9 · the Growth of an Empirical Cartography in Hellenistic Greece
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The Mediterranean: One Sea, Many Names
The 14th International Seminar on Sea Names Geography, Sea Names, and Undersea Feature Names The Mediterranean: One sea, many names Pokoly Bela (Senior Adviser, Committee on Geographical Names, Ministry of Agriculture and Regional Development, Hungary) 1.An Important Sea 1.1. The Mediterranean Sea, covering an area of 2,5 million sq. kms, holds its importance in its geographical position. Wedged between Europe, Asia and Africa, it is lined by no less than 21 independent states. Of all countries of the world at least one in ten has a coastline along its shores. Fig. 1. The Countries around the Mediterranean Sea 1.2. Indeed the sea has, over the centuries, lost some of its overwhelming position. With the expanding contacts to the Far East and with the exploration of the „new” continents, it was realized that it is no longer the centre of earth. 1.3 With the opening of the Suez Canal, with the discoveries of vastly important oil and gas deposits in the Middle East, and with expanding international contacts and tourism it has witnessed a comeback in the past two centuries. 2. It is not possible to highlight all aspects of this sea however, so I need to look some aspects of its naming. 2.1. As with all seas, local people of ancient times, unaware of other seas called it The 324 The 14th International Seminar on Sea Names Geography, Sea Names, and Undersea Feature Names Sea. Similarly with other seas, it was also called Great Sea by local peoples living along its shores. 2.2. -
The Corvus, the Roman Boarding Device
Wright State University CORE Scholar Classics Ancient Science Fair Religion, Philosophy, and Classics Spring 2020 The Corvus, the Roman Boarding Device Jacob Stickel Wright State University - Main Campus, [email protected] Follow this and additional works at: https://corescholar.libraries.wright.edu/ancient_science_fair Part of the Ancient History, Greek and Roman through Late Antiquity Commons, History of Science, Technology, and Medicine Commons, and the Military History Commons Repository Citation Stickel , J. (2020). The Corvus, the Roman Boarding Device. Dayton, Ohio. This Presentation is brought to you for free and open access by the Religion, Philosophy, and Classics at CORE Scholar. It has been accepted for inclusion in Classics Ancient Science Fair by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. A philological examination of Eratosthenes’ calculation of Earth’s circumference Kelly Staver1 1 Wright State University, Dayton, Ohio, U.S.A. Introduction Errors in Eratosthenes ’ Assumptions Historical Inconsistencies of Eratosthenes’ Final Result • A Greek mathematician named Eratosthenes calculated an accurate measurement Two of Eratosthene’s five assumtpions are either mistaken or questionable at • Cleomedes and John Philophus state Eratosthenes’ result was 250,000, whereas of the Earth’s circumference, that being 250,000 stades or close to Earth’s actual best: many others such as Vitruvius, Martianus Capella, Strabo, and many others state circumference of 40,120 km,¹ in Hellenistic Alexandria, Egypt circa 240 B.C.E.² • Assumption (1) is incorrect. The longitudinal difference between it was 252,000 stades.¹⁴ • To do this, Eratosthenes’ utilized the distance between Alexandria and Syene and Syene and Alexandria is about 3 degrees.⁶ • Benefits of 252,000 stades: gnomon measurements taken in Syene and Alexandria at noon on the summer • Assumption (2) is questionable since we do not know how long a • Yields a clean 700 stades per circular degree.¹⁵ solstice.³ stadion is. -
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 -
Configurations on Centers of Bankoff Circles 11
CONFIGURATIONS ON CENTERS OF BANKOFF CIRCLES ZVONKO CERINˇ Abstract. We study configurations built from centers of Bankoff circles of arbelos erected on sides of a given triangle or on sides of various related triangles. 1. Introduction For points X and Y in the plane and a positive real number λ, let Z be the point on the segment XY such that XZ : ZY = λ and let ζ = ζ(X; Y; λ) be the figure formed by three mj utuallyj j tangenj t semicircles σ, σ1, and σ2 on the same side of segments XY , XZ, and ZY respectively. Let S, S1, S2 be centers of σ, σ1, σ2. Let W denote the intersection of σ with the perpendicular to XY at the point Z. The figure ζ is called the arbelos or the shoemaker's knife (see Fig. 1). σ σ1 σ2 PSfrag replacements X S1 S Z S2 Y XZ Figure 1. The arbelos ζ = ζ(X; Y; λ), where λ = jZY j . j j It has been the subject of studies since Greek times when Archimedes proved the existence of the circles !1 = !1(ζ) and !2 = !2(ζ) of equal radius such that !1 touches σ, σ1, and ZW while !2 touches σ, σ2, and ZW (see Fig. 2). 1991 Mathematics Subject Classification. Primary 51N20, 51M04, Secondary 14A25, 14Q05. Key words and phrases. arbelos, Bankoff circle, triangle, central point, Brocard triangle, homologic. 1 2 ZVONKO CERINˇ σ W !1 σ1 !2 W1 PSfrag replacements W2 σ2 X S1 S Z S2 Y Figure 2. The Archimedean circles !1 and !2 together. -
