Nexus Network Journal: Leonardo da Vinci: Architecture and Mathematics

Sylvie Duvernoy 

Nexus Network Journal, vol. 10, number 1

Birkhäuser | 2008 | 200 páginas | pdf | 24 Mb

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Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This book examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry.

CONTENTS

Letter from the Guest Editor

5 SYLVIE DUVERNOY. An Introduction to Leonardo’s Lattices Leonardo da Vinci: Architecture and Mathematics

13 KIM WILLIAMS. Transcription and Translation of Codex Atlanticus, fol. 899 v

17 RINUS ROELOFS. Two- and Three-Dimensional Constructions Based on Leonardo Grids

27 BIAGIO DI CARLO. The Wooden Roofs of Leonardo and New Structural Research

39 SYLVIE DUVERNOY. Leonardo and Theoretical Mathematics

51 MARK REYNOLDS. The Octagon in Leonardo’s Drawings

77 JOÃO PEDRO XAVIER. Leonardo’s Representational Technique for Centrally- Planned Temples

101 VESNA PETRESIN ROBERT. Perception of Order and Ambiguity in Leonardo’s Design Concepts

129 CHRISTOPHER GLASS. Leonardo’s Successors Geometer’s Angle

149 RACHEL FLETCHER. Dynamic Root Rectangles Part Two: Root-Two Rectangles and Design Applications Didactics

179 JANE BURRY and ANDREW MAHER. The Other Mathematical Bridge

Book Reviews

195 MICHAEL OSTWALD. A Theory of General Ethics: Human Relationships, Nature and the Built Environment by Warwick Fox

199 SARAH CLOUGH EDWARDS. Inigo Jones and the Classical Tradition by Christy Anderson

203 SYLVIE DUVERNOY. Architecture and Mathematics in Ancient Egypt by Corinna Rossi

Educational Studies in Mathematics, Vol 2

Springer Netherlands | 1969 - 1970

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1-15: Patrick Suppes, Elizabeth F. Loftus and Max Jerman -> Problem-solving on a computer-based teletype
16-31: E. Fischbein, Ileana Pampu and I. Mînzat -> Initiation aux probabilités à l'école élémentaire
32-58: Hans Freudenthal -> A teachers course colloquium on sets and logic
59-68: Floyd R. Vest -> A catalog of models for the operations of addition and subtraction of whole numbers
69-79: Maurice Glaymann -> Initiation to vector spaces
80-114: ICMI report on mathematical contests in secondary education (olympiads) I
115-122: M. Bruckheimer and N. Gowar -> Apparent conflicts in maths education
123-133: Erich Wittmann -> The development of self-reliant thinking in mathematics teaching
135-138: Hans Freudenthal -> Allocution du premier congrès international de l'enseignement mathématique lyon, 24–31 Août 1969
139-159: Bent Christiansen -> Induction and deduction in the learning of mathematics and in mathematical instruction
160-179: W. Servais -> Logique et enseignement mathématique
180-188: J. V. Armitage -> The relation between abstract and ‘concrete’ mathematics at school
189-200: R. Gauthier -> Essai d'individualisation de l'enseignement
201-211: G. G. Maslova -> Le développement des idées et des concepts mathématiques fondamentaux dans l'enseignement des enfants de 7 à 15 ans
212-231: A. Roumanet -> Une classe de mathématique: Motivations et méthodes
232-244: E. G. Begle -> The role of research in the improvement of mathematics education
245-256: A. Delessert -> De quelques problèmes touchant à la formation des maîtres de mathématiques
257-269: Arthur Engel -> The relevance of modern fields of applied mathematics for mathematical education
270-278: André Revuz -> Les premiers pas en analyse
279-289: A. Markouchevitch -> Certains problèmes de l'enseignement des mathéma atiques à l'école
290-306: E. Fischbein -> Enseignement mathématique et développement intellectuel
307-332: Emma Castelnuovo -> Différentes représentations utilisant la notion de barycentre
333-345: Frédérique Papy -> Minicomputer
346-359: Bryan Thwaites -> The role of the computer in school mathematics
360-370: Zofia Krygowska -> Le texte mathématique dans l'enseignement
371-392: Hans-Georg Steiner -> Magnitudes and rational numbers—A didactical analysis
393-404: H. O. Pollak -> How can we teach applications of mathematics?
405-414: Paul C. Rosenbloom -> Vectors and symmetry
416: Resolutions of the First International Congress on Mathematical Education
417-418: Résolutions du Premier Congrès International de l'Enseignement Mathématique
419-429: Ferenc Genzwein -> The system and the organization of further training for the mathematics teachers of the secondary schools in Budapest
430-437: E. Georgescu-Buzāu, N. Matei and Gr. Bānescu -> The importance of appropriate problems in the teaching of mathematics
438-445: Max Jerman -> A counting model for simple addition
446-468: Richard S. Long, Nancy S. Meltzer and Peter J. Hilton -> Research in mathematics education
469-475: E. E. Biggs -> Communication on primary education in mathematics
476-477: Bert K. Waits -> Relative effectiveness of two different television techniques and one large lecture technique for teaching large enrollment college mathematics courses
478-495: John C. Egsgard -> Some ideas in geometry that can be taught from K-6
496-500: Bruce R. Vogeli -> Sweep away all cows, ghosts, dragons and devils

