The Mathematical Gazette Index for 1894 to 1908
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Islamic Geometric Patterns Jay Bonner
Islamic Geometric Patterns Jay Bonner Islamic Geometric Patterns Their Historical Development and Traditional Methods of Construction with a chapter on the use of computer algorithms to generate Islamic geometric patterns by Craig Kaplan Jay Bonner Bonner Design Consultancy Santa Fe, New Mexico, USA With contributions by Craig Kaplan University of Waterloo Waterloo, Ontario, Canada ISBN 978-1-4419-0216-0 ISBN 978-1-4419-0217-7 (eBook) DOI 10.1007/978-1-4419-0217-7 Library of Congress Control Number: 2017936979 # Jay Bonner 2017 Chapter 4 is published with kind permission of # Craig Kaplan 2017. All Rights Reserved. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. -
Second Rapport Intermédiaire
Compte-rendu intermédiaire 01/04/2016-31/03/2107 Projet ANR- AA-PPPP-000 Cirmath Circulations des mathématiques dans et par les journaux : histoire, territoires et publics Programme xxxxx 200x A IDENTIFICATION ................................................................ 3 B LIVRABLES ET JALONS ......................................................... 4 C RAPPORT D’AVANCEMENT SUR LA PERIODE CONCERNEE (01/04/16- 31/03/17) .................................................................... 6 C.1 Description des travaux effectués ............................................. 6 C.1.1 Rappel : Une présentation rapide du programme de recherche de Cirmath 6 C.1.2 Le séminaire Cirmath 7 C.1.3 Les colloques Cirmath 7 C.1.4 La base de données des journaux mathématiques - Cirmath-data 8 C.1.5 Conclusion 11 C.2 Résultats marquants (si applicable) ........................................ 11 C.3 Réunions du consortium (si applicable) ................................... 11 C.4 Commentaires libres............................................................. 12 D IMPACT DU PROJET DEPUIS LE DEBUT ...................................... 13 D.1 Indicateurs d’impact ............................................................. 13 D.2 Liste des publications et communications ................................ 14 Référence du formulaire : ANR-FORM-090601-02-01 D.2.1 Liste des publications et communications directement liées au projet Cirmath. 14 D.2.2 Liste des publications et communications des membres du projet Cirmath ayant trait à la thématique de la circulation -
The Walk of Life Vol
THE WALK OF LIFE VOL. 03 EDITED BY AMIR A. ALIABADI The Walk of Life Biographical Essays in Science and Engineering Volume 3 Edited by Amir A. Aliabadi Authored by Zimeng Wan, Mamoon Syed, Yunxi Jin, Jamie Stone, Jacob Murphy, Greg Johnstone, Thomas Jackson, Michael MacGregor, Ketan Suresh, Taylr Cawte, Rebecca Beutel, Jocob Van Wassenaer, Ryan Fox, Nikolaos Veriotes, Matthew Tam, Victor Huong, Hashim Al-Hashmi, Sean Usher, Daquan Bar- row, Luc Carney, Kyle Friesen, Victoria Golebiowski, Jeffrey Horbatuk, Alex Nauta, Jacob Karl, Brett Clarke, Maria Bovtenko, Margaret Jasek, Allissa Bartlett, Morgen Menig-McDonald, Kate- lyn Sysiuk, Shauna Armstrong, Laura Bender, Hannah May, Elli Shanen, Alana Valle, Charlotte Stoesser, Jasmine Biasi, Keegan Cleghorn, Zofia Holland, Stephan Iskander, Michael Baldaro, Rosalee Calogero, Ye Eun Chai, and Samuel Descrochers 2018 c 2018 Amir A. Aliabadi Publications All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. ISBN: 978-1-7751916-1-2 Atmospheric Innovations Research (AIR) Laboratory, Envi- ronmental Engineering, School of Engineering, RICH 2515, University of Guelph, Guelph, ON N1G 2W1, Canada It should be distinctly understood that this [quantum mechanics] cannot be a deduction in the mathematical sense of the word, since the equations to be obtained form themselves the postulates of the theory. Although they are made highly plausible by the following considerations, their ultimate justification lies in the agreement of their predictions with experiment. —Werner Heisenberg Dedication Jahangir Ansari Preface The essays in this volume result from the Fall 2018 offering of the course Control of Atmospheric Particulates (ENGG*4810) in the Environmental Engineering Program, University of Guelph, Canada. -
Modeling Bacteria-Phage Interactions and Its Implications for Phage
