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Two Editions of Ibn Al-Haytham's Completion of the Conics
Historia Mathematica 29 (2002), 247–265 doi:10.1006/hmat.2002.2352 Two Editions of Ibn al-Haytham’s Completion of the Conics View metadata, citation and similar papers at core.ac.uk brought to you by CORE Jan P. Hogendijk provided by Elsevier - Publisher Connector Mathematics Department, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht, Netherlands E-mail: [email protected] The lost Book VIII of the Conics of Apollonius of Perga (ca. 200 B.C.) was reconstructed by the Islamic mathematician Ibn al-Haytham (ca. A.D. 965–1041) in his Completion of the Conics. The Arabic text of this reconstruction with English translation and commentary was published as J. P. Hogendijk, Ibn al-Haytham’s Completion of the Conics (New York: Springer-Verlag, 1985). In a new Arabic edition with French translation and commentary (R. Rashed, Les mathematiques´ infinitesimales´ du IXe au XIe siecle.´ Vol. 3., London: Al-Furqan Foundation, 2000), it was claimed that my edition is faulty. In this paper the similarities and differences between the two editions, translations, and commentaries are discussed, with due consideration for readers who do not know Arabic. The facts will speak for themselves. C 2002 Elsevier Science (USA) C 2002 Elsevier Science (USA) C 2002 Elsevier Science (USA) 247 0315-0860/02 $35.00 C 2002 Elsevier Science (USA) All rights reserved. 248 JAN P. HOGENDIJK HMAT 29 AMS subject classifications: 01A20, 01A30. Key Words: Ibn al-Haytham; conic sections; multiple editions; Rashed. 1. INTRODUCTION The Conics of Apollonius of Perga (ca. 200 B.C.) is one of the fundamental texts of ancient Greek geometry. -
Guido Fubini-Ghiron
Intellectuals Displaced from Fascist Italy Firenze University Press 2019- Guido Fubini-Ghiron Go to personal file When he was almost 60, he was expelled from the Polytechnic University of Link to other connected Lives on the move: Turin because he was Jewish. Known as one of the sharpest and most intelligent Italian analysts, he decided to continue his brilliant work on Fubini Mario Fubini Ghiron Eugenio 1 differential geometry abroad, hoping for a better future for him and his family . (Eugene) Fubini Ghiron Gino He immediately left for Paris, and soon found himself welcomed to Princeton. His two sons, expelled in Italy at the beginning of their academic career, also found their way to the USA and stayed there. Formative years in Paris He was born in Venice on 19 January 1879 to Lazzaro Fubini, a mathematics teacher at the machinist school, and to Zoraide Torre. At only nine years old, he was enrolled at Foscarini High School in Venice, achieving, in his eight years of ginnasio and liceo [junior high school and high school], perfect grades (all 10s) in mathematics2. In 1896, at seventeen years old, he enrolled in the Facoltà di Matematica [School of Mathematics] at the Scuola normale superiore of Pisa, «where many scholars became passionate about research in geometry»3. A student of Ulisse Dini, Eugenio Bertini and, above all, Luigi Bianchi, he graduated with honors in 1900 with a thesis titled «Il parallelismo di Clifford negli spazi ellittici» [Clifford’s parallelism in elliptical spaces]4. 1 Letter of 30 October 1938 from Tullio Levi-Civita to Oswald Veblen from the Institute for Advanced Study at Princeton University, translated and reported on the Università Bocconi’s website, section Rubriche <http://matematica-old.unibocconi.it> (accessed 2 February 2019). -
February 19, 2016
