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Papers by Athanase Papadopoulos

Research paper thumbnail of Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory

Geometriae Dedicata, Jan 31, 2012

Research paper thumbnail of In the Tradition of Thurston II -- Geometry and Groups

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Research paper thumbnail of On hyperbolic geometry and the history of its reception

HAL (Le Centre pour la Communication Scientifique Directe), 2010

Research paper thumbnail of Timelike Hilbert geometry of the spherical simplex

arXiv (Cornell University), Mar 8, 2023

Research paper thumbnail of Transitional geometry

EMS Press eBooks, Apr 30, 2015

Research paper thumbnail of Deforming hyperbolic hexagons with applications to the arc and the Thurston metrics on Teichmüller spaces

HAL (Le Centre pour la Communication Scientifique Directe), 2015

Research paper thumbnail of On hyperbolic analogues of some classical theorems in spherical geometry

HAL (Le Centre pour la Communication Scientifique Directe), 2014

Research paper thumbnail of Surveys in Geometry I

Research paper thumbnail of Euler and Maupertuis on the Figure of the Earth

Research paper thumbnail of Réseaux ferroviaires et courbes simples sur une surface (Train tracks and simple curves on surfaces)

HAL (Le Centre pour la Communication Scientifique Directe), 1983

Research paper thumbnail of René Thom: From mathematics to philosophy

HAL (Le Centre pour la Communication Scientifique Directe), Aug 17, 2022

Research paper thumbnail of On the classification of mapping class actions on Thurston's asymmetric metric

arXiv (Cornell University), Oct 17, 2011

Research paper thumbnail of Thurston's Asymmetric Metric on the Space of Singular Flat Metrics with a Fixed Quadrangulatioṅ

HAL (Le Centre pour la Communication Scientifique Directe), Nov 18, 2021

Research paper thumbnail of Christiaan Huygens : Écrits sur la musique et le son

HAL (Le Centre pour la Communication Scientifique Directe), 2021

International audienceThe book contains all the texts written by Christiaan Huygens on music theo... more International audienceThe book contains all the texts written by Christiaan Huygens on music theory and the theory of sound, with translations from the Latin into French. These texts are accompanied by mathematical, physical, musical, biographical and historical notes, and several essays explaining the place of Huygens' works in the sciences and arts literature since the seventeenth century till our days.Le présent volume réunit tous les textes de Christiaan Huygens sur la musique et sur la théorie du son, avec une traduction en français de tous ceux qui sont originellement écrits en ­latin. Ces textes sont accompagnés de commentaires mathématiques, musicaux et historiques, d’une biographie de Christiaan Huygens, d’extraits de sa correspondance sur la ­musique, ainsi que de plusieurs essais expliquant la place de son œuvre dans la littérature musicale et dans la musique, depuis le dix-septième siècle jusqu’à nos jours.Cet ouvrage sera spécialement utile aux étudiants et chercheurs en musique et en acoustique, mais il s’adresse aussi à un public plus large, en particulier à toutes les personnes intéressées par l’alliage entre la science et l’art, par l’histoire des sciences et leur transmission, notamment par la vie culturelle dans l’espace européen du dix-septième siècle

Research paper thumbnail of Leohnard Euler, Ecrits sur la musique, Vol. 2

Le second volume des œuvres d'Euler sur la musique est divise en cinq parties. La premiere pa... more Le second volume des œuvres d'Euler sur la musique est divise en cinq parties. La premiere partie contient une biographie d’Euler ainsi qu’une introduction a la place de la musique dans l’œuvre generale de cet auteur. La seconde partie contient les trois memoires d'Euler sur la musique : Conjecture sur la raison de quelques dissonances generalement recues dans la musique (presente a l’Academie des sciences de Berlin en 1760), Du veritable caractere de la musique moderne (presente a la meme Academie en 1764) et le memoire De harmoniae veris principiis per speculum musicum repraesentatis (presente en 1773 a l’Academie des sciences de Saint-Petersbourg) traduit du latin. Ces trois memoires sont accompagnes d’introductions et de notes historiques et techniques. La troisieme partie presente des extraits des Lettres a une princesse d’Allemagne qui concernent la musique et le son, ainsi que des notes et commentaires sur ces extraits. La quatrieme partie est centree sur la correspon...

