双曲精神病的发作

Q4 Social Sciences

College Mathematics Journal Pub Date : 2023-08-08 DOI:10.1080/07468342.2023.2231314

Tevian Dray

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引用次数: 0

摘要

摘要利用双曲月形导出了双曲三角形的角缺陷面积公式，与用(椭圆)月形表示椭圆三角形的角过剩面积的论证类似。然后讨论了这种结构的几个教学特点。本文的基本思想是由作者的一名学生作为非欧几里得几何课程的一部分在一个受监督的研究项目中探讨的[引文8]。那篇文章，反过来，是建立在[引文]中给出的论点的大纲之上的，而[引文]也以稍微不同的形式给出了[引文3，引文5，引文6]，其中归功于高斯1832年的一封信。这里给出的处理方法首先出现在作者的免费在线图书[Citation2]中，其中还包含一些使用GeoGebra [Citation7]构建的图形的交互式版本。注1不要将克莱因盘与双曲几何的贝尔特拉米-克莱因模型混淆，后者有时也被称为克莱因盘双曲三角形有时被称为2/3-理想三角形然而，SSS同余是不成立的，否则所有的双曲月子都是同余的!说明SSS同余是由SAS同余推导出来的证明在哪里失败了?关键的身份(7)可以使用SAS直接验证，而不需要像(8)那样调用理想三角形。https://math.oregonstate.edu/ ~ tevian) 1976年在麻省理工学院获得数学学士学位，1981年在伯克利大学获得数学博士学位，之后做了几年物理学博士后，现在是俄勒冈州立大学的数学教授。他在数学物理方面的传统研究，以及他为改进二年级微积分教学所做的努力，都把几何放在了最重要的位置。他指导矢量微积分桥项目，并写了几本强调几何的书，包括印刷和在线。

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Hyperbolic Lunes

Summary The formula for the area of a hyperbolic triangle in terms of its angle defect is derived using hyperbolic lunes, in analogy with the argument using (elliptic) lunes to express the area of an elliptic triangle in terms of its angle excess. Several pedagogical features of this construction are then discussed.

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来源期刊

College Mathematics Journal Social Sciences-Education

CiteScore

0.20

自引率

0.00%

发文量