论文标题
关于尼古拉斯 - 奥古斯特透明的注释：在准构映射的起源（出现在teichm {ü} ller理论手册的第七卷中）
A note on Nicolas-Auguste Tissot: At the origin of quasiconformal mappings (to appear in Vol. VII of the Handbook of Teichm{ü}ller Theory)
论文作者
论文摘要
Nicolas-Auguste Tessot（1824--1897）是法国数学家和制图师。他介绍了一种工具，该工具以``pthsot indicatrix''的名字而在地理学家中闻名，并在二十世纪上半叶被广泛使用。这是椭圆场的图形表示，在地理图的每个点上指示该地图的变形，无论是方向还是大小。在给定点表示的每个椭圆形都是图像域（通常说是代表地面表面的球体）中的无限圆的图像，该图像通过实现地理图的投影。从数学角度来看，西托托（Tessot）广泛研究了从球体上映射到欧几里得平面上的变形，他还开发了一种理论，用于对一般表面之间的映射变形。他的想法与那些是关于准文字映射的作品起源的想法，这些映射是由Gr {Ö} tzsch，Lavrentieff，Ahlfors和Teichm {ü} ller开发几十年的。 gr {Ö} tzsch在他的论文中提到了透明的作品，在他为文章的某些图纸中，pstotot indicatrix表示。 Teichm {ü} ller在他的基本论文之一的历史部分中提到了透镜的名字，他指出，地理学家最初使用了准文献映射。 关于准文献映射的所有已知历史报告中缺少透明的名称。在本文中，我们报告了透视的这项工作，表明准文献映射的理论具有实际的起源。 本文的最终版本将出现在第1卷中。 Teichm {ü}手册的VII（欧洲数学学会出版社，2020年）。
Nicolas-Auguste Tissot (1824--1897) was a French mathematician and cartographer. He introduced a tool which became known among geographers under the name ``Tissot indicatrix'', and which was widely used during the first half of the twentieth century in cartography. This is a graphical representation of a field of ellipses, indicating at each point of a geographical map the distorsion of this map, both in direction and in magnitude. Each ellipse represented at a given point is the image of an infinitesimal circle in the domain of the map (generally speaking, a sphere representing the surface of the earth) by the projection that realizes the geographical map. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane, and he also developed a theory for the distorsion of mappings between general surfaces. His ideas are close to those that are at the origin of the work on quasiconformal mappings that was developed several decades after him by Gr{ö}tzsch, Lavrentieff, Ahlfors and Teichm{ü}ller. Gr{ö}tzsch, in his papers, mentions the work of Tissot, and in some of the drawings he made for his articles, the Tissot indicatrix is represented. Teichm{ü}ller mentions the name Tissot in a historical section in one of his fundamental papers in which he points out that quasiconformal mappings were initially used by geographers. The name Tissot is missing from all the known historical reports on quasiconformal mappings. In the present article, we report on this work of Tissot, showing that the theory of quasiconformal mappings has a practical origin. The final version of this article will appear in Vol. VII of the Handbook of Teichm{ü}ller Theory (European Mathematical Society Publishing House, 2020).
