作为三角函数的椭圆函数的初步论述

L. Al-ossmi
{"title":"作为三角函数的椭圆函数的初步论述","authors":"L. Al-ossmi","doi":"10.35316/alifmatika.2023.v5i1.1-20","DOIUrl":null,"url":null,"abstract":"This article concerns the examination of trigonometric identities from an elliptic perspective. The treatment of elliptic functions presented herein adheres to a structure analogous to the traditional exposition of trigonometric functions, with the exception that an ellipse replaces the unit circle. The degree of similarity between the elliptic functions and their trigonometric counterparts is moderated by the periodicity of the so-called El- functions. These identities not only establish the values of the functions, but also establish a correlation between their ratios and the major and minor axes of the underlying ellipse. The resemblance between the functions is somewhat modified by the periodic nature of the El-identities, whereby each ratio is associated with the major and minor axis of the ellipse. This article adopts the notation (E) to denote the El- functions and distinguish them from the opposite circular functions.","PeriodicalId":192872,"journal":{"name":"Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An elementary treatise on elliptic functions as trigonometry\",\"authors\":\"L. Al-ossmi\",\"doi\":\"10.35316/alifmatika.2023.v5i1.1-20\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article concerns the examination of trigonometric identities from an elliptic perspective. The treatment of elliptic functions presented herein adheres to a structure analogous to the traditional exposition of trigonometric functions, with the exception that an ellipse replaces the unit circle. The degree of similarity between the elliptic functions and their trigonometric counterparts is moderated by the periodicity of the so-called El- functions. These identities not only establish the values of the functions, but also establish a correlation between their ratios and the major and minor axes of the underlying ellipse. The resemblance between the functions is somewhat modified by the periodic nature of the El-identities, whereby each ratio is associated with the major and minor axis of the ellipse. This article adopts the notation (E) to denote the El- functions and distinguish them from the opposite circular functions.\",\"PeriodicalId\":192872,\"journal\":{\"name\":\"Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35316/alifmatika.2023.v5i1.1-20\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35316/alifmatika.2023.v5i1.1-20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本文从椭圆的角度考察三角恒等式。本文对椭圆函数的处理遵循类似于传统三角函数的结构,不同之处在于椭圆取代了单位圆。椭圆函数和它们的三角函数之间的相似程度是由所谓的El-函数的周期性所缓和的。这些恒等式不仅建立了函数的值,而且建立了它们的比值与基础椭圆的长轴和短轴之间的相关性。函数之间的相似性被el恒等式的周期性性质所修正,即每个比值都与椭圆的长轴和短轴相关联。本文采用符号(E)来表示El-函数,并将其与相反的圆函数区分开来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
An elementary treatise on elliptic functions as trigonometry
This article concerns the examination of trigonometric identities from an elliptic perspective. The treatment of elliptic functions presented herein adheres to a structure analogous to the traditional exposition of trigonometric functions, with the exception that an ellipse replaces the unit circle. The degree of similarity between the elliptic functions and their trigonometric counterparts is moderated by the periodicity of the so-called El- functions. These identities not only establish the values of the functions, but also establish a correlation between their ratios and the major and minor axes of the underlying ellipse. The resemblance between the functions is somewhat modified by the periodic nature of the El-identities, whereby each ratio is associated with the major and minor axis of the ellipse. This article adopts the notation (E) to denote the El- functions and distinguish them from the opposite circular functions.
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
自引率
0.00%
发文量
0
期刊最新文献
Journey to the cosmos: Navigating stellar evolution with differential equations Mathematical Olympiad issues to identify students' reasoning ability using Polya's model Computational thinking ability becomes a predictor of mathematical critical thinking ability Development of numeracy skills: Analysis of students in junior high schools in Ambon City based on teacher's perspective Students' analysis literacy and numeracy in linear algebra: A comparison across personality types
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1