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Leonardo da Vinci described the arch as "two weaknesses which, leaning on each other, become a strength," a metaphor for the way that science and art lean on each other to strengthen our lives.

Such principles not only provide an order for the formal elements, they ground the architecture in timeless values and provide an order for the formal elements, they ground the architecture in timeless values and provide a source of cultural meaning.

This issue is dedicated to various kinds of patterns in architecture. Buthayna Eilouti and Amer Al-Jokhadar address patterns in shape grammars in the ground plans of Mamluk madrasas, religious schools. Giulio Magli goes back further in history, to the age of Greek colonies in Italy before they were conquered by the Romans, to examine patterns in urban design. In Traditional Patterns in Pyrgi of Chios: Mathematics and Community Charoula Stathopoulou examines the geometric patterns that decorate the buildings of the town of Pyrgi, on the Greek island of Chios. Curve Fitting is a study of ways to construct a function so that its graph most closely approximates the pattern given by a set of points. Dirk Huylebrouck¿s paper examines how a pattern of points extracted from an arch might be associated to a precise mathematical curve. James Harris looks at the designs of Frank Lloyd Wright and Piet Mondrian to extract the rules of their pattern generation and propose possible applications.

This issue is dedicated to Mechanics in Architecture. It explores the latest findings in the science of structural mechanics, including the behavior of structures, internal forces, and deformation. It also explores the development of new structural systems designed to resist thrusts resulting from new architectural forms.

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.

This volume features a collection of papers dedicated to "Canons of Form-Making", in honor of the 500th anniversary of the birth of architect Andrea Palladio (1508-1580).

Baroque architect and mathematician Guarino Guarini is the subject of this issue of the Nexus Network Journal.

The title of this issue of the Nexus Network Journal, "Architecture, Mathematics and Structure," is deliberately ambiguous. But on a deeper level, the fundamental concept of structure is what connects architecture to mathematics. Both architecture and mathematics are highly structured formal systems expressed through a symbolic language.

In celebration of the 2009 International Year of Astronomy, this issue of the Nexus Network Journal is devoted to relationships between astronomy, mathematics and architecture. Papers in this issue look at how astronomy influenced architecture and urban design.

Letter From The Editor.- Letter From The Editor.- Architecture, Mathematics and Perspective.- Giotto and Renaissance Perspective.- Perspective, a Visionary Process: The Main Generative Road for Crossing Dimensions.- Perspective in a box.- Juan Bautista Villalpando and the Nature and Science of Architectural Drawing.- Perspective versus Stereotomy: From Quattrocento Polyhedral Rings to Sixteenth-Century Spanish Torus Vaults.- The Sunlight Effect of the Kukulc¿Pyramid or The History of a Line.- Some Adaptations of Relativity in the 1920s and the Birth of Abstract Architecture.- Book Reviews.- The Mirror, the Window, and the Telescope: How Renaissance Linear Perspective Changed Our Vision of the Universe.- The Geometry of an Art. The History of Perspective from Alberti to Monge.- Forma y Representaci¿n. Un An¿sis Geom¿ico.

Through time, thought has reflected on the visible processes and products of material craft to explain and train the invisible workings of the mind. Mythic parables, geometric proofs, memory arts, poems, algorithms, buildings and cities emerge from the intercourse of measure and explication.

Letter from the Editor.- Letter from the Editor.- Recalling Eero Saarinen 1910-2010.- How the Gateway Arch Got its Shape.- Saarinen's Shell Game: Tensions, Structures, and Sounds at MIT.- The Next Largest Thing: The Spatial Dimensions of Liturgy in Eliel and Eero Saarinen's Christ Church Lutheran, Minneapolis.- Morphocontinuity in the work of Eero Saarinen.- Eero Saarinen, Eduardo Catalano and the Influence of Matthew Nowicki: A Challenge to Form and Function.- Eero Saarinen's North Christian Church in Columbus, Indiana.- Other Research.- On the Modular Design of Mughal Riverfront Funerary Gardens.- Discontinuous Double-shell Domes through Islamic eras in the Middle East and Central Asia: History, Morphology, Typologies, Geometry, and Construction.- At the Other End of the Sun's Path: A New Interpretation of Machu Picchu.- The Body, the Temple and the Newtonian Man Conundrum.- Book Review.- The Symbol at Your Door: Number and Geometry in Religious Architecture of the Greek and Latin Middle Ages.- Conference Report.- Architecture and Mathematics. A seminar to celebrate Professor emeritus Staale Sinding-Larsen's 80th birthday.- Erratum.- Erratum to: The Sunlight Effect of the Kukulcán Pyramid or The History of a Line.

This is an outgrowth of the session by the same name which took place during the eighth international, interdisciplinary conference "Nexus 2010: Relationships between Architecture and Mathematics, held in Porto, Portugal, in June 2010.

from the creation of a design system involving a parametric shape grammar with descriptions to generate urban block layouts within a defined spatial region, to a novel example of a kinetic shape grammar simulating human body movements.

2) issue of the Nexus Network Journal features eight papers that resulted from the eighth international, interdisciplinary conference entitled "Nexus 2010: Relationships between Architecture and Mathematics, held in Porto, Portugal, in June 2010.

This book explores Persian architecture and mathematics, including domed structures and two-dimensional patterns, elaborate geometry and complex three-dimensional structures of historic monuments, from mathematical ideas to architectonic structures.

This title features papers that examine issues in digital fabrication as well as different mathematical instruments applied to architecture, including geometric tracing systems, proportional systems, descriptive geometry and correspondence analysis.

What the papers in this issue make especially evident is that information technology has had an impact at a much deeper level as well: architecture itself can now be considered as a manifestation of information and as a complex system.

This book presents an exploration of the arch from the points of view of architecture, mathematics, engineering, construction history, and cultural symbolism. The arch, one of the most beautiful ways that architects invented to go from "herea to "there, a spans greater distances and sustains larger loads than a simple post and beam structure, but because it is also more complex, an Eastern proverb called it "the structure that never sleeps.a Leonardo da Vinci described the arch as "two weaknesses which, leaning on each other, become a strength, a a metaphor for the way that science and art lean on each other to strengthen our lives.