Words, Lines, Diagrams, Images: Towards a History of Scientific
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Mathematics Is a Gentleman's Art: Analysis and Synthesis in American College Geometry Teaching, 1790-1840 Amy K
Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2000 Mathematics is a gentleman's art: Analysis and synthesis in American college geometry teaching, 1790-1840 Amy K. Ackerberg-Hastings Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Higher Education and Teaching Commons, History of Science, Technology, and Medicine Commons, and the Science and Mathematics Education Commons Recommended Citation Ackerberg-Hastings, Amy K., "Mathematics is a gentleman's art: Analysis and synthesis in American college geometry teaching, 1790-1840 " (2000). Retrospective Theses and Dissertations. 12669. https://lib.dr.iastate.edu/rtd/12669 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margwis, and improper alignment can adversely affect reproduction. in the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. -
B.Casselman,Mathematical Illustrations,A Manual Of
1 0 0 setrgbcolor newpath 0 0 1 0 360 arc stroke newpath Preface 1 0 1 0 360 arc stroke This book will show how to use PostScript for producing mathematical graphics, at several levels of sophistication. It includes also some discussion of the mathematics involved in computer graphics as well as a few remarks about good style in mathematical illustration. To explain mathematics well often requires good illustrations, and computers in our age have changed drastically the potential of graphical output for this purpose. There are many aspects to this change. The most apparent is that computers allow one to produce graphics output of sheer volume never before imagined. A less obvious one is that they have made it possible for amateurs to produce their own illustrations of professional quality. Possible, but not easy, and certainly not as easy as it is to produce their own mathematical writing with Donald Knuth’s program TEX. In spite of the advances in technology over the past 50 years, it is still not a trivial matter to come up routinely with figures that show exactly what you want them to show, exactly where you want them to show it. This is to some extent inevitable—pictures at their best contain a lot of information, and almost by definition this means that they are capable of wide variety. It is surely not possible to come up with a really simple tool that will let you create easily all the graphics you want to create—the range of possibilities is just too large. -
Semantic Foundation of Diagrammatic Modelling Languages
Universität Leipzig Fakultät für Mathematik und Informatik Institut für Informatik Johannisgasse 26 04103 Leipzig Semantic Foundation of Diagrammatic Modelling Languages Applying the Pictorial Turn to Conceptual Modelling Diplomarbeit im Studienfach Informatik vorgelegt von cand. inf. Alexander Heußner Leipzig, August 2007 betreuender Hochschullehrer: Prof. Dr. habil. Heinrich Herre Institut für Medizininformatik, Statistik und Epidemologie (I) Härtelstrasse 16–18 04107 Leipzig Abstract The following thesis investigates the applicability of the picto- rial turn to diagrammatic conceptual modelling languages. At its heart lies the question how the “semantic gap” between the for- mal semantics of diagrams and the meaning as intended by the modelling engineer can be bridged. To this end, a pragmatic ap- proach to the domain of diagrams will be followed, starting from pictures as the more general notion. The thesis consists of three parts: In part I, a basic model of cognition will be proposed that is based on the idea of conceptual spaces. Moreover, the most central no- tions of semiotics and semantics as required for the later inves- tigation and formalization of conceptual modelling will be intro- duced. This will allow for the formalization of pictures as semi- otic entities that have a strong cognitive foundation. Part II will try to approach diagrams with the help of a novel game-based F technique. A prototypical modelling attempt will reveal basic shortcomings regarding the underlying formal foundation. It will even become clear that these problems are common to all current conceptualizations of the diagram domain. To circumvent these difficulties, a simple axiomatic model will be proposed that allows to link the findings of part I on conceptual modelling and formal languages with the newly developed con- cept of «abstract logical diagrams». -
Inviwo — a Visualization System with Usage Abstraction Levels
