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Pedro Nunes and the Retrogression of the Sun
Pedro Nunes and the Retrogression of the Sun Peter Lynch School of Mathematics & Statistics University College Dublin Irish Mathematical Society, Annual Meeting IT Sligo, 31 August 2017 Outline Introduction Pedro Nunes Analysis of Solar Retrogression Variation of the Azimuthal Angle Sources Intro Nunes Regression Variation Refs Outline Introduction Pedro Nunes Analysis of Solar Retrogression Variation of the Azimuthal Angle Sources Intro Nunes Regression Variation Refs Background How I learned about this question. I Recreational Maths Conference in Lisbon. I Henriques Leitão gave a talk on Pedro Nunes. I Claim: The Sun sometimes reverses direction. I My reaction was one of scepticism. I Initially, I could not prove the result. I Later I managed to prove retrogression occurs. I I hope that I can convince you of this, too. Intro Nunes Regression Variation Refs Things We All Know Well I The Sun rises in the Eastern sky. I It follows a smooth and even course. I It sets in the Western sky. The idea that the compass bearing of the Sun might reverse seems fanciful. But that was precisely what Portuguese mathematician Pedro Nunes showed in 1537. Intro Nunes Regression Variation Refs Obelisk serving as a Gnomon Path of Sun traces a hyperbola Intro Nunes Regression Variation Refs Nunes made an amazing prediction: In certain circumstances, the shadow cast by the gnomon of a sun dial moves backwards. Nunes’ prediction was counter-intuitive: We expect the azimuthal angle to increase steadily. If the shadow on the sun dial moves backwards, the Sun must reverse direction or retrogress. Nunes’ discovery came long before Newton or Galileo or Kepler, and Copernicus had not yet published his heliocentric theory. -
The History of Cartography, Volume 3
THE HISTORY OF CARTOGRAPHY VOLUME THREE Volume Three Editorial Advisors Denis E. Cosgrove Richard Helgerson Catherine Delano-Smith Christian Jacob Felipe Fernández-Armesto Richard L. Kagan Paula Findlen Martin Kemp Patrick Gautier Dalché Chandra Mukerji Anthony Grafton Günter Schilder Stephen Greenblatt Sarah Tyacke Glyndwr Williams The History of Cartography J. B. Harley and David Woodward, Founding Editors 1 Cartography in Prehistoric, Ancient, and Medieval Europe and the Mediterranean 2.1 Cartography in the Traditional Islamic and South Asian Societies 2.2 Cartography in the Traditional East and Southeast Asian Societies 2.3 Cartography in the Traditional African, American, Arctic, Australian, and Pacific Societies 3 Cartography in the European Renaissance 4 Cartography in the European Enlightenment 5 Cartography in the Nineteenth Century 6 Cartography in the Twentieth Century THE HISTORY OF CARTOGRAPHY VOLUME THREE Cartography in the European Renaissance PART 1 Edited by DAVID WOODWARD THE UNIVERSITY OF CHICAGO PRESS • CHICAGO & LONDON David Woodward was the Arthur H. Robinson Professor Emeritus of Geography at the University of Wisconsin–Madison. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2007 by the University of Chicago All rights reserved. Published 2007 Printed in the United States of America 1615141312111009080712345 Set ISBN-10: 0-226-90732-5 (cloth) ISBN-13: 978-0-226-90732-1 (cloth) Part 1 ISBN-10: 0-226-90733-3 (cloth) ISBN-13: 978-0-226-90733-8 (cloth) Part 2 ISBN-10: 0-226-90734-1 (cloth) ISBN-13: 978-0-226-90734-5 (cloth) Editorial work on The History of Cartography is supported in part by grants from the Division of Preservation and Access of the National Endowment for the Humanities and the Geography and Regional Science Program and Science and Society Program of the National Science Foundation, independent federal agencies. -
Jaarverslag 2019 Embassy of the Free Mind Jaarverslag 2019 Embassy of the Free Mind Inhoudsopgave