Educational Studies in Mathematics - Volume 10

Springer |1979

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1: Alan Bishop -> Editorial statement
3-40: E. Fischbein, D. Tirosh and P. Hess -> The intuition of infinity
41-66: Adolf AF Ekenstam and Margita Nilsson -> A new approach to the assessment of children's mathematical competence
67-70: Hans Freudenthal -> Rings and string
71-83: B. V. Gnedenko and Z. Khalil -> The mathematical education of engineers
85-133: David S. Fielker -> Strategies for teaching geometry to younger children
135-146: Alan J. Bishop -> Visualising and mathematics in a pre-technological culture
147-159: Emma Castelnuovo and Daniela et Claudio Gori-Giorgi -> Le lancement des projectiles
161-197: J. L. Austin and A. G. Howson -> Language and mathematical education
199-225: M. Vandewiele and W. D'Hondt -> La perception de quelques difficultés en mathématiques par les professeurs en classe de troisième dans l'enseignement secondaire au sénégal
227-243: Johnston Anderson -> Objective testing in elementary analysis
245-262: F. Lowenthal and R. Severs -> Langage, jeu et activite mathematique
263-274: Gérard Vergnaud -> The acquisition of arithmetical concepts
135-146: Alan J. Bishop -> Visualising and mathematics in a pre-technological culture
275-303: Hans Freudenthal -> Ways to report on empirical research in education
305-322: M. A. (Ken) Clements -> Sex differences in mathematical performance: An historical perspective
323-359: E. Castelnuovo, D. Gori-Giorgi and C. Gori-Giorgi -> Coniques et gravitation universelle
361-387: A. W. Bell -> The learning of process aspects of mathematics
389-401: Elizabeth Fennema -> Women and girls in mathematics—Equity in mathematics education
403-420: Jan Brink and Leen Streefland -> Young children (6–8)-ratio and proportion
421-434: M. Sueur, J. -P. Lamarche and P. Marthe -> Locutions inductrices et distractrices: ‘de plus que’, ‘de moins que’
435-442: Frank Swetz and Ying-King Yu -> Mathematical olympiads in the People's Republic of China
443-485: F. Pluvinage -> Loto-questionnaires (pour l'evaluation et l'auto-controle en mathématiques)

Reposto a pedido de William V

iSquared - 9 a 1

iSquared is a quarterly magazine which sheds light on the growing number of real-world applications of mathematics. Modern mathematics is widely used in fields as diverse as biology, physics, engineering and economics, although many people are unaware of its importance for both everyday life and cutting-edge research. From the study of cancer growth to understanding the human genome, from dealing with climate change to the development of new communication technologies, mathematics is playing a vital role at the frontier of scientific advancement.

