205 research outputs found
Herbert Busemann (1905--1994). A biography for his Selected Works edition
This is a biography of Herbert Busemann (1905--1994). The final version will
appear in Volume I of the Selected Works of Herbert Busemann (2 volumes,
Springer Verlag, to appear in 2017)
Nicolas-Auguste Tissot: A link between cartography and quasiconformal theory
Nicolas-Auguste Tissot (1824--1897) published a series of papers on
cartography in which he introduced a tool which became known later on, among
geographers, under the name of the "Tissot indicatrix." This tool was broadly
used during the twentieth century in the theory and in the practical aspects of
the drawing of geographical maps. The Tissot indicatrix is a graphical
representation of a field of ellipses on a map that describes its distortion.
Tissot studied extensively, from a mathematical viewpoint, the distortion of
mappings from the sphere onto the Euclidean plane that are used in drawing
geographical maps, and more generally he developed a theory for the distorsion
of mappings between general surfaces. His ideas are at the heart of the work on
quasiconformal mappings that was developed several decades after him by
Gr{\"o}tzsch, Lavrentieff, Ahlfors and Teichm{\"u}ller. Gr{\"o}tzsch mentions
the work of Tissot and he uses the terminology related to his name (in
particular, Gr{\"o}tzsch uses the Tissot indicatrix). Teichm{\"u}ller mentions
the name of Tissot in a historical section in one of his fundamental papers
where he claims that quasiconformal mappings were used by geographers, but
without giving any hint about the nature of Tissot's work. The name of Tissot
is also missing from all the historical surveys on quasiconformal mappings. In
the present paper, we report on this work of Tissot. We shall also mention some
related works on cartography, on the differential geometry of surfaces, and on
the theory of quasiconformal mappings. This will place Tissot's work in its
proper context. The final version of this paper will appear in the journal
Arch. Hist. Exact Sciences
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