JAARVERSLAG 2019 EMBASSY OF THE FREE MIND JAARVERSLAG 2019 EMBASSY OF THE FREE MIND INHOUDSOPGAVE RESULTATEN 2019 5 CIJFERS STICHTING HET WERELDHART 6 CIJFERS STICHTING BIBLIOTHECA PHILOSOPHICA HERMETICA 10 RESULTATEN 2019 EMBASSY OF THE FREE MIND FINANCIËN COMMUNICATIE ¤ Tentoonstelling: KABBALA & ¤ Totale lasten: organisatie ¤ Online community van 62.931 ALCHEMIE: 13-6 t/m 16-11 i.s.m € 627.605, projecten € 215.880 naar 80.176 gegroeid (+30%) de Ets Haim bibliotheek van ¤ Ontvangen periodieke ¤ 40% van de Instagram het Joods Cultureel Kwartier schenkingen: € 875.000 volgers zijn tussen de 25 en Tentoonstelling: OOG VOOR ¤ Ontvangen donaties bedrijven 34 jaar oud, van de fysieke DE WERELD. De visionaire € 158.747 museumbezoekers is 30% tussen denker Jacob Böhme: 14-12-19 ¤ Ontvangen losse donaties de 18 – 34 jaar oud t/m 18-4-20 i.s.m de Staatliche particulieren €8.489 ¤ Youtube: 11 nieuwe video’s, Kunstsammlungen Dresden ¤ Vriendenstructuur: € 12.355 incl. gratis live streams ¤ Programmering met totaal ontvangen van vrienden, pioniers van evenementen, met 63 unieke evenementen en patronen en € 70.000 van als populairste video de zoals lezingen, concerten, vrijdenkers lezing ‘Lecture, ‘Kabbalah, conferenties, cursussen en ¤ Inkomsten uit zaalhuur: € 33.740 messianism and magic’ - Part I’, Museumnacht ¤ Restauratie voorgevel: € 170.000, 1.600 views ¤ 1203 aanmeldingen voor gedekt door bijdragen van fondsen ¤ Pers: Trouw, rondleidingen (Oude Boek, Capitalavecmanagement. algemeen, kinderen, fr, Glamour.nl, AVclub.nl, thematisch) Boingboing.net, -
Jfr Mathematics for the Planet Earth
SOME MATHEMATICAL ASPECTS OF THE PLANET EARTH José Francisco Rodrigues (University of Lisbon) Article of the Special Invited Lecture, 6th European Congress of Mathematics 3 July 2012, KraKow. The Planet Earth System is composed of several sub-systems: the atmosphere, the liquid oceans and the icecaps and the biosphere. In all of them Mathematics, enhanced by the supercomputers, has currently a key role through the “universal method" for their study, which consists of mathematical modeling, analysis, simulation and control, as it was re-stated by Jacques-Louis Lions in [L]. Much before the advent of computers, the representation of the Earth, the navigation and the cartography have contributed in a decisive form to the mathematical sciences. Nowadays the International Geosphere-Biosphere Program, sponsored by the International Council of Scientific Unions, may contribute to stimulate several mathematical research topics. In this article, we present a brief historical introduction to some of the essential mathematics for understanding the Planet Earth, stressing the importance of Mathematical Geography and its role in the Scientific Revolution(s), the modeling efforts of Winds, Heating, Earthquakes, Climate and their influence on basic aspects of the theory of Partial Differential Equations. As a special topic to illustrate the wide scope of these (Geo)physical problems we describe briefly some examples from History and from current research and advances in Free Boundary Problems arising in the Planet Earth. Finally we conclude by referring the potential impact of the international initiative Mathematics of Planet Earth (www.mpe2013.org) in Raising Public Awareness of Mathematics, in Research and in the Communication of the Mathematical Sciences to the new generations. -
The Spherical Spiral
The Spherical Spiral Chris Wilson and Geoff Zelder Multivariable Calculus-50C College of the Redwoods 08 Dec. 2008 Abstract Just about everyone is familiar with sirals in two dimensions but not often is a spiral seen as navigating a 3 dimensional sphere. Suprisingly there a several groundbreaking applications of the spherical spiral and with minor adjustments many three dimensional curves can be obtained from the basic equation of the spherical spiral. 1 Spherical Coordinates The spherical spiral is very similar to a sphere in spherical coordinates and actually relatively simple using spherical coordinates. The basic equations for spherical coordinates are: x = ρ sin φ cos θ y = ρ sin φ sin θ z = ρ cos φ By letting φ run from 0 to π, and by letting θ run from 0 to 2π this creates a perfect shpere. The Spherical Spiral The spiral is very similar in it's equations as we let, x = ρ cos θ cos φ y = ρ sin θ cos φ z = − sin φ In this case we let θ run from 0 to kπ where the greater k is the more times the spiral will circumnavigate the sphere. We let φ = tan−1 aβ, where a determines how far apart the spirals are and β determines how high up and down the spirals start. In a sense a determines and increment of angle that φ will range through and the β determines the start and stop angles of φ. Parametrizing the Spherical Spiral The spherical sprial can be parametretrized into terms of t and finally we arrive at, x = p cos t 1+α2t2 y = p sin t 1+α2t2 z = p αt 1+α2t2 Here α is the angle along the longitude and t is the legth of the trip. -
