Cad Logicdia - Dessau International Architecture graduate school

Prof. Daniel DendraIrina Michaela Bogdan - Valentina De León

SS-2009

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 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.

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