In iSquared Magazine you can find:

• A wide variety of feature articles about how maths is used in the modern world

• News of the latest developments at the forefront of mathematical research

• Reviews of recently released books on mathematical topics

• Biographies of celebrated mathematicians

• Interviews with people for whom mathematics is a crucial element of their work

• A range of puzzles for you to try your hand at

Site da revista: http://www.isquaredmagazine.co.uk/

Autumn, 2009 – Issue 9 Pdf – 37,7 Mb -link	Winter, 2009/2010 – Issue 10 Pdf – 68,5 Mb -link
WHERE ARE ALL THE WOMEN? Gwyneth Stallard asks why women are underrepresented in mathematics, particularly at the top end of the career spectrum ONE WOMEN AND HER THEOREM Véronique Pagé takes a look at the life of the mathematician Emmy Noether, and explains why Noether’s theorem is such an significant result for physics LEADING THE WAY Australian professor Cheryl Praeger is one of the top mathematicians of her generation. Lucinda Matthews has been finding out about her life and her work in the field of group theory WOMEN IN MATHS TODAY Mathematicians Sarah Waters and Helen Webster answer our questions about their careers, their mathematics and their aspirations for the future GREAT MATHEMATICIANS The life of Sophie Germain, who overcame the disadvantages of her sex to make some important contributions to number theory and elasticity BOOK REVIEWS Leaning Towards Infinity by Sue Woolfe, a novel about mathematics and motherhood, The Mathematics of Sex by Ceci and Williams, an investigation of the gender gap in maths-based fields	SHOPPING BY NUMBERS Jennie Lees looks at the how online  retailers use mathematics to generate personalised product recommendations for their customers WHERE OPERATIONAL RESEARCH BEGAN Cathy Buchanan explores the early  history of Operational Research, a field which came into its own during the Second World War   MATHEMATICS AND THE FUTURE OF TRANSPORT Transport mathematician John Hammersley introduces Véronique Pagé to a new type of transportation system, and explains how mathematical models are being used in its development MATHEMATICAL HISTORIES Peter Rowlett describes some of the ciphers used by ancient and medieval cryptographers, and shows how to go about breaking them  GREAT MATHEMATICIANS The life of Henri Poincaré, who was one of history’s great mathematical geniuses and who contributed to an impressive range of fields during his lifetime, both pure and applied  BOOK REVIEW The Math Book by Clifford A. Pickover, a journey through the key “milestones” in mathematical history, from 150 million B. C. to the present day
Spring, 2010 – Issue 11 Pdf – 53 Mb -link	Summer, 2010 – Issue 12 Pdf – 33,8 Mb -link
THE REMARKABLE SERIES OF JOSEPH FOURIER Véronique Pagé explains how a controversial nineteenth century mathematics paper spawned a field whose applications now range from  electronic music to crystallography 14 MATHS, MOLECULES AND MEDICAL IMAGING Anna Faherty talks to GlaxoSmithKline mathematician Roger Gunn about the role of mathematical modelling and image analysis techniques in the development of pharmaceutical drugs OUR OWN CORRESPONDENT Former foreign correspondent Alex Bellos discusses mathematics, journalism and researching his new book of ‘dispatches’ from the mathematical world MATHEMATICAL HISTORIES Peter Rowlett looks at how cosmological theories evolved over time as scientists gradually improved their understanding of the universe  through the use of mathematics and astronomical observation BOOK REVIEWS Mythematics by Michael Huber, a book  of problems based on the twelve labours of Hercules;  Alex’s Adventures in Numberland by Alex Bellos, an exploration of the land of mathematics	THE SOLITON: A WAVE LESS ORDINARY Benjamin Skuse describes how a special type of wave called the soliton went from being almost universally ignored to being both widely studied and highly valued for its practical applications, after its existence was proved mathematically MODELS FOR LIFE  Sarah Shepherd explains why discrete models for biological cells are becoming more and more popular, and shows how one such model has been applied to the simulation of cancer invasion and the phenomenon of cell sorting MATHEMATICAL HISTORIES Peter Rowlett looks at the development of probability theory, a field that owes its existence to mathematicians such as Cardano, Pascal, Huygens and Bernoulli  GREAT MATHEMATICIANS The life of the great Isaac Newton, whose many contributions to science include calculus and his laws of mechanics BOOK REVIEWS Duel at Dawn by Amir Alexander, which explores the narratives of mathematics;  Number Freak by Derrick Niederman, a compendium of integers

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iSquared - 5 a 8

iSquared is a quarterly magazine which sheds light on the growing number of real-world applications of mathematics. Modern mathematics is widely used in fields as diverse as biology, physics, engineering and economics, although many people are unaware of its importance for both everyday life and cutting-edge research. From the study of cancer growth to understanding the human genome, from dealing with climate change to the development of new communication technologies, mathematics is playing a vital role at the frontier of scientific advancement.