Implementing Eratosthenes' Discovery in the Classroom: Educational
Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas Decamp, C. de Hosson To cite this version: Nicolas Decamp, C. de Hosson. Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention. Science and Education, Springer Verlag, 2012, 21 (6), pp.911-920. 10.1007/s11191-010-9286-3. hal-01663445 HAL Id: hal-01663445 https://hal.archives-ouvertes.fr/hal-01663445 Submitted on 18 Dec 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. Sci & Educ DOI 10.1007/s11191-010-9286-3 Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas De´camp • Ce´cile de Hosson Ó Springer Science+Business Media B.V. 2010 Abstract This paper presents a critical analysis of the accepted educational use of the method performed by Eratosthenes to measure the circumference of Earth which is often considered as a relevant means of dealing with issues related to the nature of science and its history. This method relies on a number of assumptions among which the parallelism of sun rays. The assumption of sun rays parallelism (if it is accurate) does not appear spontaneous for students who consider sun rays to be divergent. -
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https://ntrs.nasa.gov/search.jsp?R=19710025504 2020-03-11T22:36:49+00:00Z View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NASA Technical Reports Server General Disclaimer One or more of the Following Statements may affect this Document This document has been reproduced from the best copy furnished by the organizational source. It is being released in the interest of making available as much information as possible. This document may contain data, which exceeds the sheet parameters. It was furnished in this condition by the organizational source and is the best copy available. This document may contain tone-on-tone or color graphs, charts and/or pictures, which have been reproduced in black and white. This document is paginated as submitted by the original source. Portions of this document are not fully legible due to the historical nature of some of the material. However, it is the best reproduction available from the original submission. Produced by the NASA Center for Aerospace Information (CASI) 6 X t B ICC"m date: July 16, 1971 955 L'Enfant Plaza North, S. W Washington, D. C. 20024 to Distribution B71 07023 from. J. W. Head suhiecf Derivation of Topographic Feature Names in the Apollo 15 Landing Region - Case 340 ABSTRACT The topographic features in the region of the Apollo 15 landing site (Figure 1) are named for a number of philosophers, explorers and scientists (astronomers in particular) representing periods throughout recorded history. It is of particular interest that several of the individuals were responsible for specific discoveries, observations, or inventions which considerably advanced the study and under- standing of the moon (for instance, Hadley designed the first large reflecting telescope; Beer published classic maps and explanations of the moon's surface). -
The University of Western Ontario Department of Philosophy Comprehensive Exam Reading List Early Modern Philosophy (1580-1800)
The University of Western Ontario Department of Philosophy Comprehensive Exam Reading List Early Modern Philosophy (1580-1800) Michael Montaigne. “Apology for Raymond Sebond.” Translated by Roger Ariew and Marjorie Grene. Indianapolis: Hackett Publishing, 2003. [164] Rene Descartes. Meditations on First Philosophy and The Second and Fourth Sets of Objections and Replies. Volume 2 of The Philosophical Writings of Descartes. Translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press, 1984. [133] Thomas Hobbes. Leviathan. Edited by Edwin Curley. Indianapolis: Hackett Publishing, 1994. Parts I and II. [239] Baruch Spinoza. The Ethics. In Baruch Spinoza: Ethics, Treatise on the Emendation of the Intellect and Selected Letters. Translated by Samuel Shirley. Indianapolis: Hackett Publishing, 1992. Parts I and II. [70] Nicolas Malebranche. Search after Truth. In Nicolas Malebranche: Philosophical Selections. Edited by Steven Nadler. Indianapolis: Hackett Publishing, 1992. [144] G.W. Leibniz. “Primary Truths,” “Discourse on Metaphysics,” “The Correspondence with Arnauld” and “The Principles of Nature and Grace.” In G.W. Leibniz: Philosophical Essays. Translated by Roger Ariew and Daniel Garber. Indianapolis: Hackett Publishing, 1989. [65] John Locke. An Essay concerning Human Understanding. Edited by Kenneth Winkler. Indianapolis: Hackett Publishing, 1996. II.i-xxxiii, III.iii and vi, and IV.i-iv and xi- xvi. [217] John Locke. Two Treaties of Government. Edited by Peter Laslett. Cambridge: Cambridge University Press, 1960. Second Treatise. [161] The British Moralists (Shaftesbury, Mandeville, Hutcheson, and Butler). The British Moralists 1650-1800. Volume 1, Hobbes – Gay. Edited by D.D. Raphael. Pp. 169- 188, 229-236, 261-299, and 325-364. [73] Pierre Bayle. -
Archaeology and History of Lydia from the Early Lydian Period to Late Antiquity (8Th Century B.C.-6Th Century A.D.)