Research paper thumbnail of The boundary of a torsion-free hyperbolic group as a semi-Markovian space

Research paper thumbnail of On the legacy of Ibn Al-Haytham: an exposition based on the work of Roshdi Rashed

We report of the work of Ibn al-Haytham, an Arabic scholar who was settled in Cairo in the eleven... more We report of the work of Ibn al-Haytham, an Arabic scholar who was settled in Cairo in the eleventh century and who worked in several fields, including mathematics, physics and philosophy. We review some of of his work on optics, astronomy, number theory and especially spherical geometry. Our report is mostly based on the critical editions published by Roshdi Rashed, a specialist of Ibn al-Haytham and the world expert on Arabic and Greek mathematics and their interaction. We also provide the reader with a report on the life of Ibn al-Haytham, his influence, and the general background in which he flourished.

Research paper thumbnail of Nasir al-Din al-Tusi's treatise on the quadrilateral: The art of being exhaustive

We comment on some combinatorial aspects of Nasir al-Din al-Tusi's treatise on the quadrilate... more We comment on some combinatorial aspects of Nasir al-Din al-Tusi's treatise on the quadrilateral, a 13th century work on spherical trigonometry. The final version of this paper will appear in Ganita Bharati (the Bulletin of the Indian Society for History of Mathematics).

Research paper thumbnail of A Commentary on Teichmüller’s paper Vollständige Lösung einer Extremalaufgabe der quasikonformen Abbildung

Handbook of Teichmüller Theory, Volume VI

We comment on Teichmuller 's paper "Vollstandige Losung einer Extremalaufgabe der quasik... more We comment on Teichmuller 's paper "Vollstandige Losung einer Extremalaufgabe der quasikonformen Abbildung" (Complete solution of an ex-tremal problem of the quasiconformal mapping),, published in 1941. In this paper, Teichmuller gives a proof of the existence of extremal quasiconformal mappings in the case of the pentagon (disc with five distinguished points on the boundary). The final version of this paper will appear as a chapter in Volume VI of the Handbook of Teichmuller theory.

Research paper thumbnail of Arc length as a global conformal parameter for analytic curves

Journal of Mathematical Analysis and Applications, 2017

Abstract We show that arc length is a global conformal parameter for analytic curves and that thi... more Abstract We show that arc length is a global conformal parameter for analytic curves and that this parameter can be used to decide whether the domain of definition of an analytic curve can be extended or not. The maximal extension with respect to the arc length parameter is the largest possible extension (over all parametrizations of the curve). Our proof is elementary, simple and short. Several examples are given in the plane, and the results remain true for curves in an arbitrary Euclidean space R k .

Research paper thumbnail of Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory

Geometriae Dedicata, Jan 31, 2012

Research paper thumbnail of In the Tradition of Thurston II -- Geometry and Groups

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Research paper thumbnail of On hyperbolic geometry and the history of its reception

HAL (Le Centre pour la Communication Scientifique Directe), 2010

Research paper thumbnail of Timelike Hilbert geometry of the spherical simplex

arXiv (Cornell University), Mar 8, 2023

Research paper thumbnail of Transitional geometry

EMS Press eBooks, Apr 30, 2015

Research paper thumbnail of Deforming hyperbolic hexagons with applications to the arc and the Thurston metrics on Teichmüller spaces

HAL (Le Centre pour la Communication Scientifique Directe), 2015

Research paper thumbnail of On hyperbolic analogues of some classical theorems in spherical geometry

HAL (Le Centre pour la Communication Scientifique Directe), 2014

Research paper thumbnail of Surveys in Geometry I

Research paper thumbnail of Euler and Maupertuis on the Figure of the Earth

Research paper thumbnail of Réseaux ferroviaires et courbes simples sur une surface (Train tracks and simple curves on surfaces)

HAL (Le Centre pour la Communication Scientifique Directe), 1983

Research paper thumbnail of René Thom: From mathematics to philosophy

HAL (Le Centre pour la Communication Scientifique Directe), Aug 17, 2022

Research paper thumbnail of On the classification of mapping class actions on Thurston's asymmetric metric

arXiv (Cornell University), Oct 17, 2011

Research paper thumbnail of Thurston's Asymmetric Metric on the Space of Singular Flat Metrics with a Fixed Quadrangulatioṅ