In iSquared Magazine you can find:

• A wide variety of feature articles about how maths is used in the modern world

• News of the latest developments at the forefront of mathematical research

• Reviews of recently released books on mathematical topics

• Biographies of celebrated mathematicians

• Interviews with people for whom mathematics is a crucial element of their work

• A range of puzzles for you to try your hand at

Site da revista: http://www.isquaredmagazine.co.uk/

Autumn, 2008 – Issue 5 Pdf – 54 Mb -link	Winter, 2008/2009 – Issue 6 Pdf – 71 Mb -link
The mathematical origins of string theory 8 Andrew Dalrymple The story of how one of the most promising candidates for a “theory of everything” developed from the discovery of an application for a 200-year-old mathematical equation. Modelling the big freeze 18 Jacqueline Whitcombe How mathematics can help scientists to understand the dynamics of ice ages. The story of modern statistics 30 Philip Robinson The birth and evolution of statistics, from its origins in probability theory and the study of annuity tables to the development of the field as we know it today. Mathematical greats 14 The life of Blaise Pascal, one of the greatest thinkers of the seventeenth century. Book reviews 24 Lewis Carroll in Numberland, by Robin Wilson How many socks make a pair? by Rob Eastaway Interview 26 Rüdiger Jehn, mission analyst at the European Space Agency, discusses his work and the importance of mathematics for space science. Puzzles 36	The shape of time 8 Véronique Pagé How Einstein’s theories of relativity completely altered our view of space and time. The unnatural nature of asymptotic approximations 18 Phil Trinh The Devil’s divergence: Why mathematicians pay a high a price in their attempts to approximate real-world phenomena. The limits of computation 30 By Graeme Taylor An exploration of Turing machines, the P vs. NP problem and Artificial Intelligence. Special review: The Story of Maths 14 A review of the recent BBC4 programme on the history of mathematics. Mathematical greats 16 The story of George Green, the miller-mathematician of Nottingham. Book review 24 Professor Stewart’s Cabinet of Mathematical Curiosities, by Ian Stewart. Interview 26 Keith Briggs, a mathematician in BT’s research department, explains why mathematics has an important role to play in the telecommunications industry. Puzzles 36
Spring, 2009 – Issue 7 Pdf – 33 Mb -link	Summer, 2009 – Issue 8 Pdf – 38,5 Mb -link
SYMMETRY MAN Marcus du Sautoy tells Jacqueline  Whit combe about his research into  symmetry and his new position as  Simonyi Professor for the Public  Understanding of Science CHAINS, CRAYONS  AND SOCIAL NETWORKS Samantha Lam looks at some of the  applications of graph theory, including  the study of online social networks DRINKING THE STARS Mathematics can be used to investigate the interesting behaviour of bubbles,  Daniel Sutton explains ARROWS HAVE A POINT PART 1: THE LANGUAGE OF  MATHEMATICS David Stern and Michael Obiero explore the language of quivers and show how they enable us to study algebra using pictures GREAT MATHEMATICIANS The life of Carl Friedrich Gauss, who contributed to a wide range of fields and is ranked as one of the greatest mathematicians who ever lived BOOK REVIEW Naming Infinity, by Loren Graham and  Jean-Michel Kantor, which tells the story  of how mysticism was a key influence  for Russian mathematicians and their research into the nature of infinity	WEAPONS OF FINANCIAL  MASS DESTRUCTION The economic crisis was caused by a failure to understand the maths behind  financial products, says Kate Roberts ARROWS HAVE A POINT PART 2: MATHEMATICS AND PATTERNS David Stern and Michael Obiero conclude their two-part article on quivers with a look at the patterns that arise in quiver family trees  CLEARING THE WATERS Mathematical models show that it is dangerous for governments to make  compromises over water pollution,  explains Cian Murphy SAFETY IN NUMBERS Kirstie Pelling talks to Keith Still about his work on modelling crowds HOW DO SHAPES FILL SPACE? Edmund Harriss gives a brief introduction to tilings NEWS Wolfram Alpha, London murders, swine flu, tsunami modelling, and more BOOK REVIEWS A Mathematical Nature Walk, by John Adam, which looks at the mathematics  of the natural world  Finding  Pythagoras, a mathematical mystery novel by Arturo Sangalli  GREAT MATHEMATICIANS The life and works of the legendary  mathematician and engineer Archimedes

