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In mathematics, the intersection of two or more objects is another, usually "smaller" object. All objects are presumed to lie in a certain common space except in set theory, where the intersection of arbitrary sets is defined. The intersection is one of basic concepts of geometry. Intuitively, the intersection of two or more objects is a new object that lies in each of original objects. An intersection can have various geometric shapes, but a point is the most common in a plane geometry.

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  • Intersection
  • 交點
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  • 交点是指线与线、线与面相交的点。在幾何學上(准确地说在欧几里德空间中),兩條直線如非平行,必存在交點。引申下去,一切事物相交接的時間或空間,都可被稱為交點。
  • In mathematics, the intersection of two or more objects is another, usually "smaller" object. All objects are presumed to lie in a certain common space except in set theory, where the intersection of arbitrary sets is defined. The intersection is one of basic concepts of geometry. Intuitively, the intersection of two or more objects is a new object that lies in each of original objects. An intersection can have various geometric shapes, but a point is the most common in a plane geometry.
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  • In mathematics, the intersection of two or more objects is another, usually "smaller" object. All objects are presumed to lie in a certain common space except in set theory, where the intersection of arbitrary sets is defined. The intersection is one of basic concepts of geometry. Intuitively, the intersection of two or more objects is a new object that lies in each of original objects. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Definitions vary in different contexts: set theory formalizes the idea that a smaller object lies in a larger object with inclusion, and the intersection of sets is formed of elements that belong to all intersecting sets. It is always defined, but may be empty. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of original objects. In this approach an intersection can be sometimes undefined, such as for parallel lines. In both cases the concept of intersection relies on logical conjunction. Algebraic geometry defines intersections in its own way with intersection theory.Euclidean geometry deals with the intersections of planar and solid shapes.
  • 交点是指线与线、线与面相交的点。在幾何學上(准确地说在欧几里德空间中),兩條直線如非平行,必存在交點。引申下去,一切事物相交接的時間或空間,都可被稱為交點。
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