HAL (Le Centre pour la Communication Scientifique Directe), Nov 18, 2021

Research paper thumbnail of Christiaan Huygens : Écrits sur la musique et le son

HAL (Le Centre pour la Communication Scientifique Directe), 2021

International audienceThe book contains all the texts written by Christiaan Huygens on music theo... more International audienceThe book contains all the texts written by Christiaan Huygens on music theory and the theory of sound, with translations from the Latin into French. These texts are accompanied by mathematical, physical, musical, biographical and historical notes, and several essays explaining the place of Huygens' works in the sciences and arts literature since the seventeenth century till our days.Le présent volume réunit tous les textes de Christiaan Huygens sur la musique et sur la théorie du son, avec une traduction en français de tous ceux qui sont originellement écrits en ­latin. Ces textes sont accompagnés de commentaires mathématiques, musicaux et historiques, d’une biographie de Christiaan Huygens, d’extraits de sa correspondance sur la ­musique, ainsi que de plusieurs essais expliquant la place de son œuvre dans la littérature musicale et dans la musique, depuis le dix-septième siècle jusqu’à nos jours.Cet ouvrage sera spécialement utile aux étudiants et chercheurs en musique et en acoustique, mais il s’adresse aussi à un public plus large, en particulier à toutes les personnes intéressées par l’alliage entre la science et l’art, par l’histoire des sciences et leur transmission, notamment par la vie culturelle dans l’espace européen du dix-septième siècle

Research paper thumbnail of Leohnard Euler, Ecrits sur la musique, Vol. 2

Le second volume des œuvres d'Euler sur la musique est divise en cinq parties. La premiere pa... more Le second volume des œuvres d'Euler sur la musique est divise en cinq parties. La premiere partie contient une biographie d’Euler ainsi qu’une introduction a la place de la musique dans l’œuvre generale de cet auteur. La seconde partie contient les trois memoires d'Euler sur la musique : Conjecture sur la raison de quelques dissonances generalement recues dans la musique (presente a l’Academie des sciences de Berlin en 1760), Du veritable caractere de la musique moderne (presente a la meme Academie en 1764) et le memoire De harmoniae veris principiis per speculum musicum repraesentatis (presente en 1773 a l’Academie des sciences de Saint-Petersbourg) traduit du latin. Ces trois memoires sont accompagnes d’introductions et de notes historiques et techniques. La troisieme partie presente des extraits des Lettres a une princesse d’Allemagne qui concernent la musique et le son, ainsi que des notes et commentaires sur ces extraits. La quatrieme partie est centree sur la correspon...

Research paper thumbnail of The boundary of a torsion-free hyperbolic group as a semi-Markovian space

Research paper thumbnail of On the legacy of Ibn Al-Haytham: an exposition based on the work of Roshdi Rashed

We report of the work of Ibn al-Haytham, an Arabic scholar who was settled in Cairo in the eleven... more We report of the work of Ibn al-Haytham, an Arabic scholar who was settled in Cairo in the eleventh century and who worked in several fields, including mathematics, physics and philosophy. We review some of of his work on optics, astronomy, number theory and especially spherical geometry. Our report is mostly based on the critical editions published by Roshdi Rashed, a specialist of Ibn al-Haytham and the world expert on Arabic and Greek mathematics and their interaction. We also provide the reader with a report on the life of Ibn al-Haytham, his influence, and the general background in which he flourished.

Research paper thumbnail of Nasir al-Din al-Tusi's treatise on the quadrilateral: The art of being exhaustive

We comment on some combinatorial aspects of Nasir al-Din al-Tusi's treatise on the quadrilate... more We comment on some combinatorial aspects of Nasir al-Din al-Tusi's treatise on the quadrilateral, a 13th century work on spherical trigonometry. The final version of this paper will appear in Ganita Bharati (the Bulletin of the Indian Society for History of Mathematics).

Research paper thumbnail of A Commentary on Teichmüller’s paper Vollständige Lösung einer Extremalaufgabe der quasikonformen Abbildung

Handbook of Teichmüller Theory, Volume VI

We comment on Teichmuller 's paper "Vollstandige Losung einer Extremalaufgabe der quasik... more We comment on Teichmuller 's paper "Vollstandige Losung einer Extremalaufgabe der quasikonformen Abbildung" (Complete solution of an ex-tremal problem of the quasiconformal mapping),, published in 1941. In this paper, Teichmuller gives a proof of the existence of extremal quasiconformal mappings in the case of the pentagon (disc with five distinguished points on the boundary). The final version of this paper will appear as a chapter in Volume VI of the Handbook of Teichmuller theory.

Research paper thumbnail of Arc length as a global conformal parameter for analytic curves

Journal of Mathematical Analysis and Applications, 2017

Abstract We show that arc length is a global conformal parameter for analytic curves and that thi... more Abstract We show that arc length is a global conformal parameter for analytic curves and that this parameter can be used to decide whether the domain of definition of an analytic curve can be extended or not. The maximal extension with respect to the arc length parameter is the largest possible extension (over all parametrizations of the curve). Our proof is elementary, simple and short. Several examples are given in the plane, and the results remain true for curves in an arbitrary Euclidean space R k .