Incidence (geometry)

（重定向自Incidence axiom）

In geometry, an incidence relation is a binary relation between different types of objects that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, $P$ , and a line, $l$ , sometimes denoted $P I l$ . If $P I l$ the pair $(P, l)$ is called a flag. There are many expressions used in common language to describe incidence (for example, a line passes through a point, a point lies in a plane, etc.) but the term "incidence" is preferred because it does not have the additional connotations that these other terms have, and it can be used in a symmetric manner, reflecting this property of the relation. Statements such as "line $l 1$ intersects line $l 2$ " are also statements about incidence relations, but in this case, it is because this is a shorthand way of saying that "there exists a point $P$ that is incident with both line $l 1$ and line $l 2$ ". When one type of object can be thought of as a set of the other type of object (viz., a plane is a set of points) then an incidence relation may be viewed as containment.

词汇	Incidence axiom
分类	英语词汇英语翻译词典
释义	Incidence axiom 英语百科 Incidence (geometry) （重定向自Incidence axiom） In geometry, an incidence relation is a binary relation between different types of objects that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, $P$ , and a line, $l$ , sometimes denoted $P I l$ . If $P I l$ the pair $(P, l)$ is called a flag. There are many expressions used in common language to describe incidence (for example, a line passes through a point, a point lies in a plane, etc.) but the term "incidence" is preferred because it does not have the additional connotations that these other terms have, and it can be used in a symmetric manner, reflecting this property of the relation. Statements such as "line $l 1$ intersects line $l 2$ " are also statements about incidence relations, but in this case, it is because this is a shorthand way of saying that "there exists a point $P$ that is incident with both line $l 1$ and line $l 2$ ". When one type of object can be thought of as a set of the other type of object (viz., a plane is a set of points) then an incidence relation may be viewed as containment.
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