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The three semester M.Arch. II program establishes an investi gativeand rigorous ramework or experimentation and research intoarchitecture and architectural design. Option studios, seminars,and the fnal thesis are opportunities or both individual a nd collec-tive work on themes/practices that examine existing assumptionsin architecture. Some o these studios and courses, in 2004-05,have looked closely at logics o organization in urban, institu-tional, and architectural systems; state transportation networks;algorithms, rule-based systems, and digital mapping; constraintsand limits; theories o suraces; mathematics and topology; prob-

lems o the vertical; biological and physical systems; the politicso architecture; interace and media; theories o technology andmaterials; and questions o history in architectural work.

The program questions the multitude o assumptions thatlie behind the architectural conventions o program, site, anddesign methodology in order to create new design processes andstrategies. The program also brings the student into the manyprovocative discussions and practices currently underway in thediscipline and practice o architecture.

Jason Vigneri-Beane, coordinator

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M.Arch II Thesis

Master in Architecture II Thesis

Master in Architecture II Thesis Advisor

Peter Macapia

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Thesis Design

Peter Macapia, critic

Each year we select a topic o particular but open-endedrelevance that raises undamental questions about archi-tecture as a discipl ine, including its history, techniques, andpotential. This year we ocus on the question o its use omathematics and we pose the ollowing: In what way ismathematics internal to architecture and what is its his-tory? What has it contributed to architecture, to the logico its discipline, to built orm, or to its identity? More pre-cisely, is its internality paradigmatic or purely instrumental?And what is its contemporary status? Each thesis projecthas taken up these questions in a dierent way, reinventingtheir meaning and their sense.

a. Anushka Kalbagb. Armando Araiza

Mathematics in ArchitectureStudent Selected Sites

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Thesis Design

Mathematics in Architecture

Peter Macapia, critic

Although it is doubtul that there are any decisive answers,examining these questions through design techniqueswill enable the student to acquire a unique and prooundrelation to the specifcity o architecture as a discipline,particularly today in the context o its massive technologi-cal transormation. For, given the act that computationaldesign has increasingly pushed (almost entirely throughmathematical fnesse) the parameters o what is conceiv-able in terms o orm, it seems crucial that we play anactive role in rethinking this adventure both critically andenthusiastically. And yet, the problem is not merely given.It requires invention, historical insight, contemporary analy-sis, and, above all, a design context.

Student Selected Sites

a. A aron Whiteb. Chri stian Rietzke

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Thesis Design

Mathematics in Architecture

Peter Macapia, critic

Architecture has traditionally been concerned in one wayor another with mathematics as a language o continuity:the continuity between a conceptual diagram and construc-tion, or the continuity between a particular organization omatter (tectonics) and its appearance (orm). But althoughmathematics - and particularly geometry - has served as theone o the primary media or the conceptualization o conti-nuity, it has oten done so with a kind o duplicity. There arenumerous and dierent kinds in both practice and theory,but they are more or less similar to Vitruviuss account otemple design where he prescribes two mutually exclusiveuses o geometry. On the one hand, he prescribes an idealPlatonic geometry or the design and orm o the temple,and, on the other, he prescribes an instrumental geometryto resolve the problems o appearance in the fnal construc-tion. The reason is that once a temple is built, geometryseects have a tendency to drit and, thereore, certain inter-ventions become necessary, such as entasis (the applica-tion o a curve to orthogonal elements) in order to provideconsistency between idea and appearance, concept andperormance, law and event, truth and sense. This secondintroduction o geometry, then, is quite dierent: it covers

not general laws, but rather that which is too-specifc, theremainder that disturbs the equilibrium o the general, thatwhich organizes matter as such.

While it is true that this remainder is olded backinto the general through the economy o a geometricaloperation, geometry-- and all that it implies by technique-- no longer means the same thing. It operates between ageneral law on the Symbolic level o Form (Eidos) and asspecifc instrument o intervention or that which is, as itwere, too-specifc.

Student Selected Sites

a. M ario Vergarab. Jae hong Lee

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Thesis Design

Mathematics in Architecture

Peter Macapia, critic

Student Selected Sites

a. Margaret Kirkb. Lilian Gendelman

I, historically, architecture has regarded itsel as a disciplinethat mediates general laws and specic qualities and expe-riences, rom a theoretical and mathematical point o view,it has usually assumed that the specic unolds rom thelawulness o the general i.e. that there pre-exist math-ematical truths. And, up until the late 18th century, suchassertions were primarily Platonist in character (though attimes more Aristotelian, as in Gothic). Since the late 18thand 19th century, however, new regimes o analysis haveorced various revisions o architectures general technical

and conceptual tools (rom tectonics to program). Math-ematics has similarly undergone a remarkable transorma-tion in terms o concepts o coherence and continuity. Forexample, in order to acquire a mathematical picture o rateso change in complex material phenomena such as fow,mathematicians began to exchange concepts o numericaldiscreteness with concepts o unctional relations, that is,patterns and continuities. As a result o this and similarmathematical shits, the space o geometrical thinkingin architecture has begun to biurcate into various orms oanalytical mathematics such as innitesimal calculus andtopology. These shits have engendered much more than

novel conceptions o orm; they have orced architecture torethink the categories o its ontology and its tools.

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