Bibliography of the Publications of Abraham Wasserstein
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Mathematicians
MATHEMATICIANS [MATHEMATICIANS] Authors: Oliver Knill: 2000 Literature: Started from a list of names with birthdates grabbed from mactutor in 2000. Abbe [Abbe] Abbe Ernst (1840-1909) Abel [Abel] Abel Niels Henrik (1802-1829) Norwegian mathematician. Significant contributions to algebra and anal- ysis, in particular the study of groups and series. Famous for proving the insolubility of the quintic equation at the age of 19. AbrahamMax [AbrahamMax] Abraham Max (1875-1922) Ackermann [Ackermann] Ackermann Wilhelm (1896-1962) AdamsFrank [AdamsFrank] Adams J Frank (1930-1989) Adams [Adams] Adams John Couch (1819-1892) Adelard [Adelard] Adelard of Bath (1075-1160) Adler [Adler] Adler August (1863-1923) Adrain [Adrain] Adrain Robert (1775-1843) Aepinus [Aepinus] Aepinus Franz (1724-1802) Agnesi [Agnesi] Agnesi Maria (1718-1799) Ahlfors [Ahlfors] Ahlfors Lars (1907-1996) Finnish mathematician working in complex analysis, was also professor at Harvard from 1946, retiring in 1977. Ahlfors won both the Fields medal in 1936 and the Wolf prize in 1981. Ahmes [Ahmes] Ahmes (1680BC-1620BC) Aida [Aida] Aida Yasuaki (1747-1817) Aiken [Aiken] Aiken Howard (1900-1973) Airy [Airy] Airy George (1801-1892) Aitken [Aitken] Aitken Alec (1895-1967) Ajima [Ajima] Ajima Naonobu (1732-1798) Akhiezer [Akhiezer] Akhiezer Naum Ilich (1901-1980) Albanese [Albanese] Albanese Giacomo (1890-1948) Albert [Albert] Albert of Saxony (1316-1390) AlbertAbraham [AlbertAbraham] Albert A Adrian (1905-1972) Alberti [Alberti] Alberti Leone (1404-1472) Albertus [Albertus] Albertus Magnus -
The Geodetic Sciences in Byzantium
The geodetic sciences in Byzantium Dimitrios A. Rossikopoulos Department of Geodesy and Surveying, Aristotle University of Thessaloniki [email protected] Abstract: Many historians of science consider that geodeasia, a term used by Aristotle meaning "surveying", was not particularly flourishing in Byzantium. However, like “lo- gistiki” (practical arithmetic), it has never ceased to be taught, not only at public universi- ties and ecclesiastical schools, as well as by private tutors. Besides that these two fields had to do with problems of daily life, Byzantines considered them necessary prerequisite for someone who wished to study philosophy. So, they did not only confine themselves to copying and saving the ancient texts, but they also wrote new ones, where they were ana- lyzing their empirical discoveries and their technological achievements. This is the subject of this paper, a retrospect of the numerous manuscripts of the Byzantine period that refer to the development of geodesy both in teaching and practices of surveying, as well as to mat- ters relating to the views about the shape of the earth, the cartography, the positioning in travels and generally the sciences of mapping. Keywords: Geodesy, geodesy in Byzantium, history of geodesy, history of surveying, history of mathematics. Περίληψη: Πολλοί ιστορικοί των επιστημών θεωρούν ότι η γεωδαισία, όρος που χρησι- μοποίησε ο Αριστοτέλης για να ορίσει την πρακτική γεωμετρία, την τοπογραφία, δεν είχε ιδιαίτερη άνθιση στο Βυζάντιο. Ωστόσο, όπως και η “λογιστική”, δεν έπαψε ποτέ να διδά- σκεται όχι μόνο στα κοσμικά πανεπιστήμια, αλλά και στις εκκλησιαστικές σχολές, καθώς επίσης και από ιδιώτες δασκάλους. Πέρα από το ότι οι δύο αυτοί κλάδοι είχαν να κάνουν με προβλήματα της καθημερινής ζωής των ανθρώπων, οι βυζαντινοί θεωρούσαν την διδα- σκαλία τους απαραίτητη προϋπόθεση ώστε να μπορεί κανείς να παρακολουθήσει μαθήμα- τα φιλοσοφίας. -
Bibliography
Bibliography Afshar, Iraj: Bibliographie des Catalogues des Manuscrits Persans. Tehran: 1958. Almagest: see Ptolemy. Apollonius: Apollonii Pergaei quae Graece exstant cum commentariis Eutocii (ed. J. L. Heiberg), 2 vols. Leipzig: 1891, 1893. Arberry, A. J. : The Chester Beatty Library, A Handlist of the Arabic Manuscripts, Vol. VII. Dublin: 1964. Archimedes: Archimedis Opera Omnia cum commentariis Eutocii, (iterum ed. J. L. Heiberg), 3 vols. Leipzig: 1910-1915. Archimedes: see also Heath. Aristarchus of Samos: On the Sizes and Distances of the Sun and Moon (ed. T. Heath). Oxford: 1913. Aristotle, Nicomachean Ethics: Aristotelis Ethica Nicomachea (ed. I. Bywater). Oxford: 1894. Aristotle, Prior Analytics: Aristotelis Analytica Priora et Posteriora (ed. W. D. Ross and L. Minio-Paluello). Oxford: 1964. Autolycus: J. Mogenet, Autolycus de Pitane. Louvain, 1950 (Universite de Louvain, Recueil de Travaux d'Histoire et de Philologie, 3e. Serie Fasc. 37). Awad, Gurgis: "Arabic Manuscripts in American Libraries". Sumer 1, 237-277 (1951). (Arabic). Bachmann, Peter: Galens Abhandlung dariiber, dal3 der vorziigliche Arzt Philosoph sein mul3. Gottingen: 1965 (Ak. Wiss. Gottingen, Nachrichten Phil. -hist. Kl. 1965.1). Belger, C.: "Ein neues Fragmentum Mathematicum Bobiense". Hermes 16, 261-84 (1881). Boilot, D. J.: "L'oeuvre d'al-Beruni, essai bibliographique". Melanges de l'Institut Dominicain d'Etudes Orientales du Caire ~, 161-256 (1955). Bretschneider, C. A.: Die Geometrie und die Geometer vor Eukleides. Leipzig: 1870. 217 Bib Ziography Brockelmann, Carl: Geschichte der Arabischen Litteratur, zweite den Supplementbanden angepasste Aunage, 2 vols. Leiden: 1943, 1949 [GAL] [and] Supplementbande I-III. Leiden: 1937, 1938, 1942 [S]. Bulmer-Thomas, I.: "Conon of Samos". Dictionary of Scientific Biography III, (New York), 391 (1971). -
On Some Borrowed and Misunderstood Problems in Greek Catoptrics
On Some Borrowed and Misunderstood Problems in Greek Catoptrics by ALEXANDERJONES Optics was one of the first sciences to which ancient Greek mathe- maticians attempted to apply the apparatus of geometry. They were most successful in describing geometrically certain phenomena of per- spective (as in Euclid’s Optics and parts of Pappus’s Collection, Book 6),less so in catoljtrics, the study of mirrors.’ The problems typically encountered in the surviving writings on catoptrics fall into two classes: those dealing with the reflection of rays cast from a luminous source such as the sun upon minors of plane or curved surface, and those involving the projection of lines of sight from the eye by way of a minor to an object. The most basic problem of the first class, to make a burning mirror, is solved correctly in Diocles’s On Burning Mirrors (ca. 200 B.C.) with both spherical and parabolic mirrors; other prob- lems were investigated by Diocles, by Anthemius (ca. A.D. 620) in his On Paradoxical Devices, and doubtless by other authors in the cen- turies between.2 In general these problems were amenable to geo- metrical treatment in antiquity because Hellenistic geometers were equipped to study the tangent lines to a wide range of curves (or the tangent planes to analogous surfaces) and the behaviour of straight lines in a given direction or through a given point .and inflected at the curve or surface at equal angles to the tangent at the point of in- cidence. Problems of the other class, in which it was required to make an ar- rangement of mirrors or a mirror with a special curvature, such that a *Institute for the History and Philosophy of Science and Technology, Victoria College, Univer- sity of Toronto, Toronto, Canada MSS 1K7. -
The Byzantine Empire (Eastern Roman Empire) Latin
The Byzantine Empire (Eastern Roman Empire) Latin Greek 667 BCE: Greek colonists founded Byzantium 324 CE: Constantine refounded the city as Nova Roma or Constantinople The fall of Rome in 476 ended the western half of Portrait of Constantine, ca. the Roman Empire; the eastern half continued as 315–330 CE. Marble, approx. 8’ the Byzantine Empire, with Constantinople as its 6” high. capital. Early Byzantine Art 6-8th c. The emperor Justinian I ruled the Byzantine Empire from 527 until 565. He is significant for his efforts to regain the lost provinces of the Western Roman Empire, his codification of Roman law, and his architectural achievements. Justinian as world conqueror (Barberini Ivory) Detail: Beardless Christ; Justinian on his horse mid-sixth century. Ivory. The Byzantine Empire , ca 600 Theocracy Government by divine guidance or by officials who are regarded as divinely guided. Justinian as world conqueror (Barberini Ivory), mid-sixth century. Ivory, 1’ 1 1/2” X 10 1/2”. Louvre, Paris. In Orthodox Christianity the central article of faith is the Christ blesses equality of the three aspects the emperor of the Trinity of Father, Son and Holy Spirit. Personificati All other versions of on of Christianity were considered Victory heresies. Personification of Earth Justinian as world conqueror (Barberini Ivory), mid-sixth Barbarians bearing tribute century. Ivory, 1’ 1 1/2” X 10 1/2”. Louvre, Paris. Comparison: Ara Pacis Augustae, Female personification (Tellus; mother earth?), panel from the east facade of the, Rome, Italy, 13–9 BCE. Marble, approx. 5’ 3” high. Comparison: Equestrian statue of Marcus Aurelius, from Rome, Italy, ca. -