Dokuz Eylül University – DEU The Research Center for the Archaeology of Western Anatolia – EKVAM Colloquia Anatolica et Aegaea Congressus internationales Smyrnenses IX Archaeology and history of Lydia from the early Lydian period to late antiquity (8th century B.C.-6th century A.D.). An international symposium May 17-18, 2017 / Izmir, Turkey ABSTRACTS Edited by Ergün Laflı Gülseren Kan Şahin Last Update: 21/04/2017. Izmir, May 2017 Websites: https://independent.academia.edu/TheLydiaSymposium https://www.researchgate.net/profile/The_Lydia_Symposium 1 This symposium has been dedicated to Roberto Gusmani (1935-2009) and Peter Herrmann (1927-2002) due to their pioneering works on the archaeology and history of ancient Lydia. Fig. 1: Map of Lydia and neighbouring areas in western Asia Minor (S. Patacı, 2017). 2 Table of contents Ergün Laflı, An introduction to Lydian studies: Editorial remarks to the abstract booklet of the Lydia Symposium....................................................................................................................................................8-9. Nihal Akıllı, Protohistorical excavations at Hastane Höyük in Akhisar………………………………10. Sedat Akkurnaz, New examples of Archaic architectural terracottas from Lydia………………………..11. Gülseren Alkış Yazıcı, Some remarks on the ancient religions of Lydia……………………………….12. Elif Alten, Revolt of Achaeus against Antiochus III the Great and the siege of Sardis, based on classical textual, epigraphic and numismatic evidence………………………………………………………………....13. Gaetano Arena, Heleis: A chief doctor in Roman Lydia…….……………………………………....14. Ilias N. Arnaoutoglou, Κοινὸν, συμβίωσις: Associations in Hellenistic and Roman Lydia……….……..15. Eirini Artemi, The role of Ephesus in the late antiquity from the period of Diocletian to A.D. 449, the “Robber Synod”.……………………………………………………………………….………...16. Natalia S. Astashova, Anatolian pottery from Panticapaeum…………………………………….17-18. Ayşegül Aykurt, Minoan presence in western Anatolia……………………………………………...19. -
The Ptolemies: an Unloved and Unknown Dynasty. Contributions to a Different Perspective and Approach
THE PTOLEMIES: AN UNLOVED AND UNKNOWN DYNASTY. CONTRIBUTIONS TO A DIFFERENT PERSPECTIVE AND APPROACH JOSÉ DAS CANDEIAS SALES Universidade Aberta. Centro de História (University of Lisbon). Abstract: The fifteen Ptolemies that sat on the throne of Egypt between 305 B.C. (the date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII) are in most cases little known and, even in its most recognised bibliography, their work has been somewhat overlooked, unappreciated. Although boisterous and sometimes unloved, with the tumultuous and dissolute lives, their unbridled and unrepressed ambitions, the intrigues, the betrayals, the fratricides and the crimes that the members of this dynasty encouraged and practiced, the Ptolemies changed the Egyptian life in some aspects and were responsible for the last Pharaonic monuments which were left us, some of them still considered true masterpieces of Egyptian greatness. The Ptolemaic Period was indeed a paradoxical moment in the History of ancient Egypt, as it was with a genetically foreign dynasty (traditions, language, religion and culture) that the country, with its capital in Alexandria, met a considerable economic prosperity, a significant political and military power and an intense intellectual activity, and finally became part of the world and Mediterranean culture. The fifteen Ptolemies that succeeded to the throne of Egypt between 305 B.C. (date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII), after Alexander’s death and the division of his empire, are, in most cases, very poorly understood by the public and even in the literature on the topic. -
Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets
Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets Indubala I Satija Department of Physics, George Mason University , Fairfax, VA 22030, USA (Dated: April 28, 2021) Abstract We describe various kaleidoscopic and self-similar aspects of the integral Apollonian gaskets - fractals consisting of close packing of circles with integer curvatures. Self-similar recursive structure of the whole gasket is shown to be encoded in transformations that forms the modular group SL(2;Z). The asymptotic scalings of curvatures of the circles are given by a special set of quadratic irrationals with continued fraction [n + 1 : 1; n] - that is a set of irrationals with period-2 continued fraction consisting of 1 and another integer n. Belonging to the class n = 2, there exists a nested set of self-similar kaleidoscopic patterns that exhibit