Faces of Geometry: II Edition

Preface
Organizing Board
Contents
Contributors
The Siege of Florence Between Chorography and Scenography
	1 Introduction
	2 The Urban Survey in Florence in the Sixteenth Century
	3 Geometric Analysis of the Fresco
	4 Towards a Chorography
	5 The Conclusion, a Scenography
	References
From the Earth to the Moon: Two Stories of Women and Mathematics
	1 Introduction
	2 Refrigerator Ladies
		2.1 Human Computers and Ballistics from World War II
		2.2 From Man to Machine: Eniac Hardware and Software
		2.3 Refrigerator Ladies
	3 From the Earth to the Moon
		3.1 Margaret Hamilton
		3.2 Moon Mathematics
		3.3 Put the Experience to Good Use
	References
Mathematics for Social Integration
	1 Introduction
	2 StreetMath: The Learning Environment
	3 Examples of Activities
	4 Findings and Conclusions
	References
Stanley Kubrick’s Perfection and the Divine Proportion
	1 Introduction
	2 Notes on the Concept of Golden Proportion
	3 Kubrick and Mathematics
	4 Kubrick and the Golden Number
	5 Conclusions
	Filmography
	References
Roses in Architecture: One Symbol, Different Objects
	1 Introduction
	2 Observe and Combine
		2.1 Piazza Del Campidoglio in Rome
		2.2 Skyscraper 30 St. Mary Axe London
	3 Conclusions
	References
The Fibonacci Numbers: A Link with Geometry, Art and Music
	1 Introduction
	2 Fibonacci: Geometry and Art
	3 Fibonacci and Music
	References
The Importance of Geometrical Properties in Industrial Turbofan Design
	1 Beauty and Efficiency
	2 Turbofan
	3 Geometry
	4 Considerations on the General Design of the Volute
	5 Experimental Study
	6 Results and Discussion
	7 Perspectives of Future Research Activity Related to the Turbomachinery Volute Optimal Geometry
	References
The Geometry of Beauty
	1 The Triangle
	2 A Particular Polygon: The Golden Rectangle
	3 From the Golden Spiral to the Helicoid
	References
Resiliency in Geometric Aggregation and Social Connectivity: Anna Bofill Levi and the Taller de Arquitectura
	1 Thinking and Practicing Out of the ‘Block’:  Anna Bofill Levi
		1.1 Groundbreaking Multidisciplinarity for Freedom
	2 Resiliency in Voids Full of Possibilities: Anna Bofill Levi’s “Theory of Form”
		2.1 Adaptabilities to Inhabiting Needs, Buildings Techniques, Time and Cost Constraints
		2.2 Prefabrication, Industrialization or Traditional Local Building Techniques
		2.3 The Standard Time of Construction for Non-standarized Architectural Bodies
	3 Porosity and Adaptability for Thermo-Hygrometric Control and Socio-Cultural Environmentalism in a Gender Perspective
	References
Christine de Pizan and Her Treatise on Fortifications (1410)
	1 Introduction
	2 The Book of the City of Ladies (1405)
	3 The Book of Feats of Arms and of Chivalry (1410): A Short Historiography
	4 The Book of Feats of Arms and of Chivalry (1410): Topics and Issues Related to Fortifications
	References
Transposition of Biomimetical Principles into Generative Design: Example of the Species Campanula patula L
	1 Introduction
		1.1 Related Work
	2 Overview
	3 Method
	4 Freeform Curves
		4.1 Mathematical Background to Free Form Curves
	5 Modeling Process
	6 Results and Applications
	7 Discussion
	8 Conclusion
	References
Primary Masterclass Maths
	1 History and Organisation
	2 The Activities
	3 The Chosen Topics
	4 Conclusion and Evaluation
	References
Geometric Structures as Design Approach
	1 Introduction
	2 Geometric Structures
	3 Examples of Geometric Structures in Works of Art
	4 Examples of Geometric Structures in Works of Architecture
	5 Conclusions
	References
Geometrical and Fashion, the Case of Iris van Herpen
	1 Geometry and Fashion—Clothing Modelling
	2 The Role of Geometry in the Fashion Project
	3 Digital Creation
	4 Iris van Herpen
	5 Conclusions
	References
Geometrical Solution for the Trisection Problem
	1 Introduction
	2 Greek and Arab Methods
		2.1 Euclid’s Theorem
		2.2 Ptolemy’s Theorem
		2.3 Algebraic Equation
	3 Archimedes’s Method
	4 Solutions Using Algebraic Curves
		4.1 Pappus Solution
		4.2 The Solution with the Conchoid of Nicomedes
		4.3 Solution with the Use of Pascal’s Snail
		4.4 Solution Using the Maclaurin Trisectrix
	5 Letter from Jacopo Riccati to Maria Gaetana Agnesi (1751)
		5.1 Geometric Meaning
	6 Other Geometric Method: Using the Square
	7 Trisection’s Approximation of Arbitrary Angles Using Only Straightedge and Compass
	8 Conclusions
	References
Margherita Piazzolla Beloch in the Italian Mathematics Education Tradition
	1 From Algebraic Geometry to Applied Mathematics, from Rome to Ferrara
	2 The Educational Value of Mathematics
	3 A Variety of Devices to Solve Elementary Geometric Problems
	References
Grete Hermann and Effective Methods in Geometry
	1 Who Is Grete Hermann?
	2 Hermann’s Mathematical Studies in Göttingen
	3 The Doctoral Thesis of Grete Hermann and Some Developments
	4 Grete Hermann’s Work and the Physicists’ Community
	References
Perspective with Nature: Daniele Barbaro, Jean François Niceron and a Device of Giovanni Battista Vimercati
	1 Filology and Gnomonics in the Renaissance
	2 Conic Section, Gnomonics and Linear Perspective
	3 Drawing with Shade and Shadows
	4 Conclusion
	References
Geometrical Discretization for Differential Equations
	1 Finite Volume Methods
	2 Mesh Forms and Quality
	3 Example of Mesher—SnappyHexMesh
	4 Mesh Optimization
	5 Mesh Independence Study
	6 Final Considerations
	References
For Representation, a New Reality: Hybrid Immersive Models
	1 Introduction
	2 The State of the Art
	3 Method
	4 Deductions
	5 Expected and Achieved Results
	Bibliography
The Fatal Birth of Architecture: The Obligation of Order
	1 Context
	2 The Fatal Birth of Architecture. the Obligation of Order [1]
	3 Bio-Mimetic Processes and Optimization of Generative Strategies
	4 Conclusion
	References
Design of Individualized Digital Activities Fostering Strategic Planning in Linear Algebra
	1 Strategic Planning and Linear Algebra
	2 Theoretical Framework
	3 Materials and Methodology
	4 Design and Implementation Details of the IPSE
		4.1 The Structure of the IPSE
		4.2 Examples of Activities of the IPSE4
	5 Outcomes of the Study and Analysis
	6 Conclusive Discussion
	References
Measures
	1 Parallels of Mathematics and Art
	2 Measures in Mathematics
	3 Measures in Art
	References
Patterns
	1 Introduction
		1.1 What Is a Pattern?
	2 Applications of Pattern in Mitla, Čičmany and Tessellation
		2.1 Patterns in Mitla
		2.2 Patterns of Čičmany
		2.3 Tessalation Ad Voronoi Patterns
	References