English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Nicolas-Auguste Tissot (1824--1897) was a French mathematician andcartographer. He introduced a tool which became known among geographers underthe name ``Tissot indicatrix'', and which was widely used during the first halfof the twentieth century in cartography. This is a graphical representation ofa field of ellipses, indicating at each point of a geographical map thedistorsion of this map, both in direction and in magnitude. Each ellipserepresented at a given point is the image of an infinitesimal circle in thedomain of the map (generally speaking, a sphere representing the surface of theearth) by the projection that realizes the geographical map. Tissot studiedextensively, from a mathematical viewpoint, the distortion of mappings from thesphere onto the Euclidean plane, and he also developed a theory for thedistorsion of mappings between general surfaces. His ideas are close to thosethat are at the origin of the work on quasiconformal mappings that wasdeveloped several decades after him by Gr{\"o}tzsch, Lavrentieff, Ahlfors andTeichm{\"u}ller. Gr{\"o}tzsch, in his papers, mentions the work of Tissot, andin some of the drawings he made for his articles, the Tissot indicatrix isrepresented. Teichm{\"u}ller mentions the name Tissot in a historical sectionin one of his fundamental papers in which he points out that quasiconformalmappings were initially used by geographers. The name Tissot is missing fromall the known historical reports on quasiconformal mappings. In the presentarticle, we report on this work of Tissot, showing that the theory ofquasiconformal mappings has a practical origin. The final version of thisarticle will appear in Vol. VII of the Handbook of Teichm{\"u}ller Theory(European Mathematical Society Publishing House, 2020).

A note on Nicolas-Auguste Tissot: At the origin of quasiconformal mappings (to appear in Vol. VII of the Handbook of Teichm{\"u}ller Theory)