Technology and Autonomous Mechanisms in the Mediterranean - from Ancient Greece to Byzantium
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Greeks Doing Algebra
Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks. -
Champ Math Study Guide Indesign
Champions of Mathematics — Study Guide — Questions and Activities Page 1 Copyright © 2001 by Master Books, Inc. All rights reserved. This publication may be reproduced for educational purposes only. BY JOHN HUDSON TINER To get the most out of this book, the following is recommended: Each chapter has questions, discussion ideas, research topics, and suggestions for further reading to improve students’ reading, writing, and thinking skills. The study guide shows the relationship of events in Champions of Mathematics to other fields of learning. The book becomes a springboard for exploration in other fields. Students who enjoy literature, history, art, or other subjects will find interesting activities in their fields of interest. Parents will find that the questions and activities enhance their investments in the Champion books because children of different age levels can use them. The questions with answers are designed for younger readers. Questions are objective and depend solely on the text of the book itself. The questions are arranged in the same order as the content of each chapter. A student can enjoy the book and quickly check his or her understanding and comprehension by the challenge of answering the questions. The activities are designed to serve as supplemental material for older students. The activities require greater knowledge and research skills. An older student (or the same student three or four years later) can read the book and do the activities in depth. CHAPTER 1 QUESTIONS 1. A B C D — Pythagoras was born on an island in the (A. Aegean Sea B. Atlantic Ocean C. Caribbean Sea D. -
Water, Air and Fire at Work in Hero's Machines
Water, air and fire at work in Hero’s machines Amelia Carolina Sparavigna Dipartimento di Fisica, Politecnico di Torino Corso Duca degli Abruzzi 24, Torino, Italy Known as the Michanikos, Hero of Alexandria is considered the inventor of the world's first steam engine and of many other sophisticated devices. Here we discuss three of them as described in his book “Pneumatica”. These machines, working with water, air and fire, are clear examples of the deep knowledge of fluid dynamics reached by the Hellenistic scientists. Hero of Alexandria, known as the Mechanicos, lived during the first century in the Roman Egypt [1]. He was probably a Greek mathematician and engineer who resided in the city of Alexandria. We know his work from some of writings and designs that have been arrived nowadays in their Greek original or in Arabic translations. From his own writings, it is possible to gather that he knew the works of Archimedes and of Philo the Byzantian, who was a contemporary of Ctesibius [2]. It is almost certain that Heron taught at the Museum, a college for combined philosophy and literary studies and a religious place of cult of Muses, that included the famous Library. For this reason, Hero claimed himself a pupil of Ctesibius, who was probably the first head of the Museum of Alexandria. Most of Hero’s writings appear as lecture notes for courses in mathematics, mechanics, physics and pneumatics [2]. In optics, Hero formulated the Principle of the Shortest Path of Light, principle telling that if a ray of light propagates from a point to another one within the same medium, the followed path is the shortest possible. -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books. -
Citations in Classics and Ancient History
Citations in Classics and Ancient History The most common style in use in the field of Classical Studies is the author-date style, also known as Chicago 2, but MLA is also quite common and perfectly acceptable. Quick guides for each of MLA and Chicago 2 are readily available as PDF downloads. The Chicago Manual of Style Online offers a guide on their web-page: http://www.chicagomanualofstyle.org/tools_citationguide.html The Modern Language Association (MLA) does not, but many educational institutions post an MLA guide for free access. While a specific citation style should be followed carefully, none take into account the specific practices of Classical Studies. They are all (Chicago, MLA and others) perfectly suitable for citing most resources, but should not be followed for citing ancient Greek and Latin primary source material, including primary sources in translation. Citing Primary Sources: Every ancient text has its own unique system for locating content by numbers. For example, Homer's Iliad is divided into 24 Books (what we might now call chapters) and the lines of each Book are numbered from line 1. Herodotus' Histories is divided into nine Books and each of these Books is divided into Chapters and each chapter into line numbers. The purpose of such a system is that the Iliad, or any primary source, can be cited in any language and from any publication and always refer to the same passage. That is why we do not cite Herodotus page 66. Page 66 in what publication, in what edition? Very early in your textbook, Apodexis Historia, a passage from Herodotus is reproduced. -
From Ancient Greece to Byzantium