February 19, 2016 Professor HELGE HOLDEN SECRETARY OF THE INTERNATIONAL MATHEMATICAL UNION Dear Professor Holden, The Turkish Mathematical Society (TMD) as the Adhering Organization, applies to promote Turkey from Group I to Group II as a member of IMU. We attach an overview of the developments of Mathematics in Turkey during the last 10 years (2005- 2015) preceded by a historical account. With best regards, Betül Tanbay President of the Turkish Mathematical Society Report on the state of mathematics in Turkey (2005-2015) This is an overview of the status of Mathematics in Turkey, prepared for the IMU for promotion from Group I to Group II by the adhering organization, the Turkish Mathematical Society (TMD). 1-HISTORICAL BACKGROUND 2-SOCIETIES AND CENTERS RELATED TO MATHEMATICAL SCIENCES 3-NUMBER OF PUBLICATIONS BY SUBJECT CATEGORIES 4-NATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 5-INTERNATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 6-NUMBERS OF STUDENTS AND TEACHING STAFF IN MATHEMATICAL SCIENCES IN TURKEY FOR THE 2013-2014 ACADEMIC YEAR AND THE 2014-2015 ACADEMIC YEAR 7- RANKING AND DOCUMENTS OF TURKEY IN MATHEMATICAL SCIENCES 8- PERIODICALS AND PUBLICATIONS 1-HISTORICAL BACKGROUND Two universities, the Istanbul University and the Istanbul Technical University have been influential in creating a mathematical community in Turkey. The Royal School of Naval Engineering, "Muhendishane-i Bahr-i Humayun", was established in 1773 with the responsibility to educate chart masters and ship builders. Gaining university status in 1928, the Engineering Academy continued to provide education in the fields of engineering and architecture and, in 1946, Istanbul Technical University became an autonomous university which included the Faculties of Architecture, Civil Engineering, Mechanical Engineering, and Electrical and Electronic Engineering. -
Chapter 5 Product Measures
Chapter 5 Product Measures Lebesgue measure on R generalizes the notion of the length of an interval. In this chapter, we see how two-dimensional Lebesgue measure on R2 generalizes the notion of the area of a rectangle. More generally, we construct new measures that are the products of two measures. Once these new measures have been constructed, the question arises of how to compute integrals with respect to these new measures. Beautiful theorems proved in the first decade of the twentieth century allow us to compute integrals with respect to product measures as iterated integrals involving the two measures that produced the product. Furthermore, we will see that under reasonable conditions we can switch the order of an iterated integral. Main building of Scuola Normale Superiore di Pisa, the university in Pisa, Italy, where Guido Fubini (1879–1943) received his PhD in 1900. In 1907 Fubini proved that under reasonable conditions, an integral with respect to a product measure can be computed as an iterated integral and that the order of integration can be switched. Leonida Tonelli (1885–1943) also taught for many years in Pisa; he also proved a crucial theorem about interchanging the order of integration in an iterated integral. CC-BY-SA Lucarelli © Sheldon Axler 2020 S. Axler, Measure, Integration & Real Analysis, Graduate Texts 116 in Mathematics 282, https://doi.org/10.1007/978-3-030-33143-6_5 Section 5A Products of Measure Spaces 117 5A Products of Measure Spaces Products of s-Algebras Our first step in constructing product measures is to construct the product of two s-algebras. -
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DEVELOPMENTS IN THE FIELD OF MATHEMATICS AND MATHEMATICS EDUCATION IN TURKEY DURING THE PERIOD OF 1938-1980 Prof. Dr. Ali BOZKURT Gaziantep University Assist. Prof. Dr. Emrah Berkant PATOGLU** Gaziantep University Introduction When the Republic of Turkey was founded there was a drive to keep up with contemporary civilization and an ambition even to go beyond. Mustafa Kemal Ataturk tried to pave the way for the modernization based on reason and wisdom by pointing out the fact that a civilization without science cannot be modern. As in all areas, these efforts are seen in the areas of science and technology. In the newly founded Republic, basic principles relating to science and technology are