Tensile Riemann

Cad Logic dia - Dessau International Architecture graduate school Prof. Daniel Dendra Irina Michaela Bogdan - Valentina De León SS-2009


We started from a Riemann minimal surface and we modified it. We have made several modules on which we have applied different tensile forces. After that we used the modules for creating different other compositions [furniture, ornament and a pavilion shell]

Transcript of Tensile Riemann

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Cad Logicdia - Dessau International Architecture graduate school

Prof. Daniel DendraIrina Michaela Bogdan - Valentina De León


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Slitting1st Session

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Tensed Structures1st Session

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Tensed Structures2nd Sessionused functions (tan,tan)

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Tensed Structures3rd Sessionused functions (tan,tan)

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Tensed Structures4th Sessionused functions (tan,tan)

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Tensed Structures5st Session

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Minimal SurfacesStarting point_formula

used functions (tan,tan)

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1st and 2nd SessionMinimal Surfaces

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Tensed StructuresMathematicaused functions (tan,tan)

R i e m a n n S u r f a c e

A Riemann surface is a surface-likeconfiguration that covers the complexplane with several, and in generalinfinitely many, "sheets." These sheetscan have very complicated structuresand interconnections (Knopp 1996,pp. 98-99). Riemann surfaces are oneway of representing multiple-valuedfunctions.

A Riemann surface is a manifold of(real) dimension two – a surface –together with a conformal structure.Again, manifold means that locally atany point x of X, the space is supposedto be like the real plane. Thesupplement "Riemann" signifies that Xis endowed with an additionalstr ucture which al lows anglemeasurement on the manifold, namelyan equivalence class of so-calledRiemannian metrics. Two suchmetrics are considered equivalent ifthe angles they measure are the same.Choosing an equivalence class ofmetrices on X is the additional datum ofthe conformal structure.

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Tensed StructuresSnd Sessionused functions (tan,tan)

Riemann Surfaces of Inverses

of Sums of Two Trigonometric


The graphic shows some sheetsof the Riemann surface of fori n v e r s e s o f s u m s o ft r i g o n o m e t r i c f u n c t i o n sSubscript[f, 1] and Subscript[f,2] . For purely real or imaginaryp a r t s ( \ [ A l p h a ] = 0 o r\[Alpha]=1), multiple sheetscan degenerate into a singlesheet.


Starting form the RIEMANNSURFACE graphics made inMathematica we chose oneof the solutions[tan,tan] andreproduced it in a physicalmodel by using a cilindricalsurface and 2 V CUTS

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Minimal SurfacesExplorations_furniture I

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Minimal SurfacesExplorations_furniture II

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Minimal SurfacesExplorations_pavilion

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Minimal SurfacesExplorations_module I

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Minimal SurfacesExplorations_module II

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Minimal SurfacesExplorations_ornament

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Minimal SurfacesDiagrams

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