Self, Self-Fashioning, and Individuality in Late Antiquity
Culture, Religion, and Politics in the Greco-Roman World Editors Kendra Eshleman (Boston College), Teresa Morgan (University of Oxford), Laura Nasrallah (Yale University), Maren R. Niehoff (The Hebrew University of Jerusalem), and Peter Van Nuffelen (Ghent University) Advisory Board Milette Gaifman (Yale University), Martha Himmelfarb (Princeton University), Hayim Lapin (University of Maryland), Duncan MacRae (University of California, Berkeley), Jörg Rüpke (Universität Erfurt), Lieve Van Hoof (Ghent University) 4 Self, Self-Fashioning, and Individuality in Late Antiquity New Perspectives Edited by Maren R. Niehoff and Joshua Levinson Mohr Siebeck ISBN 978-3-16-158990-4 / eISBN 978-3-16-158991-1 DOI 10.1628/978-3-16-158991-1 ISSN 2510-0785 / eISSN 2568-6623 (Culture, Religion, and Politics in the Greco-Roman World) The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data are available at http://dnb.dnb.de. © 2019 Mohr Siebeck Tübingen, Germany. www.mohrsiebeck.com This book may not be reproduced, in whole or in part, in any form (beyond that permitted by copyright law) without the publisher’s written permission. This applies particularly to repro- ductions, translations and storage and processing in electronic systems. The book was typeset by epline in Böblingen using Minion typeface, printed on non-aging paper by Gulde-Druck in Tübingen, and bound by Buchbinderei Spinner in Ottersweier. Printed in Germany. Acknowledgements It is a great pleasure to acknowledge the institutions and people without whom this volume would never have emerged. The essays collected here are the fruits of an international research group on “Contours of the Self in Ancient Mediter- ranean Cultures,” which worked during the academic year of 2017–18 at the Is- rael Institute for Advanced Studies in Jerusalem. -
Geometry As Made Rigorous by Euclid and Descartes Seminar at Mimar Sinan David Pierce October 31, 2013
Geometry as made rigorous by Euclid and Descartes Seminar at Mimar Sinan David Pierce October 31, 2013 Abstract: For Immanuel Kant (born 1724), the discovery of mathematical proof by Thales of Miletus (born around 624 b.c.e.) is a revolution in human thought. Modern textbooks of analytic geometry often seem to represent a return to pre- revolutionary times. The counterrevolution is attributed to Ren´eDescartes (born 1596). But Descartes understands an- cient Greek geometry and adds to it. He makes algebra rig- orous by interpreting its operations geometrically. The definition of the real numbers by Richard Dedekind (born 1831) makes a rigorous converse possible. David Hilbert (born 1862) spells it out: geometry can be interpreted in the ordered field of real numbers, and even in certain countable ordered fields. In modern textbooks, these ideas are often entangled, mak- ing the notion of proof practically meaningless. I propose to disentangle the ideas by means of Book I of Euclid’s Elements and Descartes’s Geometry. List of Figures 1 Menaechmus’s finding of two mean proportionals . 4 1 2 Descartes’slocusproblem . 4 3 Thelocusitself ........................ 5 4 Descartes’sgeometricalsolution. 5 Mathematicians and commentators Thales of Miletus b. c. 624 Herodotus b. c. 484 Eudoxus b. 408 Aristotle b. 384 Menaechmus b. 380 Euclid fl. 300 Archimedes b. 287 Apollonius b. 262 Pappus fl. 320 Proclus b. 412 Eutocius fl. 500 Isidore of Miletus fl. 532–7 Ren´eDescartes b. 1596 Immanuel Kant b. 1724 Richard Dedekind b. 1831 David Hilbert b. 1862 Introduction Rigor in mathematics is ability to stand up under questioning. -
Heron of Alexandria and the Dome of Hagia Sophia in Istanbul