Centro Region, Portugal Challenges
© Turismo Centro Portugal © Turismo Centro Region Rural Centro Region, Portugal Village General overview Situated in the geographic centre of Portugal, the 8.9% of the gross domestic product (1). Centro Region occupies a strategic position in Portugal is not regionalized (except for the the country, with the city of Coimbra serving as Autonomous Region of the Azores and the its main educational, cultural and health-services Autonomous Region of Madeira) and its health centre. The city prides itself on being the location system follows a strong model of central of one of Europe’s oldest and most distinguished governance and financing, according to universities (the University of Coimbra, established which five administrative health regions were in 1290), Portugal’s largest hospital (Coimbra established in 1993. Each region has its own University Hospital Centre, which belongs to health administration board, answerable to the the National Health Service), the oldest and Minister of Health, and assumes responsibility largest Portuguese nursing school (Coimbra’s for the management of population health and the Nursing School), and one of the best science- provision of health-care services. The regional based incubators in the world (Pedro Nunes health administration of the Centro Region Institute). These institutions share a long history of is carried out by the Central Regional Health delivering much admired education, research and Administration, which is responsible for the transversality in the fields of medicine, health-care implementation of national health policies and services, and health sciences and technologies. the coordination of all levels of health care at the Since 2015, the consortium, Coimbra Health, regional level, in accordance with the current established by the University of Coimbra and the National Health Plan. -
Press Release Kabbalah & Alchemy
Kabbalah & Alchemy Exhibition Embassy of the Free Mind 13 June - 16 November 2019 The Embassy of the Free Mind (EFM) is proud to present its first exhibition in its new premises The House with the Heads: Kabbalah & Alchemy, which is on show from 13 June -16 November 2019. The EFM is a library, a museum and a platform for free thinking. Kabbalah and alchemy were traditionally regarded as hidden currents in European cultural history. The EFM wishes to explore with this exhibition the relatively unknown relationship between these two disciplines by means of richly illustrated manuscripts and printed books from the 16th-18th centuries, deriving from its Bibliotheca Philosophica Hermetica Collection and seven special Hebrew loans from the Amsterdam Ets Haim – Livraria Montezinos, the oldest still functioning Jewish library in the world. Closer to God Kabbalah is a Jewish mystical tradition that was passed down from generation to generation in circles of adepts. Kabbalists based themselves on the assumption that the Hebrew language was divine in origin, the language also in which God had created heaven and earth. By meditating on the letters of the Hebrew alphabet and the various divine names, kabbalists hoped to be able to come closer to God. The mystical longing to know God is also reflected in the image of the tree of life, represented in the exhibition by the oldest known printed woodcut from 1516. The ten divine attributes - Hebrew: sefirot – of this tree of life are the attributes through which God reveals himself to man. From lead to gold Alchemy has its roots in the Graeco-Roman Egypt of the first centuries CE. -
ESSWE Newsletter Vol. 12, No. 1 (Winter / Spring 2021)
