Tensile Riemann

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Transcript of Tensile Riemann
Cad Logicdia  Dessau International Architecture graduate school
Prof. Daniel DendraIrina Michaela Bogdan  Valentina De León
SS2009
Slitting1st Session
Tensed Structures1st Session
Tensed Structures2nd Sessionused functions (tan,tan)
Tensed Structures3rd Sessionused functions (tan,tan)
Tensed Structures4th Sessionused functions (tan,tan)
Tensed Structures5st Session
Minimal SurfacesStarting point_formula
used functions (tan,tan)
1st and 2nd SessionMinimal Surfaces
Tensed StructuresMathematicaused functions (tan,tan)
R i e m a n n S u r f a c e
A Riemann surface is a surfacelikeconfiguration that covers the complexplane with several, and in generalinfinitely many, "sheets." These sheetscan have very complicated structuresand interconnections (Knopp 1996,pp. 9899). Riemann surfaces are oneway of representing multiplevaluedfunctions.
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 socalledRiemannian 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.
Tensed StructuresSnd Sessionused functions (tan,tan)
Riemann Surfaces of Inverses
of Sums of Two Trigonometric
Functions
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.
Model
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
Minimal SurfacesExplorations_furniture I
Minimal SurfacesExplorations_furniture II
Minimal SurfacesExplorations_pavilion
Minimal SurfacesExplorations_module I
Minimal SurfacesExplorations_module II
Minimal SurfacesExplorations_ornament
Minimal SurfacesDiagrams