more often taught in educational institutions. Hence, developing education in scientific areas in an institutional manner and educating scientists have become a necessity. As in other scientific areas, it has been aimed to achieve advancements in the field of mathematics. In fact in the later times of Ottoman Empire era, the modernization of education began with opening institutions that were mainly using mathematics. In order to see the whole picture regarding the advancements in the field of mathematics, it is necessary to focus on the produced works of mathematicians along with the developments of the mathematics teacher education as well as changes introduced into mathematics curricula documents. In this study, therefore, we consider the developments in each of these topics during the years of 1938-1980. Developments in Mathematics regarding Undergraduate and Graduate degrees and Academic Studies Some institutions, subjected to radical reforms, have become scientific research centers with their new names and functions. -
Apollonius of Pergaconics. Books One - Seven
APOLLONIUS OF PERGACONICS. BOOKS ONE - SEVEN INTRODUCTION A. Apollonius at Perga Apollonius was born at Perga (Περγα) on the Southern coast of Asia Mi- nor, near the modern Turkish city of Bursa. Little is known about his life before he arrived in Alexandria, where he studied. Certain information about Apollonius’ life in Asia Minor can be obtained from his preface to Book 2 of Conics. The name “Apollonius”(Apollonius) means “devoted to Apollo”, similarly to “Artemius” or “Demetrius” meaning “devoted to Artemis or Demeter”. In the mentioned preface Apollonius writes to Eudemus of Pergamum that he sends him one of the books of Conics via his son also named Apollonius. The coincidence shows that this name was traditional in the family, and in all prob- ability Apollonius’ ancestors were priests of Apollo. Asia Minor during many centuries was for Indo-European tribes a bridge to Europe from their pre-fatherland south of the Caspian Sea. The Indo-European nation living in Asia Minor in 2nd and the beginning of the 1st millennia B.C. was usually called Hittites. Hittites are mentioned in the Bible and in Egyptian papyri. A military leader serving under the Biblical king David was the Hittite Uriah. His wife Bath- sheba, after his death, became the wife of king David and the mother of king Solomon. Hittites had a cuneiform writing analogous to the Babylonian one and hi- eroglyphs analogous to Egyptian ones. The Czech historian Bedrich Hrozny (1879-1952) who has deciphered Hittite cuneiform writing had established that the Hittite language belonged to the Western group of Indo-European languages [Hro]. -
Toward a Scientific and Personal Biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Rossana Tazzioli
Toward a scientific and personal biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Rossana Tazzioli To cite this version: Pietro Nastasi, Rossana Tazzioli. Toward a scientific and personal biography of Tullio Levi-Civita (1873-1941). Historia Mathematica, Elsevier, 2005, 32 (2), pp.203-236. 10.1016/j.hm.2004.03.003. hal-01459031 HAL Id: hal-01459031 https://hal.archives-ouvertes.fr/hal-01459031 Submitted on 7 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Towards a Scientific and Personal Biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Dipartimento di Matematica e Applicazioni, Università di Palermo Rossana Tazzioli, Dipartimento di Matematica e Informatica, Università di Catania Abstract Tullio Levi-Civita was one of the most important Italian mathematicians in the early part of the 20th century, contributing significantly to a number of research fields in mathematics and physics. In addition, he was involved in the social and political life of his time and suffered severe political and racial persecution during the period of Fascism. He tried repeatedly and in several cases successfully to help colleagues and students who were victims of anti-Semitism in Italy and Germany. -