Proceedings of the Third International Congress on Construction History, Cottbus, May 2009 1387 Heron of Alexandria and the Dome of Hagia Sophia in Istanbul Helge Svenshon Technische Universität Darmstadt, Germany ABSTRACT: Writings have been published under the name of Heron of Alexandria in a long period between the 1st century AD and the Byzantine middle ages. This extensive collection was issued for use by engineers, geodesists, architects as well as for other engineering related professionals and it belongs to the most important sources for the history of the ancient building trade, yet even until today it remains almost entirely overlooked. These manuals, conceived for a wider specialised readership and broadly known, also contain the mathematical and technical prerequisites, that were essential to professionally realise the concept of a building. The groundwork for this, is found in a mathematical tradition, that has been almost consistently passed down from Old-Babylonian times to the geometrical treatises of the early modern times. The comparison between Heron's texts with singular, well-preserved buildings and especially the Hagia Sophia in Istanbul, demonstrates the degree of influence this neglected source has had on the technical and built environment of antiquity. INTRODUCTION The broad reception of Roman architecture theorist Vitruvius, within architectural history, has notably contributed to scientific disregard for fields of knowledge, crucial for understanding the production of ancient architecture. While he presents a multitude of conceptual recipes for modular, ideal type architecture in his work, which had little impact in its time, further questions concerning the mathematical and technical groundwork essential for the transformation of the presented concepts into real structures were left unanswered, that is the practical realisation at the building site in all its various manifestations, such as building surveys, construction and logistics. -
A Concise History of the Philosophy of Mathematics
A Thumbnail History of the Philosophy of Mathematics "It is beyond a doubt that all our knowledge begins with experience." - Imannuel Kant ( 1724 – 1804 ) ( However naïve realism is no substitute for truth [1] ) [1] " ... concepts have reference to sensible experience, but they are never, in a logical sense, deducible from them. For this reason I have never been able to comprehend the problem of the á priori as posed by Kant", from "The Problem of Space, Ether, and the Field in Physics" ( "Das Raum-, Äether- und Feld-Problem der Physik." ), by Albert Einstein, 1934 - source: "Beyond Geometry: Classic Papers from Riemann to Einstein", Dover Publications, by Peter Pesic, St. John's College, Sante Fe, New Mexico Mathematics does not have a universally accepted definition during any period of its development throughout the history of human thought. However for the last 2,500 years, beginning first with the pre - Hellenic Egyptians and Babylonians, mathematics encompasses possible deductive relationships concerned solely with logical truths derived by accepted philosophic methods of logic which the classical Greek thinkers of antiquity pioneered. Although it is normally associated with formulaic algorithms ( i.e., mechanical methods ), mathematics somehow arises in the human mind by the correspondence of observation and inductive experiential thinking together with its practical predictive powers in interpreting future as well as "seemingly" ephemeral phenomena. Why all of this is true in human progress, no one can answer faithfully. In other words, human experiences and intuitive thinking first suggest to the human mind the abstract symbols for which the economy of human thinking mathematics is well known; but it is those parts of mathematics most disconnected from observation and experience and therefore relying almost wholly upon its internal, self - consistent, deductive logics giving mathematics an independent reified, almost ontological, reality, that mathematics most powerfully interprets the ultimate hidden mysteries of nature. -
Geometry, Light, and Cosmology in the Church of Hagia Sophia Wassim Jabi and Iakovos Potamianos