CHAPTER THREE Modeling Bacteria–Phage Interactions and Its Implications for Phage Therapy Saptarshi Sinha, Rajdeep K. Grewal, Soumen Roy1 Bose Institute, Kolkata, India 1Corresponding author: e-mail address: [email protected] Contents 1. The Bacteria–Phage Interaction 104 1.1 Discovery of Bacteriophages: A Brief History 104 1.2 Lytic and Lysogenic Cycle 106 1.3 Adsorption Rate 107 1.4 Multiplicity of Infection 109 1.5 One-Step Growth Curve 110 1.6 Phage Therapy 111 1.7 Bacteria–Phage Coevolution 113 1.8 Modeling Bacteria–Phage Interactions 113 2. Mathematical Modeling 115 2.1 Differential Equations 115 2.2 Basic Model for Bacteria–Phage Interactions 117 2.3 Resource Concentration Factor 118 2.4 Phage Resistance in Bacteria 118 2.5 Bacteria–Phage Interaction Networks 120 2.6 System of ODEs 121 2.7 Recent Developments 122 3. Computer Simulations 124 3.1 Monte Carlo Simulations 124 3.2 Probability Distribution 126 3.3 Probability of Cell Division 128 3.4 Probability of Phage Adsorption 129 3.5 Latent Period and Burst Size 130 3.6 Secondary Infection and Killing 130 4. Phage Bacteria Interaction Under Spatial Limitations 132 4.1 Formation of Plaque 132 4.2 Factors Affecting Plaque Diameter 133 4.3 Modeling of Plaque Growth as a Reaction–Diffusion System 134 # Advances in Applied Microbiology, Volume 103 2018 Elsevier Inc. 103 ISSN 0065-2164 All rights reserved. https://doi.org/10.1016/bs.aambs.2018.01.005 104 Saptarshi Sinha et al. 4.4 Traveling Wave Front Solutions 135 4.5 Cellular Automata Modeling 135 4.6 SIR-Type Modeling 136 Acknowledgments 137 References 138 Abstract Bacteriophages are more abundant than any other organism on our planet. -
A Combinatorial Analysis of Topological Dissections
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector ADVANCES IN MATHEMATICS 25, 267-285 (1977) A Combinatorial Analysis of Topological Dissections THOMAS ZASLAVSKY Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 From a topological space remove certain subspaces (cuts), leaving connected components (regions). We develop an enumerative theory for the regions in terms of the cuts, with the aid of a theorem on the Mijbius algebra of a subset of a distributive lattice. Armed with this theory we study dissections into cellular faces and dissections in the d-sphere. For example, we generalize known enumerations for arrangements of hyperplanes to convex sets and topological arrangements, enumerations for simple arrangements and the Dehn-Sommerville equations for simple polytopes to dissections with general intersection, and enumerations for arrangements of lines and curves and for plane convex sets to dissections by curves of the 2-sphere and planar domains. Contents. Introduction. 1. The fundamental relations for dissections and covers. 2. Algebraic combinatorics: Valuations and MGbius algebras. 3. Dissections into cells and properly cellular faces. 4. General position. 5. Counting low-dimensional faces. 6. Spheres and their subspaces. 7. Dissections by curves. INTRODUCTION A problem which arises from time to time in combinatorial geometry is to determine the number of pieces into which a certain geometric set is divided by given subsets. Think for instance of a plane cut by prescribed curves, as in a map of a land area crisscrossed by roads and hedgerows, or of a finite set of hyper- planes slicing up a convex domain in a Euclidean space. -
The Dehn-Sydler Theorem Explained
The Dehn-Sydler Theorem Explained Rich Schwartz February 16, 2010 1 Introduction The Dehn-Sydler theorem says that two polyhedra in R3 are scissors con- gruent iff they have the same volume and Dehn invariant. Dehn [D] proved in 1901 that equality of the Dehn invariant is necessary for scissors congru- ence. 64 years passed, and then Sydler [S] proved that equality of the Dehn invariant (and volume) is sufficient. In [J], Jessen gives a simplified proof of Sydler’s Theorem. The proof in [J] relies on two results from homolog- ical algebra that are proved in [JKT]. Also, to get the cleanest statement of the result, one needs to combine the result in [J] (about stable scissors congruence) with Zylev’s Theorem, which is proved in [Z]. The purpose of these notes is to explain the proof of Sydler’s theorem that is spread out in [J], [JKT], and [Z]. The paper [J] is beautiful and efficient, and I can hardly improve on it. I follow [J] very closely, except that I simplify wherever I can. The only place where I really depart from [J] is my sketch of the very difficult geometric Lemma 10.1, which is known as Sydler’s Fundamental Lemma. To supplement these notes, I made an interactive java applet that renders Sydler’s Fundamental Lemma transparent. The applet departs even further from Jessen’s treatment. [JKT] leaves a lot to be desired. The notation in [JKT] does not match the notation in [J] and the theorems proved in [JKT] are much more general than what is needed for [J]. -