Proceedings of the European Control Conference 2007 TuA07.4 Kos, Greece, July 2-5, 2007 Technology and Autonomous Mechanisms in the Mediterranean: From Ancient Greece to Byzantium K. P. Valavanis, G. J. Vachtsevanos, P. J. Antsaklis Abstract – The paper aims at presenting each period are then provided followed by technology and automation advances in the accomplishments in automatic control and the ancient Greek World, offering evidence that transition from the ancient Greek world to the Greco- feedback control as a discipline dates back more Roman era and the Byzantium. than twenty five centuries. II. CHRONOLOGICAL MAP OF SCIENCE & TECHNOLOGY I. INTRODUCTION It is worth noting that there was an initial phase of The paper objective is to present historical evidence imported influences in the development of ancient of achievements in science, technology and the Greek technology that reached the Greek states from making of automation in the ancient Greek world until the East (Persia, Babylon and Mesopotamia) and th the era of Byzantium and that the main driving force practiced by the Greeks up until the 6 century B.C. It behind Greek science [16] - [18] has been curiosity and was at the time of Thales of Miletus (circa 585 B.C.), desire for knowledge followed by the study of nature. when a very significant change occurred. A new and When focusing on the discipline of feedback control, exclusively Greek activity began to dominate any James Watt’s Flyball Governor (1769) may be inherited technology, called science. In subsequent considered as one of the earliest feedback control centuries, technology itself became more productive, devices of the modern era. -
The Impacts of Technological Invention on Economic Growth – a Review of the Literature Andrew Reamer1 February 28, 2014
THE GEORGE WASHINGTON INSTITUTE OF PUBLIC POLICY The Impacts of Technological Invention on Economic Growth – A Review of the Literature Andrew Reamer1 February 28, 2014 I. Introduction In their recently published book, The Second Machine Age, Erik Brynjolfsson and Andrew McAfee rely on economist Paul Krugman to explain the connection between invention and growth: Paul Krugman speaks for many, if not most, economists when he says, “Productivity isn’t everything, but in the long run it’s almost everything.” Why? Because, he explains, “A country’s ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker”—in other words, the number of hours of labor it takes to produce everything, from automobiles to zippers, that we produce. Most countries don’t have extensive mineral wealth or oil reserves, and thus can’t get rich by exporting them. So the only viable way for societies to become wealthier—to improve the standard of living available to its people—is for their companies and workers to keep getting more output from the same number of inputs, in other words more goods and services from the same number of people. Innovation is how this productivity growth happens.2 For decades, economists and economic historians have sought to improve their understanding of the role of technological invention in economic growth. As in many fields of inventive endeavor, their efforts required time to develop and mature. In the last five years, these efforts have reached a point where they are generating robust, substantive, and intellectually interesting findings, to the benefit of those interested in promoting growth-enhancing invention in the U.S. -
Chapter 8 Glossary
Technology: Engineering Our World © 2012 Chapter 8: Machines—Glossary friction. A force that acts like a brake on moving objects. gear. A rotating wheel-like object with teeth around its rim used to transmit force to other gears with matching teeth. hydraulics. The study and technology of the characteristics of liquids at rest and in motion. inclined plane. A simple machine in the form of a sloping surface or ramp, used to move a load from one level to another. lever. A simple machine that consists of a bar and fulcrum (pivot point). Levers are used to increase force or decrease the effort needed to move a load. linkage. A system of levers used to transmit motion. lubrication. The application of a smooth or slippery substance between two objects to reduce friction. machine. A device that does some kind of work by changing or transmitting energy. mechanical advantage. In a simple machine, the ability to move a large resistance by applying a small effort. mechanism. A way of changing one kind of effort into another kind of effort. moment. The turning force acting on a lever; effort times the distance of the effort from the fulcrum. pneumatics. The study and technology of the characteristics of gases. power. The rate at which work is done or the rate at which energy is converted from one form to another or transferred from one place to another. pressure. The effort applied to a given area; effort divided by area. pulley. A simple machine in the form of a wheel with a groove around its rim to accept a rope, chain, or belt; it is used to lift heavy objects. -
Epigraphic Bulletin for Greek Religion 2011 (EBGR 2011)
Kernos Revue internationale et pluridisciplinaire de religion grecque antique 27 | 2014 Varia Epigraphic Bulletin for Greek Religion 2011 (EBGR 2011) Angelos Chaniotis Electronic version URL: http://journals.openedition.org/kernos/2266 DOI: 10.4000/kernos.2266 ISSN: 2034-7871 Publisher Centre international d'étude de la religion grecque antique Printed version Date of publication: 1 November 2014 Number of pages: 321-378 ISBN: 978-2-87562-055-2 ISSN: 0776-3824 Electronic reference Angelos Chaniotis, « Epigraphic Bulletin for Greek Religion 2011 (EBGR 2011) », Kernos [Online], 27 | 2014, Online since 01 October 2016, connection on 15 September 2020. URL : http:// journals.openedition.org/kernos/2266 This text was automatically generated on 15 September 2020. Kernos Epigraphic Bulletin for Greek Religion 2011 (EBGR 2011) 1 Epigraphic Bulletin for Greek Religion 2011 (EBGR 2011) Angelos Chaniotis 1 The 24th issue of the Epigraphic Bulletin for Greek Religion presents epigraphic publications of 2011 and additions to earlier issues (publications of 2006–2010). Publications that could not be considered here, for reasons of space, will be presented in EBGR 2012. They include two of the most important books of 2011: N. PAPAZARKADAS’ Sacred and Public Land in Ancient Athens, Oxford 2011 and H.S. VERSNEL’s Coping with the Gods: Wayward Readings in Greek Theology, Leiden 2011. 2 A series of new important corpora is included in this issue. Two new IG volumes present the inscriptions of Eastern Lokris (119) and the first part of the inscriptions of Kos (21); the latter corpus is of great significance for the study of Greek religion, as it contains a large number of cult regulations; among the new texts, we single out the ‘sacred law of the tribe of the Elpanoridai’ in Halasarna. -
