用组合学计算三角形

Q4 Mathematics
Matthew Glomski, K. Peter Krog, Mason Nakamura, Elizabeth M. Reid
{"title":"用组合学计算三角形","authors":"Matthew Glomski, K. Peter Krog, Mason Nakamura, Elizabeth M. Reid","doi":"10.1080/0025570x.2023.2266346","DOIUrl":null,"url":null,"abstract":"SummaryInspired by a problem presented in a New York Times essay, we consider the number of triangles formed by a finite collection of lines in the plane, under the restrictions that no more than two lines intersect at any point and that no two are parallel. We explore the ramifications of relaxing each of these requirements, and we derive a ‘unified triangle counting formula’ for any arrangement of finitely many lines in the plane.MSC: 05B30 Additional informationNotes on contributorsMatthew GlomskiMATTHEW GLOMSKI earned his Ph.D. at the University at Buffalo and joined the mathematics faculty of Marist College. In his spare time he enjoys hiking in the nearby Catskill Mountains.K. Peter KrogK. PETER KROG earned his Ph.D. at the University of Connecticut and joined the mathematics faculty at Marist College in 1996. His mathematical interests include group theory, statistics, and combinatorics.Mason NakamuraMASON NAKAMURA is an applied mathematics student at Marist College and plans to pursue his doctorate. He enjoys golfing, hiking, and snorkeling during his time away from mathematics.Elizabeth M. ReidELIZABETH M. REID is a member of the mathematics faculty at Marist College. She earned her Ph.D. at the University at Buffalo and enjoys hiking in her spare time.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Counting Triangles with Combinatorics\",\"authors\":\"Matthew Glomski, K. Peter Krog, Mason Nakamura, Elizabeth M. Reid\",\"doi\":\"10.1080/0025570x.2023.2266346\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SummaryInspired by a problem presented in a New York Times essay, we consider the number of triangles formed by a finite collection of lines in the plane, under the restrictions that no more than two lines intersect at any point and that no two are parallel. We explore the ramifications of relaxing each of these requirements, and we derive a ‘unified triangle counting formula’ for any arrangement of finitely many lines in the plane.MSC: 05B30 Additional informationNotes on contributorsMatthew GlomskiMATTHEW GLOMSKI earned his Ph.D. at the University at Buffalo and joined the mathematics faculty of Marist College. In his spare time he enjoys hiking in the nearby Catskill Mountains.K. Peter KrogK. PETER KROG earned his Ph.D. at the University of Connecticut and joined the mathematics faculty at Marist College in 1996. His mathematical interests include group theory, statistics, and combinatorics.Mason NakamuraMASON NAKAMURA is an applied mathematics student at Marist College and plans to pursue his doctorate. He enjoys golfing, hiking, and snorkeling during his time away from mathematics.Elizabeth M. ReidELIZABETH M. REID is a member of the mathematics faculty at Marist College. She earned her Ph.D. at the University at Buffalo and enjoys hiking in her spare time.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570x.2023.2266346\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570x.2023.2266346","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

受《纽约时报》一篇文章中提出的问题的启发,我们考虑平面上有限的直线集合在不超过两条直线相交且不平行的条件下形成的三角形的数量。我们探索了放宽这些要求的后果,并推导出一个“统一三角形计数公式”,适用于平面上有限多条线的任何排列。matthew GLOMSKI在布法罗大学(University at Buffalo)获得博士学位,并加入圣母学院(Marist College)数学系。在业余时间,他喜欢在附近的卡茨基尔山脉徒步旅行。彼得KrogK。PETER KROG在康涅狄格大学获得博士学位,并于1996年加入圣母学院数学系。他的数学兴趣包括群论、统计学和组合学。Mason NAKAMURA是圣母学院应用数学专业的学生,他计划继续攻读博士学位。在不学习数学的时间里,他喜欢打高尔夫球、远足和浮潜。Elizabeth M. REID是圣母学院数学系的一员。她在布法罗大学获得博士学位,业余时间喜欢徒步旅行。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Counting Triangles with Combinatorics
SummaryInspired by a problem presented in a New York Times essay, we consider the number of triangles formed by a finite collection of lines in the plane, under the restrictions that no more than two lines intersect at any point and that no two are parallel. We explore the ramifications of relaxing each of these requirements, and we derive a ‘unified triangle counting formula’ for any arrangement of finitely many lines in the plane.MSC: 05B30 Additional informationNotes on contributorsMatthew GlomskiMATTHEW GLOMSKI earned his Ph.D. at the University at Buffalo and joined the mathematics faculty of Marist College. In his spare time he enjoys hiking in the nearby Catskill Mountains.K. Peter KrogK. PETER KROG earned his Ph.D. at the University of Connecticut and joined the mathematics faculty at Marist College in 1996. His mathematical interests include group theory, statistics, and combinatorics.Mason NakamuraMASON NAKAMURA is an applied mathematics student at Marist College and plans to pursue his doctorate. He enjoys golfing, hiking, and snorkeling during his time away from mathematics.Elizabeth M. ReidELIZABETH M. REID is a member of the mathematics faculty at Marist College. She earned her Ph.D. at the University at Buffalo and enjoys hiking in her spare time.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Mathematics Magazine
Mathematics Magazine Mathematics-Mathematics (all)
CiteScore
0.20
自引率
0.00%
发文量
68
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信