Once Upon a Party - an Anecdotal Investigation
Journal of Humanistic Mathematics Volume 11 | Issue 1 January 2021 Once Upon A Party - An Anecdotal Investigation Vijay Fafat Ariana Investment Management Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, Other Mathematics Commons, and the Other Physics Commons Recommended Citation Fafat, V. "Once Upon A Party - An Anecdotal Investigation," Journal of Humanistic Mathematics, Volume 11 Issue 1 (January 2021), pages 485-492. DOI: 10.5642/jhummath.202101.30 . Available at: https://scholarship.claremont.edu/jhm/vol11/iss1/30 ©2021 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. The Party Problem: An Anecdotal Investigation Vijay Fafat SINGAPORE [email protected] Synopsis Mathematicians and physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imi- tates their craft, and we must simply observe the deep truths hiding in their party-going behavior. Obligatory Preface It is a well-known maxim that revelries involving academics, intellectuals, and thought leaders are notoriously twisted affairs, a topologist's delight. -
Ramanujan As a Patient
Proc. Indian Acad. Sci. (Math. Sci.), Voi. 93, Nos 2 & 3, December 1984, pp. 79-100 Printed in India. Ramanujan as a patient R A RANKIN Department of Mathematics, University of Glasgow, Glasgow GI2 8QW, Scotland 1. Introduction In this article I attempt to give as full a picture as possible of Srinivasa Ramanujan's medical history during his time in England. The account is based largely on unpublished letters and documents housed in various libraries, and on information extracted from the records of public bodies. In my earlier paper [12] I was concerned mainly with his notebooks and manuscripts, although I did give a brief description of the nursing homes in which he was a patient, based on information available to me at the time. What might be called Ramanujan's domestic history is well documented [1, 5, 7, 8, 9, 10, 14], at any rate as regards incident, if not exact date, so that, in the interests of brevity, I recall only those events that have a direct bearing on my subject. I also take the opportunity (in w to amplify and extend some of the material included in [12], in the light of information more recently received, and to make a number of general comments. The source to which most frequent reference is made is the collection of unpublished papers and documents written by, or concerning, Ramanujan (1887-1920), which were passed on by G H Hardy (1877-1947) and J E Littlewood (1885-1977) to G N Watson (1886-1965) and are now housed in the Wren Library of Trinity College, Cambridge, where at one time all four were Fellows. -
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 P.M
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 p.m. Class Room: Stevenson 347-B Office: Stevenson 402 Office Hours: Tuesday & Thursday 12:30-1:30 p.m. Office Phone: 438-3739 Email: [email protected] . Web site: http://ghostofthetalkingcricket.squarespace.com Tentative Syllabus: Aug. 20 Introduction and Overview to the Course Aug. 22 French Fairy Tales in M.C. Waldrep’s Favorite Fairy Tales: Perrault’s “Cinderella, or the Little Class Slipper,” “Little Red Riding-Hood,” “Toads and Diamonds,” “The Master Cat; or, Puss in Boots.” Madame De Villeneuve’s “Beauty and the Beast,” & Perrault’s “Sleeping Beauty in the Wood” (website) Aug. 27 German Folk Tales in M.C. Waldrep’s Favorite Fairy Tales: Grimm’s” Snowdrop [Snow White],” “Rapunzel,” “Rumplestiltkin,” “The Goose-Girl,” Grimm’s “Little Red-Cap” & “Hansel and Gretel” (website) Aug. 29 Hans Christian Andersen's Literary Fairy Tales in M.C. Waldrep’ Favorite Fairy Tales: “ How to Tell a True Princess (The Princess and the Pea),” “The Nightingale,” “The Ugly Ducking,” “The Story of the Emperor’s New Clothes,” & in Hans Christian Andersen’s The Little Mermaid and Other Fairy Tales “The Little Mermaid” “The Swineherd,” “The Steadfast Tin Soldier,” “The Little Match Girl” Deadline for Sign-up for Children’s Film for Film Paper Sept. 3 English Folk Tales in M.C, Waldrep’s Favorite Fairy Tales: “Jack and the Beanstalk,” “The Ratcatcher [Pied Piper of Hamelin],” & “Three Little Pigs” Sept. 5 American Fairy Tales: Walt Disney’s film adaptation of fairy tales: “Steamboat Willie” “The Three Little Pigs” “Snow White and the Seven “Dwarfs,” “Cinderella” & “The Little Mermaid” Sept. -
