Introduction : Mathematics and design -- 1. Mathematical surfaces and seriality : Australian Wildlife Health Centre, Healesville Sanctuary, Australia / Minifie Nixon -- Beijing International Airport / Foster + Partners -- Inversion modelling, Wolverhampton, UK / John Pickering -- Sagrada Família, Barcelona, Spain / Antoni Gaudí -- Main Station Stuttgart, Germany / Ingenhoven Architects -- Disney Concert Hall, Los Angeles / Gehry Partners -- Abu Dhabi Airport, Abu Dhabi, UAE / Kohn Pedersen Fox -- 2. Chaos, complexity, emergence : Federation Square, Melbourne, Australia / Lab Architecture Studio -- Louvre Abu Dhabi, Abu Dhabi / Ateliers Jean Nouvel -- Jyväskylä Music and Arts Centre, Jyväskylä, Finland / Ocean North -- Seroussi Pavilion, Paris / Biothing -- 3. Packing and tiling : Battersea Power Station, London / Arup AGU -- The Water Cube, Beijing / PTW Architects -- Grand Egyptian Museum, Cairo / Heneghan Peng -- The Spiral Extension, Victoria & Albert Museum, London / Daniel Libeskind -- Storey Hall, Royal Melbourne Institute of Technology, Melbourne, Australia / Ashton Raggatt McDougall -- Spanish Pavilion, Expo 2005, Aichi, Japan / Foreign Office Architects -- Centre for Ideas, Victoria College of the Arts, Melbourne, Australia / Minifie Nixon -- 4. Optimization : British Museum Great Court, London / Foster + Partners -- Smithsonian Institution, Washington, D.C. / Foster + Partners -- Qatar Education City Convention Centre, Doha, Qatar / Arata Isozaki -- Melbourne Rectangular Stadium, Australia / Cox Architects -- Island City Central Park, Fukuoka, Japan / Toyo Ito -- The Pinnacle, London / Kohn Pedersen Fox -- Al Raha Development, Abu Dhabi / Foster + Partners -- Melbourne Recital Centre, Australia / Ashton Raggatt McDougall -- 5. Topology : Möbius House, Het Gooi, Netherlands / UN Studio -- Arnhem Central, Arnhem, Netherlands / UN Studio -- Paramorph II, London / Decoi Architects -- Cape Schanck House -- Blowhouse: life support unit, Mornington Peninsula, Victoria, Australia / Paul Morgan Architects -- Slavin House, Venice, California / Greg Lynn -- Klein Bottle House, Mornington Peninsula, Victoria, Australia / McBride Charles Ryan -- Möbius Bridge, Bristol, UK / Hakes Associates -- Villa Nurbs, Girona, Spain / Cloud 9 Architecture -- National Museum of Australia, Canberra, Australia / Ashton Raggatt McDougall -- Metropolitan Opera House, Taichung, Taiwan / Toyo Ito -- 6. Datascapes and multi-dimensionality : De Draai extension, Heerhugowaard, Netherlands / Karres En Brands -- freshHtwoOexpo, Zeeland, Netherlands / NOX Architects -- Streaming House, Melbourne, Australia / Minifie Nixon -- Aegis Hyposurface, Birmingham, UK / Decoi Architects -- Spoorg, Los Angeles / SERVO -- Hotel Prestige Forest, Barcelona, Spain / Cloud 9 Architecture -- Yas Hotel, Abu Dhabi, UAE / Asymptote -- Muscle ReConfigured + Interactive Wall, Delft, Netherlands / Hyperbody -- Digital Water Pavilion, Zaragoza, Spain / Carlo Ratti Associati.