Plane (geometry): Difference between revisions
imported>Miguel Adérito Trigueira (Euclidian definition for the plain man) |
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In [[Euclidean geometry]]: | In [[Euclidean geometry]]: | ||
A '''plane''' is a [[surface (geometry)|surface]] on which a [[line (geometry)|line]] [[perpendicular (geometry)|perpendicular]] to a line which lies on that surface also falls entirely on the surface. It can be described by three [[point]]s which do not lie on the same line. A line is said to lie on a surface if its points fall on the surface. Surfaces can be [[parallel (geometry)]]. | A '''plane''' is a [[surface (geometry)|surface]] on which a [[line (geometry)|line]] [[perpendicular (geometry)|perpendicular]] to a line which lies on that surface also falls entirely on the surface. It can be described by three [[point]]s which do not lie on the same line. A line is said to lie on a surface if its points fall on the surface. Surfaces can be [[parallel (geometry)|parallel]]. | ||
To distinguish between a plane and a surface think of a surface as a piece of paper (with no thickness) that could be twisted, or rolled, or crumpled up. A plane would be like that sheet of paper lying perfectly flat on a table. | To distinguish between a plane and a surface think of a surface as a piece of paper (with no thickness) that could be twisted, or rolled, or crumpled up. A plane would be like that sheet of paper lying perfectly flat on a table. | ||
A surface is usually designated by the names of the points which fall on it. Thus the surface has on it point A, point B, and point C is called surface ABC. | A surface is usually designated by the names of the points which fall on it. Thus the surface has on it point A, point B, and point C is called surface ABC. | ||
Revision as of 10:12, 14 August 2008
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A plane is a surface such that any straight line linking any two points on the surface is part of the surface. A plane is made up of an infinite number of straight lines. At its simplest, a plane can be defined by a triangle whose vertices cannot be collinear.
In Euclidean geometry: A plane is a surface on which a line perpendicular to a line which lies on that surface also falls entirely on the surface. It can be described by three points which do not lie on the same line. A line is said to lie on a surface if its points fall on the surface. Surfaces can be parallel.
To distinguish between a plane and a surface think of a surface as a piece of paper (with no thickness) that could be twisted, or rolled, or crumpled up. A plane would be like that sheet of paper lying perfectly flat on a table.
A surface is usually designated by the names of the points which fall on it. Thus the surface has on it point A, point B, and point C is called surface ABC.