The Case of Sicily, 1880–1920 Rossana Tazzioli
Interplay between local and international journals: The case of Sicily, 1880–1920 Rossana Tazzioli To cite this version: Rossana Tazzioli. Interplay between local and international journals: The case of Sicily, 1880–1920. Historia Mathematica, Elsevier, 2018, 45 (4), pp.334-353. 10.1016/j.hm.2018.10.006. hal-02265916 HAL Id: hal-02265916 https://hal.archives-ouvertes.fr/hal-02265916 Submitted on 12 Aug 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Interplay between local and international journals: The case of Sicily, 1880–1920 Rossana Tazzioli To cite this version: Rossana Tazzioli. Interplay between local and international journals: The case of Sicily, 1880–1920. Historia Mathematica, Elsevier, 2018, 45 (4), pp.334-353. 10.1016/j.hm.2018.10.006. hal-02265916 HAL Id: hal-02265916 https://hal.archives-ouvertes.fr/hal-02265916 Submitted on 12 Aug 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. -
LONG-TERM HISTORY and EPHEMERAL CONFIGURATIONS Catherine Goldstein
LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS Catherine Goldstein To cite this version: Catherine Goldstein. LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS. Interna- tional Congress of Mathematicians, Aug 2018, Rio de Janeiro, Brazil. pp.487-522. hal-02334505 HAL Id: hal-02334505 https://hal.archives-ouvertes.fr/hal-02334505 Submitted on 29 Oct 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS CATHERINE GOLDSTEIN Abstract. Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathe- matics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral configurations of mathematicians, theorems or practices. The first part of the paper explains why this change has taken place: a renewed interest in the connections between mathematics and society, an increased at- tention to the variety of components and aspects of mathematical work, and a critical outlook on historiography itself. The problems of a long-term history are illustrated and tested using a number of episodes in the nineteenth-century history of Hermitian forms, and finally, some open questions are proposed. -
February 19, 2016 Professor HELGE HOLDEN SECRETARY of THE
February 19, 2016 Professor HELGE HOLDEN SECRETARY OF THE INTERNATIONAL MATHEMATICAL UNION Dear Professor Holden, The Turkish Mathematical Society (TMD) as the Adhering Organization, applies to promote Turkey from Group I to Group II as a member of IMU. We attach an overview of the developments of Mathematics in Turkey during the last 10 years (2005- 2015) preceded by a historical account. With best regards, Betül Tanbay President of the Turkish Mathematical Society Report on the state of mathematics in Turkey (2005-2015) This is an overview of the status of Mathematics in Turkey, prepared for the IMU for promotion from Group I to Group II by the adhering organization, the Turkish Mathematical Society (TMD). 1-HISTORICAL BACKGROUND 2-SOCIETIES AND CENTERS RELATED TO MATHEMATICAL SCIENCES 3-NUMBER OF PUBLICATIONS BY SUBJECT CATEGORIES 4-NATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 5-INTERNATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 6-NUMBERS OF STUDENTS AND TEACHING STAFF IN MATHEMATICAL SCIENCES IN TURKEY FOR THE 2013-2014 ACADEMIC YEAR AND THE 2014-2015 ACADEMIC YEAR 7- RANKING AND DOCUMENTS OF TURKEY IN MATHEMATICAL SCIENCES 8- PERIODICALS AND PUBLICATIONS 1-HISTORICAL BACKGROUND Two universities, the Istanbul University and the Istanbul Technical University have been influential in creating a mathematical community in Turkey. The Royal School of Naval Engineering, "Muhendishane-i Bahr-i Humayun", was established in 1773 with the responsibility to educate chart masters and ship builders. Gaining university status in 1928, the Engineering Academy continued to provide education in the fields of engineering and architecture and, in 1946, Istanbul Technical University became an autonomous university which included the Faculties of Architecture, Civil Engineering, Mechanical Engineering, and Electrical and Electronic Engineering. -