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iSquared - 1 a 4

iSquared is a quarterly magazine which sheds light on the growing number of real-world applications of mathematics. Modern mathematics is widely used in fields as diverse as biology, physics, engineering and economics, although many people are unaware of its importance for both everyday life and cutting-edge research. From the study of cancer growth to understanding the human genome, from dealing with climate change to the development of new communication technologies, mathematics is playing a vital role at the frontier of scientific advancement.

In iSquared Magazine you can find:

• A wide variety of feature articles about how maths is used in the modern world

• News of the latest developments at the forefront of mathematical research

• Reviews of recently released books on mathematical topics

• Biographies of celebrated mathematicians

• Interviews with people for whom mathematics is a crucial element of their work

• A range of puzzles for you to try your hand at

Site da revista: http://www.isquaredmagazine.co.uk/

Autumn, 2007 – Issue 1 Pdf – 20 Mb -link	Winter, 2007/2008 – Issue 2 Pdf – 18,5 Mb -link
Optimisation on the high seas 9 Catherine Buchanan and David Stern Dynamic programming is a powerful mathematical tool which can be applied to find the quickest route between two points when travelling by sailing boat. Can mathematics solve the problem of malaria? Deborah Cromer How mathematical models can shed light on one of the world’s deadliest diseases. The mathematics of being nice 24 Graeme Taylor Mutual co-operation gives the best outcome, but what is the winning strategy in game theory’s Prisoner’s Dilemma? Survival or extinction? 30 Daniel Rowe Population viability analysis: determining whether a species will stick around. Mathematical greats 14 The life and work of the Hungarian-born US mathematician, John von Neumann. Book review 22 Symmetry and the Monster, the story of one of the greatest quests of mathematics. Puzzles 36	The key to a secure future 8 David Mireles Morales Why public-key cryptography is vital for confidential communications in the digital age. The theory of flight 16 Ophir Samson Many people are given an incorrect explanation of how aircraft achieve lift. Herewe look at how it actually works. Calculations, calculus and computing 24 Rebecca Morris Some historical applications of mathematics, from counting to route-finding. Mathematics and Poetry 28 Selections from a new book of poetry by mathematician Michael Bartholomew-Biggs. Mathematical greats 14 The life of Georg Cantor, whose theory of the infinite brought fierce oppositionfrom his contemporaries. Book review 22 The Mathematician’s Brain, by David Ruelle. Plus, a selection of other recent releases. Interview 30 Roman Hovorka explains how maths is being used to develop an artificial pancreasfor diabetes patients. Puzzles 36
Spring, 2008 – Issue 3 Pdf – 48 Mb -link	Summer, 2008 – Issue 4 Pdf – 32,5 Mb -link
Lies, damned lies, and statistics 8 Kirsty Hinchliff and John Rhodes Why hidden variables and statistical paradoxes can lead to difficulties when trying to drawvalid conclusions from data. Theoretical Neuroscience: neurons, patterns and hallucinations Nikola Venkov How mathematics is vital for the new field of theoretical neuroscience. The Möbius Strip: A beacon for uniqueness 24 Mike Watson The practical and philosophical implications of this strange mathematical object. Honouring mathematical greats 30 Simon Lazarus Mathematical prizes, from the Fields Medal to the Millennium Prize Problems. Mathematical greats 12 The life and work of D’Arcy Wentworth Thompson, the Scot who has become known as “the first biomathematician”. Book review 20 Nets, Puzzles, and Postmen, by Peter M Higgins. Interview 26 The Met Office’s John Hughes discusses maths, the carbon cycle and climate change. Puzzles 36	Chemotaxis: how bacteria move 8 Nikita Vladimirov Why mathematical modelling is useful for understanding chemotaxis, a mechanism used by bacteria to enable them to travel up chemical gradients towards nutrient-rich regions. We’re not all prisoners in here 18 Chris Gaffney How players can benefit from forming coalitions in Cooperative Game Theory. Rheology: The science of deformation and flow 30 Tim Reis The mathematics behind some of the strangest phenomena in materials science,including the “miracle” of walking on custard. Mathematical greats 14 The life and tragic early death of Alan Turing, who is famous for founding the field of computer science and for his contributions to British cryptanalysis during World War II. Book review 24 The Music of Pythagoras, by Kitty Ferguson. Interview 26 Quantitative analyst Iain Clark explains how maths is used in the world of finance. Puzzles 36