Image: Detail from Robert Vaughan (c.1600 -1660), Engraved illustration depicting two men, one seated and one kneeling below two celestial, winged angels, n.d.. Mixed material, 19cm. Beinecke Library. 1 Words from the Editor 2 Letter by the President of ESSWE to the Members 3 New Publications from ESSWE Members 8 Scholar Interviews 9 PhD Project Features 11 News from the HHP 12 Upcoming Events Words from the Editor PhD projects of Sólveig Guðmundsdóttir and Matt Wiemers are featured. Dr. Marco Pasi also brings us updates from the HHP. Finally, there are several updates on upcoming Zoom events this year. As a new Chloe Sugden season is very soon upon us, I’ll leave you with some springtime promises from William Blake: Welcome to the Winter / Spring 2021 edition of the ESSWE Newsletter! I hope that you are all keeping well, despite the malaise of The Sun does arise, this ceaseless pandemic. With great pleasure, I continue the work And make happy the skies. of our previous editors: my friends and colleagues, Dr. Christian The merry bells ring Giudice and Dr. Per Faxneld. Thanks to the Board and designer, Boris To welcome the Spring. Fernandez, we have a refreshed layout. The structure of the Newsletter The sky-lark and thrush, remains unchanged, though I have reintroduced the ‘PhD Projects The birds of the bush, Features’ section and altered the ‘New Publications’ section to include Sing louder around, occasional author and editor interviews. To the bells’ cheerful sound. While our sports shall be seen This edition, ESSWE President Dr. Andreas Kilcher makes several On the Echoing Green. -
Beleidsplan 2018-2020 + Jaarverslag 2017
JAARVERSLAG 2017 BELEIDSPLAN 2018-2020 INHOUDSOPGAVE EMBASSY OF THE FREE MIND 5 MISSIE, VISIE & REALISATIE 9 HET AMSTERDAMSE DNA VAN DE EMBASSY OF THE FREE MIND 11 VIJF KERNWAARDEN VAN DE EMBASSY OF THE FREE MIND 14 RESULTATEN 2017 17 ORGANISATIE 18 FINANCIËN & VRIENDENSTRUCTUUR 20 MARKETING & COMMUNICATIE 22 COLLECTIE 24 OVERZICHT VAN DE COLLECTIE 34 UNIEKE AANWINST IN 2017 37 PHOENIX FONDS 39 HUIS MET DE HOOFDEN 41 MUSEUM 44 UITBREIDING MUSEUMBIBLIOTHEEK 50 KENNISCENTRUM 52 VERANTWOORDING ILLUSTRATIES 62 FINANCIËLE BIJLAGEN 65 EMBASSY OF THE FREE MIND In dit jaarverslag 2017 & beleidsplan 2018- inzicht te verkrijgen in de werkelijkheid 2020 willen we je kennis laten maken met waarin we leven en bieden een manier de Embassy of the Free Mind (EFM), een om daar op strikt individuele manier initiatief van de culturele ANBI-stichting Het invulling aan te geven. Als wetenschapper, Wereldhart (WH). kunstenaar, denker of doener, kind of volwassene. Wij willen een platform bieden Amsterdam is een stad met diversiteit, aan iedereen die op ons specialisatieterrein authenticiteit, creativiteit en actief is en een ieder die dit graag breder wil ondernemerschap. Veel Amsterdammers, en helpen uitdragen. ook toeristen, ondernemers en studenten, voelen zich aangetrokken tot de geest Na dertig jaar als publiek toegankelijke van vrijheid die er heerst. De vrijheid wetenschappelijke onderzoeksbibliotheek van het woord kreeg in deze stad – die al in de Bloemstraat in Amsterdam gevestigd in de befaamde Gouden Eeuw in open te zijn geweest, zijn we nu ook officieel een communicatie stond met de rest van de museum. En dat bovendien op een heel wereld - vleugels door de vrijheid van prominente locatie in Amsterdam: het godsdienst, meningsuiting en drukpers. -
The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France Edited by Alexander Marr Donington, UK: Shaun Tyas, 2009
The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France edited by Alexander Marr Donington, UK: Shaun Tyas, 2009. Pp. xvi+224. ISBN 978--1900289-- 96--2.Cloth £40.00 Reviewed by Bernardo Mota Universidade Lisboa/Technische Universität Berlin [email protected] This is a collection of papers first presented at a conference entitled ‘The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France’ and held in the School of Art History, University of St Andrews, 12--14 May 2006. Its goal is [to] bring this much neglected polymath [Oronce Fine] to the attention of a new audience. The essays gathered here aim to cast fresh light on Fine and his myriad activities, plac- ing him within the broad socio-intellectual context of Renais- sance Europe and demonstrating his important contribution to the worlds of mathematics, instruments, and print. [9--10] The introduction [ch. 1] and epilogue [ch. 13] are excellent in uni- fying