Short Curriculum Vitae (1)
Alfonso Sorrentino Short Curriculum Vitae (1) • Personal data: Family name: Sorrentino First name: Alfonso Nationality: Italian Web site: https://www.mat.uniroma2.it/∼sorrenti/ • Education: 2008 - Ph.D. in Mathematics, Dept. of Mathematics, Princeton University (USA). xxxxxxPh.D. Supervisor: Prof. John N. Mather. 2004 - M.A. in Mathematics, Dept. of Mathematics, Princeton University (USA). 2003 - Laurea degree in Mathematics (Summa cum laude), Univ. Roma Tre (Italy). • Currrent Position: Since November 2020: Full Professor in Mathematical Analysis, Univ. Rome Tor Vergata (Italy). • Previous Positions: 2014–2020 Associate Professor in Mathematical Analysis, Univ. Rome Tor Vergata (Italy). 2012– 2014 - Researcher in Mathematical Analysis (tenured), Univ. Roma Tre (Italy). • Fellowships: Spring 2021 - Invited Professor, Institute Henri Poincaré & Univ. Paris Sorbonne (France). Spring 2020 - Research fellowship, Instit. for Pure and Applied Mathem. (IPAM), UCLA (USA). Fall 2018x- Research membership, MSRI Berkeley (USA). 2009–2012 - Herchel-Smith research fellowship in Pure Mathematics, Univ. of Cambridge (UK). 2009–2012 - Newton Trust fellowship in Mathematics, Pembroke College, Cambridge (UK). 2008–2009 - Junior research fellowship, Fondation des Sciences Mathématiques, Paris (France). 2003–2008 - Frelinghuysen Ph.D. scholarship, Princeton University (USA). 2012 - Marie Curie INdAM confund fellowship Ranked 1st with full score (Declined because xxxxx incompatible with the concurrent appointment as tenured Researcher at Univ. Roma Tre). • Awards: 2020 - International Consortium of Chinese Mathematicians Best Paper Award (Gold Medal). 2019 - Barcelona Dynamical System Prize 2019, Societat Catalana de Matemàtiques (Spain). 2018 - Guido Fubini Prize for Mathematics, Accademia delle Scienze di Torino (Italy). • Habilitations: 2018 - Italian National Habilitation (ASN) for Full Professor in Mathematical Analysis. 2018 - Italian National Habilitation (ASN) for Full Professor in Algebra and Geometry. -
Constantin Carathéodory (Türkçe Söylenişiyle: Karatodori)
138 Osmanlı Bilimi Araştırmaları VII/1 (2005) Salih Zeki’yi tanıyanlar tarafından, çoğunluğu ölümünden sonra yazılanlar, bize kişiliği hakkında önemli ayrıntılar vermektedir. Onu kişisel olarak tanıyanlar azaldıkça, Salih Zeki hakkında yapılan yayınlar gittikçe yüzeyselleşen anlatımlara ve yinelemelere dönmüştür. Son yıllarda Salih Zeki SALİH ZEKİ BEY – ÜÇ BOYUTLU BİR BİYOGRAFİ İÇİN ile ilgili yayınlar hızla artmış olmasına karşın, bunların bilinen öykülere bir şey kattığı söylenemez.4 Şeref Etker* Bir bilim adamının biyografisine üçüncü bir boyutu kazandıracak özellik: Salih Zeki Bey, bir bilim tarihçisi olarak, çalışmalarının en önemli onun evrensel bir bakış açısıyla değerlendirilerek, bilinmeyene yönelişini, saydığı bir kısmını, Doğu matematikçilerinin yaşamlarını öğrenmeye, ortaya yöntem anlayışını, ileriye bakışını, önermelerini ve tezlerini; bir Salih Zeki’yi koydukları problem ve çözümleri irdelemeye, fen dallarının gelişimine Salih Zeki yapanın ne olduğunu çözümlemek, eleştirmek, yaratılarını ve katkılarını incelemeye ayırmıştır. Yapıtlarının ortak özelliklerine bakılarak Salih eksiklerini ortaya koymak; nihayet, bu kişiliği ve yapıtını, hem çağdaş bilim Zeki bir matematik düşünürü sayılmalıdır. Değer verdiği Doğulu bilim insanlarına hem de topluma tanıtabilmektedir. adamlarını, koşullar elverdiğince genişliğine incelemiş, onları tarihte layık olduklarına inandığı konumlara yüceltmeğe çalışmıştır. Oysa, Salih Zeki için henüz tam bir kronoloji dahi oluşturulabilmiş değildir.5 Bir örnek vermek gerekirse: Salih Zeki Bey, bilinen