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL X, NO. Y, MAY 2019 1 Inviwo — A Visualization System with Usage Abstraction Levels Daniel Jonsson,¨ Peter Steneteg, Erik Sunden,´ Rickard Englund, Sathish Kottravel, Martin Falk, Member, IEEE, Anders Ynnerman, Ingrid Hotz, and Timo Ropinski Member, IEEE, Abstract—The complexity of today’s visualization applications demands specific visualization systems tailored for the development of these applications. Frequently, such systems utilize levels of abstraction to improve the application development process, for instance by providing a data flow network editor. Unfortunately, these abstractions result in several issues, which need to be circumvented through an abstraction-centered system design. Often, a high level of abstraction hides low level details, which makes it difficult to directly access the underlying computing platform, which would be important to achieve an optimal performance. Therefore, we propose a layer structure developed for modern and sustainable visualization systems allowing developers to interact with all contained abstraction levels. We refer to this interaction capabilities as usage abstraction levels, since we target application developers with various levels of experience. We formulate the requirements for such a system, derive the desired architecture, and present how the concepts have been exemplary realized within the Inviwo visualization system. Furthermore, we address several specific challenges that arise during the realization of such a layered architecture, such as communication between different computing platforms, performance centered encapsulation, as well as layer-independent development by supporting cross layer documentation and debugging capabilities. Index Terms—Visualization systems, data visualization, visual analytics, data analysis, computer graphics, image processing. F 1 INTRODUCTION The field of visualization is maturing, and a shift can be employing different layers of abstraction. -
Beyond Infinity
Copyright Copyright © 2017 by Eugenia Cheng Hachette Book Group supports the right to free expression and the value of copyright. The purpose of copyright is to encourage writers and artists to produce the creative works that enrich our culture. The scanning, uploading, and distribution of this book without permission is a theft of the author’s intellectual property. If you would like permission to use material from the book (other than for review purposes), please contact [email protected]. Thank you for your support of the author’s rights. Basic Books Hachette Book Group 1290 Avenue of the Americas, New York, NY 10104 www.basicbooks.com First published in Great Britain by Profile Books LTD, 3 Holford Yard, Bevin Way, London WC1X 9HD, www.profilebooks.com. First Trade Paperback Edition: April 2018 Published by Basic Books, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc. The Basic Books name and logo is a trademark of the Hachette Book Group. The Hachette Speakers Bureau provides a wide range of authors for speaking events. To find out more, go to www.hachettespeakersbureau.com or call (866) 376-6591. The publisher is not responsible for websites (or their content) that are not owned by the publisher. Library of Congress Control Number: 2017931084 ISBNs: 978-0-465-09481-3 (hardcover), 978-0-465-09482-0 (e-book), 978-1- 5416-4413-7 (paperback) E3-20180327-JV-PC Cover Title Page Copyright Dedication Prologue part one | THE JOURNEY 1 What Is Infinity? 2 Playing with Infinity 3 What Infinity Is Not 4 Infinity -
Arxiv:2001.11604V2 [Cs.PL] 6 Sep 2020 of Trigger Conditions, Having an in Situ Infrastructure That Simplifies Results They Desire
DIVA: A Declarative and Reactive Language for in situ Visualization Qi Wu* Tyson Neuroth† Oleg Igouchkine‡ University of California, Davis, University of California, Davis, University of California, Davis, United States United States United States Konduri Aditya§ Jacqueline H. Chen¶ Kwan-Liu Ma|| Indian Institute of Science, India Sandia National Laboratories, University of California, Davis, United States United States ABSTRACT for many applications. VTK [61] also partially adopted this ap- The use of adaptive workflow management for in situ visualization proach, however, VTK is designed for programming unidirectional and analysis has been a growing trend in large-scale scientific simu- visualization pipelines, and provides limited support for highly dy- lations. However, coordinating adaptive workflows with traditional namic dataflows. Moreover, the synchronous dataflow model is procedural programming languages can be difficult because system somewhat difficult to use and does not always lead to modular pro- flow is determined by unpredictable scientific phenomena, which of- grams for large scale applications when control flows become com- ten appear in an unknown order and can evade event handling. This plicated [19]. Functional reactive programming (FRP) [19,24,48,53] makes the implementation of adaptive workflows tedious and error- further improved this model by directly treating time-varying values prone. Recently, reactive and declarative programming paradigms as first-class primitives. This allowed programmers to write reac- have been recognized as well-suited solutions to similar problems in tive programs using dataflows declaratively (as opposed to callback other domains. However, there is a dearth of research on adapting functions), hiding the mechanism that controls those flows under these approaches to in situ visualization and analysis. -
The Idea of the Labyrinth
