordinates. ![]()
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