Engineering Philosophy Louis L
Engineering Philosophy Louis L. Bucciarelli ISBN 90-407-2318-4 Copyright 2003 by Louis L. Bucciarelli Table of Contents Introduction 1 Designing, like language, is a social process. 9 What engineers don’t know & why they believe it. 23 Knowing that and how 43 Learning Engineering 77 Extrapolation 99 Index 103 1 Introduction “Let’s stop all this philosophizing and get back to business”1 Philosophy and engineering seem worlds apart. From their remarks, we might infer that engineers value little the problems philosophers address and the analyses they pursue. Ontological questions about the nature of existence and the categorial structure of reality – what one takes as real in the world – seem to be of scant inter- est. It would appear that engineers don’t need philosophy; they know the differ- ence between the concrete and the abstract, the particular and the universal – they work within both of these domains every day, building and theorizing, testing and modeling in the design and development of new products and systems. Possible worlds are not fictions but the business they are about. As Theodore Von Karman, an aerospace engineer and educator, reportedly claimed Scientists discover the world that exists; engineers create the world that never was. Epistemological questions about the source and status of engineering knowl- edge likewise rarely draw their attention.2 Engineers are pragmatic. If their pro- ductions function in accord with their designs, they consider their knowledge justified and true. Such knowledge, they will show you, is firmly rooted in the sci- entific explanation of phenomenon which, while dated according to physicists, may still provide fertile grounds for innovative extension of their understanding of how things work or might work better. -
The Contribution of the Segovia Mint Factory to the History of Manufacturing As an Example of Mass Production in the 16Th Century
applied sciences Article The Contribution of the Segovia Mint Factory to the History of Manufacturing as an Example of Mass Production in the 16th Century Francisco García-Ahumada * and Cristina Gonzalez-Gaya * Department of Construction and Manufacturing Engineering, ETSII-Universidad Nacional de Educación a Distancia (UNED), C/Juan del Rosal 12, 28040 Madrid, Spain * Correspondence: [email protected] (F.G.-A.); [email protected] (C.G.-G.); Tel.: +34-629-67-27-37 (C.G.-G.) Received: 1 October 2019; Accepted: 26 November 2019; Published: 7 December 2019 Abstract: A new means of minting currency was first used at the Hall Mint in Tyrol in 1567. This new minting process employed a roller instead of a hammer and used hydropower to fuel the laminating and coining mills, as well as ancillary equipment, such as the forge or the lathe. In 1577, Philip II of Spain expressed his interest in the new technology and, after a successful technology transfer negotiation with the County of Tyrol, Juan de Herrera was commissioned to design a factory to accommodate this new minting process. The resulting design seamlessly integrated this new technology. The architectural layout of the factory was derived from the integration of different trades related to the manufacturing workflow, and their effective distribution within a more effective workplace allowed for better use of the hydraulic resources available, and, thus, improvements in the productivity and reliability of the manufacturing process, as well as in the quality of the finished product. Juan de Herrera’s design led to the creation of a ground-breaking manufacturing process, unparalleled in the mint industry in Europe at the time. -
Ancient Technology Honors Seminar III, Inhabiting Other Lives, FIU Honors College (IDH 2003-U01) Fall Semester – 2018
Ancient Technology Honors Seminar III, Inhabiting Other Lives, FIU Honors College (IDH 2003-U01) Fall Semester – 2018 Instructor: Dr. Jill Baker Tuesdays and Thursdays, 11.00 a.m. to 12.15 p.m. Office location: DM 233, (305) 348-4100 Classroom: GC 286 Office hours: By Appointment or Borders Café GC, 10.15-10.45 a.m. Tu/Th email: [email protected] Purpose of the Course: The purpose of this class is to explore ancient technology and engineering. Thanks to archaeological excavation, monumental buildings, gates, city walls, roads, and ships have been discovered. These sometimes-gigantic structures were constructed without the benefit of bull dozers, cranes, lifts, drills, or any of the modern tools with which we are familiar and lived in relative luxury. So, how did the ancient people move materials and build these amazing cities with surprising amenities? This class seeks to elucidate the ingenuity of the ancient mind in order to understand their technology which in turn will help us to better understand our own and apply these, and new, ideas to the future. Questions that will be addressed include what the ancients knew, when and how did they know it; what machines and tools did they use and for what purposes; how does technology and engineering help society advance; how can we apply these principles to our world and to the future? Fall Semester: The big stuff - monumental constructions, residential dwellings, urban planning, etc. Spring Semester: The smaller things – machines, maritime transportation, terrestrial transportation, medicine, time-keeping, etc. This syllabus will be distributed on the first day of class in the spring semester.