Chapter 07 16/7/07 12:32 pm Page 304 Geometry, Light, and Cosmology in the Church of Hagia Sophia Wassim Jabi and Iakovos Potamianos Designed by a physicist and a mathematician, the Hagia Sophia church in Istanbul,Turkey acted as an experimental test case in which advanced knowledge of geometrical constructs, sophisticated understanding of light behavior, and religious and cosmological beliefs combined to create a magnificent structure.While some of its design concepts are known, many remain hidden. Earthquakes have demolished parts of the church—such as the original dome. Researchers have in the past misinterpreted their observations and perpetuated false conclusions. Lastly, the lack of digital tools has until now prevented verification and analysis of prior findings. In this paper, we integrate traditional historical research, parametric digital analysis, and lighting simulation to analyze several aspects of the church. In particular, we focus on the geometry of the floor plan, the geometry of the apse, and light behavior in the original dome. Our findings point to the potential of digital tools in the discovery of a structure’s hidden features and design rules. 304 Chapter 07 16/7/07 12:32 pm Page 305 1. Introduction The Hagia Sophia church was built during the years 532–537 by the Byzantine emperor Justinian and designed by Isidore of Miletus and Anthemius of Tralles—a physicist and a mathematician respectively [1]. Its dedication to Hagia Sophia, did not refer to any saint by that name but to Christ as the Wisdom (Sophia) or Word of God made flesh, which is confirmed by the fact that the patronal feast was celebrated at Christmas, on December 25th [2], [3].This was the imperial church in which most major celebrations were held [A]. -
Reflections on the Antikythera Mechanism Inscriptions
ARTICLE IN PRESS Available online at www.sciencedirect.com Advances in Space Research xxx (2009) xxx–xxx www.elsevier.com/locate/asr Reflections on the antikythera mechanism inscriptions Maria K. Papathanassiou Faculty of Mathematics, National and Kapodistrian University of Athens, Athens, Greece Received 10 January 2008; received in revised form 30 April 2008; accepted 2 May 2008 Abstract A close look at the fragmentary inscriptions of the Antikythera Mechanism published by Freeth et al. [Freeth, T., Bitsakis, Y., Moussas, X., Seiradakis, J.H., Tselikas, A., Magkou, E., Zafeiropoulou, M., Hadland, R., Bate, D., Ramsey, A., Allen, M., Crawley, A., Hockley, P., Malzbender, T., Gelb, D., Ambrisco, W., Edmunds, M.G. Decoding the Antikythera mechanism: investigation of an ancient astronomical calculator. Nature 444 (7119), 587–591, 2006] reveals some elements, which could help to decode its function and use. The Back Door Inscription seems to give a detailed description of some external parts of the instrument and the related instructions for their use. We especially refer to the term «ecliptic» as compared to that in Ars Eudoxi and other papyri and inscriptions. The Back Plate Inscription seems to give instructions for the proper orientation and use of the instrument. The Front Door Inscription refers to the sta- tionary points of planetary motion, but only two planetary names have been read, that of Venus and Mercury, as far as we know. After a study of the works of Alexandrian scholars Ptolemy, Theon, Paulus and Heliodorus regarding the -
Archimedes - Wikipedia, the Free Encyclopedia
Archimedes - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Archimedes Archimedes From Wikipedia, the free encyclopedia Archimedes of Syracuse (Greek: Ἀρχιμήδης; Archimedes of Syracuse c. 287 BC – c. 212 BC) was a Greek (Greek: Ἀρχιμήδης) mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.[1] Archimedes is generally considered to be the greatest mathematician of antiquity and one of Archimedes Thoughtful by Fetti (1620) the greatest of all time.[2][3] He used the Born method of exhaustion to calculate the area c. 287 BC Syracuse, Sicily under the arc of a parabola with the summation Magna Graecia of an infinite series, and gave a remarkably Died accurate approximation of pi.[4] He also c. 212 BC (aged around 75) Syracuse defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and Residence Syracuse, Sicily an ingenious system for expressing very large Fields Mathematics, Physics, Engineering, Astronomy, numbers. Invention Known for Archimedes' Principle, Archimedes' screw, Archimedes died during the Siege of Syracuse Hydrostatics, Levers, Infinitesimals when he was killed by a Roman soldier despite orders that he should not be harmed.