잔글 (→결합구조) |
잔글 (→결합구조) |
||
| 15번째 줄: | 15번째 줄: | ||
a '''incidence structure''', or a '''geometric structure'''. If <math>\mathscr P</math> and <math>\mathscr L</math> are finite sets, we call <math>\sigma</math> a '''finite incidence structure'''. | a '''incidence structure''', or a '''geometric structure'''. If <math>\mathscr P</math> and <math>\mathscr L</math> are finite sets, we call <math>\sigma</math> a '''finite incidence structure'''. | ||
For given <math>p, q\in\mathscr P</math>, if <math>\exists L \in \mathscr L \text{ s.t. } (p,L),(q,L)\in \mathscr I</math>, we say '''<math>p</math> and <math>q</math> are jointed''', and we say '''<math>L</math> is decided by <math>p</math> and <math>q</math>''' if there is only one line <math>L</math>(we call it the '''join''' <math>pq:=L</math>.) Similarly, given <math>L, M\in \mathscr L</math>, if <math>\exists p \in \mathscr P \text{ s.t. } (p,L),(p,M)\in \mathscr I</math>, we say '''<math>L</math> and <math>M</math> meet''', and we say '''<math>p</math> is decided by <math>L</math> and <math>M</math>''' if there is only one point <math>p</math>(we call it the '''intersection''' <math>p:=L\cap M</math>.) | For given <math>p, q\in\mathscr P</math>, if <math>\exists L \in \mathscr L \text{ s.t. } (p,L),(q,L)\in \mathscr I</math>, we say '''<math>p</math> and <math>q</math> are jointed''', and we say '''<math>L</math> is decided by <math>p</math> and <math>q</math>''' if there is only one line <math>L</math>(we call it the '''join''' <math>pq:=L</math>.) Similarly, given <math>L, M\in \mathscr L</math>, if <math>\exists p \in \mathscr P \text{ s.t. } (p,L),(p,M)\in \mathscr I</math>, we say '''<math>L</math> and <math>M</math> meet''', and we say '''<math>p</math> is decided by <math>L</math> and <math>M</math>''' if there is only one point <math>p</math>(we call it the '''intersection''' <math>p:=L\cap M</math>.) And also denote <math>[p(\in\mathscr P)\in L (\in \mathscr L)] := [(p, L) \in \mathscr I]</math> and omit <math>\mathscr I</math>. | ||
== 평면 == | |||
We shall call incidence structures <math>\pi=(\mathscr P , \mathscr I)</math> satisfying following axioms '''planes''': | |||
* <math>\forall p, q \in\mathscr P \exists ! L \in \mathscr L \text{ s.t. }p, q\in L,</math> | |||
* <math>\forall L\in\mathscr L \exists p, q\in\mathscr P (p \ne q) \text{ s.t. } p, q \in L.</math> | |||
= 뉴턴의 운동 법칙 = | = 뉴턴의 운동 법칙 = | ||
2015년 7월 12일 (일) 22:34 판
인터위키 테스트
사영기하학
사영기하학(射影幾何學, projective geometry)은 사영변환에 대해 보존되는 성질을 연구하는 매우 추상적인 기하학이다.
결합기하학
결합기하학(incidence geometry)은 결합구조를 연구하는 학문이다. 해석기하학과 달리 점, 선, 그리고 그 결합만을 생각한다.
결합구조
Let [math]\displaystyle{ \mathscr P }[/math], [math]\displaystyle{ \mathscr L }[/math]([math]\displaystyle{ \mathscr P \cap \mathscr L = \emptyset }[/math]) and [math]\displaystyle{ \mathscr I\subseteq \mathscr P \times \mathscr L }[/math] be sets, we call
- [math]\displaystyle{ \sigma = (\mathscr P, \mathscr L, \mathscr I) }[/math]
a incidence structure, or a geometric structure. If [math]\displaystyle{ \mathscr P }[/math] and [math]\displaystyle{ \mathscr L }[/math] are finite sets, we call [math]\displaystyle{ \sigma }[/math] a finite incidence structure.
For given [math]\displaystyle{ p, q\in\mathscr P }[/math], if [math]\displaystyle{ \exists L \in \mathscr L \text{ s.t. } (p,L),(q,L)\in \mathscr I }[/math], we say [math]\displaystyle{ p }[/math] and [math]\displaystyle{ q }[/math] are jointed, and we say [math]\displaystyle{ L }[/math] is decided by [math]\displaystyle{ p }[/math] and [math]\displaystyle{ q }[/math] if there is only one line [math]\displaystyle{ L }[/math](we call it the join [math]\displaystyle{ pq:=L }[/math].) Similarly, given [math]\displaystyle{ L, M\in \mathscr L }[/math], if [math]\displaystyle{ \exists p \in \mathscr P \text{ s.t. } (p,L),(p,M)\in \mathscr I }[/math], we say [math]\displaystyle{ L }[/math] and [math]\displaystyle{ M }[/math] meet, and we say [math]\displaystyle{ p }[/math] is decided by [math]\displaystyle{ L }[/math] and [math]\displaystyle{ M }[/math] if there is only one point [math]\displaystyle{ p }[/math](we call it the intersection [math]\displaystyle{ p:=L\cap M }[/math].) And also denote [math]\displaystyle{ [p(\in\mathscr P)\in L (\in \mathscr L)] := [(p, L) \in \mathscr I] }[/math] and omit [math]\displaystyle{ \mathscr I }[/math].
평면
We shall call incidence structures [math]\displaystyle{ \pi=(\mathscr P , \mathscr I) }[/math] satisfying following axioms planes:
- [math]\displaystyle{ \forall p, q \in\mathscr P \exists ! L \in \mathscr L \text{ s.t. }p, q\in L, }[/math]
- [math]\displaystyle{ \forall L\in\mathscr L \exists p, q\in\mathscr P (p \ne q) \text{ s.t. } p, q \in L. }[/math]
뉴턴의 운동 법칙
뉴턴의 운동 법칙(Newton's laws of motion)은 아이작 뉴턴에 의해 정립된 세 가지 물리 법칙이다.
역사
제1 법칙: 관성의 법칙
외력이 없을 때 어떤 물체의 질량중심은 일정한 속도 (또는 운동량)을 가지고 운동한다.
관성의 법칙을 만족하는 기준틀(좌표계)를 관성기준틀(관성좌표계, 관성계)라 부르고, 즉 이는 등속도 운동을 하는 기준틀을 말한다.