{"title":"几何概率计算的一个三角形","authors":"N. Aharonyan, H. O. Harutyunyan","doi":"10.46991/pysu:a/2017.51.3.211","DOIUrl":null,"url":null,"abstract":"In the paper, using a relationship between probability $P(L(\\omega)\\subset \\mathbf {D}) $ that a random segment of length $l$ in $R^{n}$ having a common point with body $D$ entirely lying in $D$ and the covariogram of $D$, we obtain the explicit form of $P(L(\\omega)\\subset \\mathbf {D}) $ for any triangle on the plane.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"GEOMETRIC PROBABILITY CALCULATION FOR A TRIANGLE\",\"authors\":\"N. Aharonyan, H. O. Harutyunyan\",\"doi\":\"10.46991/pysu:a/2017.51.3.211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the paper, using a relationship between probability $P(L(\\\\omega)\\\\subset \\\\mathbf {D}) $ that a random segment of length $l$ in $R^{n}$ having a common point with body $D$ entirely lying in $D$ and the covariogram of $D$, we obtain the explicit form of $P(L(\\\\omega)\\\\subset \\\\mathbf {D}) $ for any triangle on the plane.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.3.211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.3.211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
本文利用R^{n}$中长度为$ L $的随机线段有一个公点且体$D$完全在$D$上的概率$P(L(\omega)\子集\mathbf {D}) $与$D$的协变函数之间的关系，得到了平面上任意三角形的$P(L(\omega)\子集\mathbf {D}) $的显式形式。
In the paper, using a relationship between probability $P(L(\omega)\subset \mathbf {D}) $ that a random segment of length $l$ in $R^{n}$ having a common point with body $D$ entirely lying in $D$ and the covariogram of $D$, we obtain the explicit form of $P(L(\omega)\subset \mathbf {D}) $ for any triangle on the plane.
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