·THE IDEA OF · THE LABYRINTH · THE IDEA OF · THE LABYRINTH from Classical Antiquity through the Middle Ages Penelope Reed Doob CORNELL UNIVERSITY PRESS ITHACA AND LONDON Open access edition funded by the National Endowment for the Humanities/Andrew W. Mellon Foundation Humanities Open Book Program. Copyright © 1990 by Cornell University First printing, Cornell Paperbacks, 1992 Second paperback printing 2019 All rights reserved. Except for brief quotations in a review, this book, or parts thereof, must not be reproduced in any form without permission in writing from the publisher. For information, address Cornell University Press, Sage House, 512 East State Street, Ithaca, New York 14850. Visit our website at cornellpress.cornell.edu. Printed in the United States of America ISBN 978-0-8014-2393-2 (cloth: alk. paper) ISBN 978-1-5017-3845-6 (pbk.: alk. paper) ISBN 978-1-5017-3846-3 (pdf) ISBN 978-1-5017-3847-0 (epub/mobi) Librarians: A CIP catalog record for this book is available from the Library of Congress An open access (OA) ebook edition of this title is available under the following Creative Commons license: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0): https://creativecommons.org/licenses/ by- nc-nd/4.0/. For more information about Cornell University Press’s OA program or to download our OA titles, visit cornellopen.org. Jacket illustration: Photograph courtesy of the Soprintendenza Archeologica, Milan. For GrahamEric Parker worthy companion in multiplicitous mazes and in memory of JudsonBoyce Allen and Constantin Patsalas Contents List of Plates lX Acknowledgments: Four Labyrinths xi Abbreviations XVll Introduction: Charting the Maze 1 The Cretan Labyrinth Myth 11 PART ONE THE LABYRINTH IN THE CLASSICAL AND EARLY CHRISTIAN PERIODS 1. -
Reconstruction of the Interpretation of Geometric Diagrams of Primary School Children Based on Actions on Various Materials - a Semiotic Perspective on Actions
International Electronic Journal of Mathematics Education 2021, 16(3), em0650 e-ISSN: 1306-3030 https://www.iejme.com Research Article OPEN ACCESS Reconstruction of the Interpretation of Geometric Diagrams of Primary School Children Based on Actions on Various Materials - A Semiotic Perspective on Actions Lara Kristina Billion 1* 1 Goethe University Frankfurt, Frankfurt am Main, GERMANY *Corresponding Author: [email protected] Citation: Billion, L. K. (2021). Reconstruction of the Interpretation of Geometric Diagrams of Primary School Children Based on Actions on Various Materials - A Semiotic Perspective on Actions. International Electronic Journal of Mathematics Education, 16(3), em0650. https://doi.org/10.29333/iejme/11068 ARTICLE INFO ABSTRACT Received: 18 Jan. 2021 This paper adopts a semiotic perspective on mathematical learning according to Peirce, in which the actions on Accepted: 17 May 2021 material arrangements are considered the bases for diagrammatic work. The focus is on the learner’s actions using digital and analogue material arrangements which are the starting point for the reconstruction of the learner’s mathematical interpretations. In this paper a qualitative interpretative paradigm is adopted for the reconstruction. Specifically, a semiotic specification of the context analysis according to Mayring and an adoption of Vogel, is carried out. The reconstruction of the mathematical interpretation is presented with a focus on a geometrical problem that third graders are working on. Finally, the results of several cases are compared to identify possible differences between the analysed actions when using digital and analogue material arrangements. Keywords: semiotics, mathematics education, actions on material, mathematical interpretation of diagrams, primary school INTRODUCTION In mathematics education, a cognitive psychological perspective largely determines the perception of actions on the learning material and the focus is on their function as means of illustration. -
Sum 41 Alive
SSUMUM 4411 AALIVELIVE IS SCREAMO B.S.? FLORIA’S FUEL IAN BLURTON~MINISTRY~THE TEA PARTY~WILDHEARTS CLAIRE STANSFIELD~MOONEY SUZUKI~DFA 1979 THE JERRY CAN The summer is the season of rock. Tours roll across the coun- try like mobile homes in a Florida hurricane. The most memo- rable for this magazine/bar owner were the Warped Tour and Wakestock, where such bands as Bad Religion, Billy Talent, Alexisonfire, Closet Monster, The Trews and Crowned King had audiences in mosh-pit frenzies. At Wakestock, in Wasaga Beach, Ont., Gasoline, Fox Racing, and Bluenotes rocked so hard at their two-day private cottage party that local authorities shut down the stage after Magneta Lane and Flashlight Brown. Poor Moneen didn't get to crush the eardrums of the drunken revellers. That was day one! Day two was an even bigger party with the live music again shut down. The Reason, Moneen and Crowned King owned the patio until Alexisonfire and their crew rolled into party. Gasoline would also like to thank Chuck (see cover story) and other UN officials for making sure that the boys in Sum41 made it back to the Bovine for another cocktail, despite the nearby mortar and gunfire during their Warchild excursion. Nice job. Darryl Fine Editor-in-Chief CONTENTS 6 Lowdown News 8 Ian Blurton and C’mon – by Keith Carman 10 Sum41 – by Karen Bliss 14 Floria Sigismondi – by Nick Krewen 16 Alexisonfire and “screamo” – by Karen Bliss 18 Smash it up – photos by Paula Wilson 20 Whiskey and Rock – by Seth Fenn 22 Claire Stansfield – by Karen Bliss 24 Tea Party – by Mitch Joel -