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Educational Studies in Mathematics - vol 18

Educational Studies in Mathematics
Springer Netherlands
1987

Volume 18, Number 1 / February 1987

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Artigos:

Common logical errors in English and ChineseR. Zepp, J. Monin and C. L. Lei

Fonctions du code symbolique dans le discours mathématiqueFrançoise Boschet

The secondary school mathematics curriculum in ChinaF. K. S. Leung

A framework for assessing mathematical creativity in school childrenDerek W. Haylock

Ghosts of diophantusEon Harper

Private tutoring a hidden educational problemMansour G. A. Hussein

Book reviews* H. N. Jahnke -> George Adams -- Geometrische und Graphische Versuche oder Beschreibung der mathematischen Instrumente, deren man sich in der Geometrie, der Zivilund Militär-Vermessung, beim Nivellieren und in der Perspektive bedient (1985, ISBN: 3534093089)* Ole Skovsmose -> R. Fischer und G. Malle, unter Mitarbeit von H. Bürger -- Mensch und Mathematik (1985)

Announcements 


Volume 18, Number 2 / May 1987  

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Artigos: 

An investigation of young children's academic arithmetic contextsPaul Cobb

Integrated column arithmetic according to progressive schematisationA. Treffers

Processus de preuve et situations de validationNicolas Balacheff

Using problem solving teaching styles to prepare candidates for the CXC basic proficiency examinationsIan Isaacs

A tale of 804.573 horses: Arithmetic teaching in Victoria 1860–1914Rachel Griffiths

Book reviews* Josette Adda -> Serge Lang -- Des jeunes et des maths. Un chercheur rencontre des collégiens (1986, ISBN: 2701104963)* Anna Sierpińska -> Dydaktyka Matematyki


Volume 18, Number 3 / August 1987   

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Artigos: 

Guest editorial
Josette Adda

Coming alive in school math and beyond
Hassler Whitney

Ability stereotyping in mathematics
Kenneth Ruthven

Teacher student interaction: A case study
Gilah C. Leder

The reality and potential of correcting pupils' work in mathematics
Stella Baruk

From failure to success: Changing the experience of adult learners of mathematics
Leone Burton

Roos and José, two children in a mixed ability group
Rijkje Dekker

A cautionary note
B. F. Sherman

Response to ‘a cautionary note’
Gilah C. Leder

Book reviews
* Lucia Grugnetti -> Rosie Walden and Valerie Walkerdine -- Girls and Mathematics (1985)
* Colette Laborde -> A. G. Howson and J. P. Kahane (eds.) -- The Influence of Computers and Informatics on Mathematics and Its Teaching (1986, ISBN: 0521324025, 0521311896)

Volume 18, Number 4 / November 1987   

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Artigos: 

Learning to apply numbers to natureHelen Watson

Linking logo, levels and language in mathematicsA. T. Olson, T. E. Kieren e S. Ludwig

Humanities students and epistemological obstacles related to limitsAnna Sierpińska

Factors contributing to mathematical problem-solving performance: An exploratory studyNina Kay Buchanan

A calculator, a tape recorder, and thouDavid S. Fielker

Factors affecting girls' learning of mathematics in SudanA. B. Pollitt, J. W. Searl e A. S. El Sheikh

Videodisc technology and mathematics educationNeil Straker

Book review* Peter Damerow -> Schubring, Gert -- Die entstehung des mathematiklehrerberufs im 19. Jahrhundert. Studien u. Materialien zum prozeß d. Professionalisierung in preußen (1810–1870)

Announcement