Finite Projective Geometries 243
FINITE PROJECTÎVEGEOMETRIES* BY OSWALD VEBLEN and W. H. BUSSEY By means of such a generalized conception of geometry as is inevitably suggested by the recent and wide-spread researches in the foundations of that science, there is given in § 1 a definition of a class of tactical configurations which includes many well known configurations as well as many new ones. In § 2 there is developed a method for the construction of these configurations which is proved to furnish all configurations that satisfy the definition. In §§ 4-8 the configurations are shown to have a geometrical theory identical in most of its general theorems with ordinary projective geometry and thus to afford a treatment of finite linear group theory analogous to the ordinary theory of collineations. In § 9 reference is made to other definitions of some of the configurations included in the class defined in § 1. § 1. Synthetic definition. By a finite projective geometry is meant a set of elements which, for sugges- tiveness, are called points, subject to the following five conditions : I. The set contains a finite number ( > 2 ) of points. It contains subsets called lines, each of which contains at least three points. II. If A and B are distinct points, there is one and only one line that contains A and B. HI. If A, B, C are non-collinear points and if a line I contains a point D of the line AB and a point E of the line BC, but does not contain A, B, or C, then the line I contains a point F of the line CA (Fig. -
Circles in Areals
Circles in areals 23 December 2015 This paper has been accepted for publication in the Mathematical Gazette, and copyright is assigned to the Mathematical Association (UK). This preprint may be read or downloaded, and used for any non-profit making educational or research purpose. Introduction August M¨obiusintroduced the system of barycentric or areal co-ordinates in 1827[1, 2]. The idea is that one may attach weights to points, and that a system of weights determines a centre of mass. Given a triangle ABC, one obtains a co-ordinate system for the plane by placing weights x; y and z at the vertices (with x + y + z = 1) to describe the point which is the centre of mass. The vertices have co-ordinates A = (1; 0; 0), B = (0; 1; 0) and C = (0; 0; 1). By scaling so that triangle ABC has area [ABC] = 1, we can take the co-ordinates of P to be ([P BC]; [PCA]; [P AB]), provided that we take area to be signed. Our convention is that anticlockwise triangles have positive area. Points inside the triangle have strictly positive co-ordinates, and points outside the triangle must have at least one negative co-ordinate (we are allowed negative masses). The equation of a line looks like the equation of a plane in Cartesian co-ordinates, but note that the equation lx + ly + lz = 0 (with l 6= 0) is not satisfied by any point (x; y; z) of the Euclidean plane. We use such equations to describe the line at infinity when doing projective geometry. -
EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics the Open University Milton Keynes MK7 6AA, UK E-Mail: [email protected]
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania e-mail: [email protected] NEWSLETTER No. 47 KRZYSZTOF CIESIELSKI Mathematics Institute March 2003 Jagiellonian University Reymonta 4 EMS Agenda ................................................................................................. 2 30-059 Kraków, Poland e-mail: [email protected] Editorial by Sir John Kingman .................................................................... 3 STEEN MARKVORSEN Department of Mathematics Executive Committee Meeting ....................................................................... 4 Technical University of Denmark Building 303 Introducing the Committee ............................................................................ 7 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] An Answer to the Growth of Mathematical Knowledge? ............................... 9 SPECIALIST EDITORS Interview with Vagn Lundsgaard Hansen .................................................. 15 INTERVIEWS Steen Markvorsen [address as above] Interview with D V Anosov .......................................................................... 20 SOCIETIES Krzysztof Ciesielski [address as above] Israel Mathematical Union ......................................................................... 25 EDUCATION Tony Gardiner