Point (geometry): Difference between revisions
imported>Boris Tsirelson (correction) |
imported>Boris Tsirelson (sets of points) |
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A point is made up of no other parts. | A point is made up of no other parts. | ||
The extremities of a [[line (geometry)|line]] segment are points. | The extremities of a [[line (geometry)|line]] segment are points. | ||
Geometric objects, such as lines, planes, line segments, triangles, circles, disks, spheres, balls, cubes etc., are often (but not always) treated as [[set]]s of points. | |||
In [[Euclidean geometry]]: | In [[Euclidean geometry]]: | ||
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Any [[plane (geometry)|plane]] can be completely defined by three distinct points that are not all part of the same [[line (geometry)|line]]. | Any [[plane (geometry)|plane]] can be completely defined by three distinct points that are not all part of the same [[line (geometry)|line]]. | ||
Any two [[line (geometry)|lines]] that lay on a single [[plane (geometry)|plane]] and are not [[parallel (geometry)|parallel]] (nor coincide) intersect at a single point. | Any two [[line (geometry)|lines]] that lay on a single [[plane (geometry)|plane]] and are not [[parallel (geometry)|parallel]] (nor coincide) intersect at a single point. | ||
Three | Three planes typically intersect at a single point (though in special cases their intersection can be [[empty set|empty]], a line, or a plane). | ||
Revision as of 22:50, 5 April 2010
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A point is a mathematical object in geometry which has a position but neither length nor breadth nor depth. A point is made up of no other parts. The extremities of a line segment are points. Geometric objects, such as lines, planes, line segments, triangles, circles, disks, spheres, balls, cubes etc., are often (but not always) treated as sets of points.
A line is made up of an infinite number of points. Any line can be completely defined by two distinct points. Any plane can be completely defined by three distinct points that are not all part of the same line. Any two lines that lay on a single plane and are not parallel (nor coincide) intersect at a single point. Three planes typically intersect at a single point (though in special cases their intersection can be empty, a line, or a plane).