three-fold symmetry. Furthermore, the even n hierarchy is found to mimic the recursive structure of the tree that generates all Pythagorean triplets arXiv:2104.13198v1 [math.GM] 21 Apr 2021 1 Integral Apollonian gaskets(IAG)[1] such as those shown in figure (1) consist of close packing of circles of integer curvatures (reciprocal of the radii), where every circle is tangent to three others. These are fractals where the whole gasket is like a kaleidoscope reflected again and again through an infinite collection of curved mirrors that encodes fascinating geometrical and number theoretical concepts[2]. The central themes of this paper are the kaleidoscopic and self-similar recursive properties described within the framework of Mobius¨ transformations that maps circles to circles[3]. FIG. 1: Integral Apollonian gaskets. -
Cornish Archaeology 41–42 Hendhyscans Kernow 2002–3
© 2006, Cornwall Archaeological Society CORNISH ARCHAEOLOGY 41–42 HENDHYSCANS KERNOW 2002–3 EDITORS GRAEME KIRKHAM AND PETER HERRING (Published 2006) CORNWALL ARCHAEOLOGICAL SOCIETY © 2006, Cornwall Archaeological Society © COPYRIGHT CORNWALL ARCHAEOLOGICAL SOCIETY 2006 No part of this volume may be reproduced without permission of the Society and the relevant author ISSN 0070 024X Typesetting, printing and binding by Arrowsmith, Bristol © 2006, Cornwall Archaeological Society Contents Preface i HENRIETTA QUINNELL Reflections iii CHARLES THOMAS An Iron Age sword and mirror cist burial from Bryher, Isles of Scilly 1 CHARLES JOHNS Excavation of an Early Christian cemetery at Althea Library, Padstow 80 PRU MANNING and PETER STEAD Journeys to the Rock: archaeological investigations at Tregarrick Farm, Roche 107 DICK COLE and ANDY M JONES Chariots of fire: symbols and motifs on recent Iron Age metalwork finds in Cornwall 144 ANNA TYACKE Cornwall Archaeological Society – Devon Archaeological Society joint symposium 2003: 149 archaeology and the media PETER GATHERCOLE, JANE STANLEY and NICHOLAS THOMAS A medieval cross from Lidwell, Stoke Climsland 161 SAM TURNER Recent work by the Historic Environment Service, Cornwall County Council 165 Recent work in Cornwall by Exeter Archaeology 194 Obituary: R D Penhallurick 198 CHARLES THOMAS © 2006, Cornwall Archaeological Society © 2006, Cornwall Archaeological Society Preface This double-volume of Cornish Archaeology marks the start of its fifth decade of publication. Your Editors and General Committee considered this milestone an appropriate point to review its presentation and initiate some changes to the style which has served us so well for the last four decades. The genesis of this style, with its hallmark yellow card cover, is described on a following page by our founding Editor, Professor Charles Thomas. -
Astronomy and Hipparchus
CHAPTER 9 Progress in the Sciences: Astronomy and Hipparchus Klaus Geus Introduction Geography in modern times is a term which covers several sub-disciplines like ecology, human geography, economic history, volcanology etc., which all con- cern themselves with “space” or “environment”. In ancient times, the definition of geography was much more limited. Geography aimed at the production of a map of the oikoumene, a geographer was basically a cartographer. The famous scientist Ptolemy defined geography in the first sentence of his Geographical handbook (Geog. 1.1.1) as “imitation through drafting of the entire known part of the earth, including the things which are, generally speaking, connected with it”. In contrast to chorography, geography uses purely “lines and label in order to show the positions of places and general configurations” (Geog. 1.1.5). Therefore, according to Ptolemy, a geographer needs a μέθοδος μαθεματική, abil- ity and competence in mathematical sciences, most prominently astronomy, in order to fulfil his task of drafting a map of the oikoumene. Given this close connection between geography and astronomy, it is not by default that nearly all ancient “geographers” (in the limited sense of the term) stood out also as astronomers and mathematicians: Among them Anaximander, Eudoxus, Eratosthenes, Hipparchus, Poseidonius and Ptolemy are the most illustrious. Apart from certain topics like latitudes, meridians, polar circles etc., ancient geography also took over from astronomy some methods like the determina- tion of the size of the earth or of celestial and terrestrial distances.1 The men- tioned geographers Anaximander, Eudoxus, Hipparchus, Poseidonius and Ptolemy even constructed instruments for measuring, observing and calculat- ing like the gnomon, sundials, skaphe, astrolabe or the meteoroscope.2 1 E.g., Ptolemy (Geog.