the content of the essays. Alexander Marr (introduction) briefly describes the scholarship about Fine and explains the need to reevalu- ate the role of this mathematician. Fine’s biography is presented and a short abstract of each paper is added. Stephen Clucas (epilogue) gathers the main ideas stressed through the book. Chapters 2 and 3 show how Fine fought for a strong institu- tional and epistemological foothold for ‘embedding mathematics in sixteenth-century French intellectual culture’ [10]. Isabelle Pantin looks at the material context of Fine’s teaching (his appointment, the teaching of mathematics at the Collège Royal, the program of studies that he promoted) and Angela Axworthy looks at Fine’s epis- temological views on the status of mathematics, inscribing them in the tradition that extends from Antiquity to the celebrated Quaes- tio de certitudine mathematicarum. -
Pedro Nunes and the Retrogression of the Sun Introduction in Northern
Irish Math. Soc. Bulletin Number 81, Summer 2018, 23{30 ISSN 0791-5578 Pedro Nunes and the Retrogression of the Sun PETER LYNCH What has been will be again, what has been done will be done again; there is nothing new under the sun. Ecclesiastes 1:9 Introduction In northern latitudes we are used to the Sun rising in the East, following a smooth and even course through the southern sky and setting in the West. The idea that the compass bearing of the Sun might reverse seems fanciful. But that was precisely what Por- tuguese mathematician Pedro Nunes showed in 1537. Nunes made an amazing prediction: in certain circumstances, the shadow cast by the gnomon of a sun dial moves backwards. Nunes' prediction was counter-intuitive. We are all familiar with the steady progress of the Sun across the sky and we expect the az- imuthal angle or compass bearing to increase steadily. If the shadow on the sun dial moves backwards, the Sun must reverse direction or retrogress. Nunes' discovery came long before Newton or Galileo or Kepler, and Copernicus had not yet published his heliocentric the- ory. The retrogression had never been seen by anyone and it was a remarkable example of the power of mathematics to predict physical behaviour. Nunes himself had not seen the effect, nor had any of the tropical navigators or explorers whom he asked. Nunes was aware of the link between solar regression and the bib- lical episode of the sun dial of Ahaz (Isaiah, 38:7{9). However, what he predicted was a natural phenomenon, requiring no miracle. -
Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics
Studies in Logic Volume 26 Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics Volume 17 Reasoning in Simple Type Theory. Festschrift in Honour of Peter B. Andrews on His 70th Birthday. Christoph Benzmüller, Chad E. Brown and Jörg Siekmann, eds. Volume 18 Classification Theory for Abstract Elementary Classes Saharon Shelah Volume 19 The Foundations of Mathematics Kenneth Kunen Volume 20 Classification Theory for Abstract Elementary Classes, Volume 2 Saharon Shelah Volume 21 The Many Sides of Logic Walter Carnielli, Marcelo E. Coniglio, Itala M. Loffredo D’Ottaviano, eds. Volume 22 The Axiom of Choice John L. Bell Volume 23 The Logic of Fiction John Woods, with a Foreword by Nicholas Griffin Volume 24 Studies in Diagrammatology and Diagram Praxis Olga Pombo and Alexander Gerner Volume 25 The Analytical Way: Proceedings of the 6th European Congress of Analytical Philosophy Tadeusz Czarnecki, Katarzyna Kijania-Placek, Olga Poller and Jan Woleski , eds. Volume 26 Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics Albrecht Heeffer and Maarten Van Dyck, eds. Studies in Logic Series Editor Dov Gabbay [email protected] Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics Edited by Albrecht Heeffer and Maarten Van Dyck © Individual author and College Publications 2010. All rights reserved. ISBN 978-1-84890-017-2 College Publications Scientific Director: Dov Gabbay Managing Director: Jane Spurr Department of Computer Science King’s College London, Strand, London WC2R 2LS, UK http://www.collegepublications.co.uk Original cover design by orchid creative www.orchidcreative.co.uk Printed by Lightning Source, Milton Keynes, UK All rights reserved.