这份笔记包含了 Fall 2021, Analytic Geometry 课程的最后一部分内容, 谈到了一点非欧几何和仿射空间. 第一部分是我课堂所作笔记, 语言不够熟练, 而第二部分则是则是根据讲义整理, 更加清晰严谨. 本文使用 Zhihu O…
Euclidean affine spaces, in two and three dimensions, are the objects of classical geometry and correspond to our physical universe. Their structure is rich and has been studied for thousands of years, starting with the Greeks; as a consequence, there is a wealth of results and we've had ...
A New Foundation Of Non- Euclidean, Affine, Real Projective and Euclidean Geometry The concepts of the non-Euclidean plane geometry can be defined in terms of the notions joining and intersecting of geometric entities as follows: 1 We ca... K Menger 被引量: 0发表: 2002年 The Geometry of ...
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are introduced here, and the main formulas extend those of ...
Euclidean and non-Euclidean geometry : an analytical approach This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acqu... Ryan,PatrickJ - Euclidean and non-Euclidean geometry : an analytical approach ...
Euclidean and non-Euclidean geometry are types of metric geometry, in which the lengths of line segments and the sizes of angles may be measured and compared. Projective geometry, on the other hand, is more general and includes the metric geometries as a special case; pure projective geometry ...
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Affine mappings of translation surfaces: geometry and arithmetic 1. Introduction. Translation surfaces naturally arise in the study of billiards in rational polygons (see [ZKa]). To any such polygon P, there corresponds ... C Judge,E Gutkin - 《Duke Mathematical Journal》 被引量: 355发表: ...
the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric sur...
Non-quadratic Euclidean Complete Affine Maximal Type Hypersurfaces for θ∈(0,(N-1)/N]documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{...