Legends of the West
1 This novel is dedicated to Vivian Towlerton For the memories of good times past 2 This novel was written mostly during the year 2010 CE whilst drinking the fair-trade coffee provided by the Caffé Vita and Sizizis coffee shops in Olympia, Washington Most of the research was conducted during the year 2010 CE upon the free Wi-Fi provided by the Caffé Vita and Sizizis coffee shops in Olympia, Washington. My thanks to management and staff. It was good. 3 Excerpt from Legends of the West: Spotted Tail said, “Now, let me tell you the worst thing about the Wasicu, and the hardest thing to understand: They do not understand choice...” This caused a murmur of consternation among the Lakota. Choice was choice. What was not there to not understand? Choice is the bedrock tenet of our very view of reality. The choices a person makes are quite literally what makes that person into who they are. Who else can tell you how to be you? One follows one’s own nature and one’s own inner voice; to us this is sacrosanct. You can choose between what makes life beautiful and what makes life ugly; you can choose whether to paint yourself in a certain manner or whether to wear something made of iron — or, as was the case with the famous Cheyenne warrior Roman Nose — you could choose to never so much as touch iron. In battle you choose whether you should charge the enemy first, join the main thrust of attack, or take off on your own and try to steal his horses. -
MERJ Booklet TEXT.Qxd
Mathematics Education Research Journal 2004, Vol. 16, No. 1, 41-70 Strategies Employed by Upper Secondary Students for Overcoming or Exploiting Conditions Affecting Accessibility of Applications Tasks1 Gloria Stillman University of Melbourne A cognitive/metacognitive framework is presented for analysing applications tasks and responses to these. Conditions facilitating or impeding access to such tasks at the upper secondary level were identified using qualitative data analysis techniques within this framework. Strategies employed in exploiting, or overcoming these conditions were identified. A well-developed repertoire of cognitive and metacognitive strategies together with a rich store of mathematical knowledge, real-world knowledge and experiences, and comprehension skills facilitated access. This was enhanced by metacognitive knowledge encouraging student engagement with the task and by students imagining they were in the task situation. Once moderate skill had been achieved in accessing these applications, coordination and integration of multiple representations, further cues, and mathematical processes and procedures became critical. The use of applications in secondary classrooms for both teaching and assessment is receiving increasing attention in many countries, for example, Australia (Queensland Board of Senior Secondary School Studies [QBSSSS], 1992, 2000), the Netherlands (Gravemeijer & Doorman, 1999), Uganda (Ekol, 2004), and Canada (Roulet & Suurtamm, 2004). According to Blum and Niss (1991), there are essentially five arguments -
C 2020 by Simone Claire Sisneros-Thiry. All Rights Reserved. COMBINATORIAL NUMBER THEORY THROUGH DIAGRAMMING and GESTURE
c 2020 by Simone Claire Sisneros-Thiry. All rights reserved. COMBINATORIAL NUMBER THEORY THROUGH DIAGRAMMING AND GESTURE BY SIMONE CLAIRE SISNEROS-THIRY DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate College of the University of Illinois at Urbana-Champaign, 2020 Urbana, Illinois Doctoral Committee: Professor Bruce Berndt, Chair Professor Bruce Reznick, Director of Research Professor Matthew Ando Professor Rochelle Guti´errez Abstract Within combinatorial number theory, we study a variety of problems about whole numbers that include enumerative, diagrammatic, or computational elements. We present results motivated by two different areas within combinatorial number theory: the study of partitions and the study of digital representations of integers. We take the perspective that mathematics research is mathematics learning; existing research from mathematics education on mathematics learning and problem solving can be applied to mathematics research. We illustrate this by focusing on the concept of diagramming and gesture as mathematical practice. The mathematics presented is viewed through this lens throughout the document. Joint with H. E. Burson and A. Straub, motivated by recent results working toward classifying (s; t)-core partitions into distinct parts, we present results on certain abaci diagrams. We give a recurrence (on s) for generating polynomials for s-core abaci diagrams with spacing d and maximum position strictly less than ms − r for positive integers s, d, m, and r. In the case r = 1, this implies a recurrence for (s; ms − 1)-core partitions into d-distinct parts, generalizing several recent results. We introduce the sets Q(b; fd1; d2; : : : ; dkg) to be integers that can be represented as quotients of integers that can be written in base b using only digits from the set fd1; : : : ; dkg.