Modelli matematici per le applicazioni 2015-16

Corso opzionale Lauree Magistrali, docenti Corrado Falcolini e Laura Tedeschini Lalli

orario lezioni a.a. 2015-16: mercoledì ore 14-16 aula Morandi, venerdì ore 11-13 aula Sabbatini

AVVISO AGLI STUDENTI: durante questo primo mese abbiamo radunato alcune parole-chiave e concetti-chiave comuni agli articoli di ricerca che avete scelto. Faremo lezione su questo.

C’è anche altro materale disponibile, ad esempio:

Costruzione dell’icosaedro con rettangolo aurei,  costuzione del rettangolo aureo,

 

Programma del corso:

prima parte del corso (un mese): reading course +seminar course.

ogni studente legge un articolo di ricerca, scelto tra alcuni pubblicati su Nexus Network Journal oppure sugli atti della conferenza annuale Advances in Architectural Geometry. Seminario individuale, ogni studente racconta a tutti gli altri il contenuto ed i metodi dell’articolo scelto.

rassegna dei vari software usati finora, di quali siano dedicati, e quali integrabili.

lezioni frontali: approfondimento del concetto di metrica e di curvatura, già affrontato nel corso precedente; integrazione in aspetti progettuali.

seconda parte del corso: integrazione in progetto personale.

 

qualche riferimento.

un buon libro: Pottmann, Architectural Geometry

il libro è da integrare su alcuni temi, perché a volte lascia un pò l’amaro in bocca agli studenti autodidatti, incuriosendoli , ma non esponendo né le argomentazioni, né le applicazioni. Siamo qua per questo. In particolare, il capitolo sulla curvatura è chiaro.

Elenco degli articoli scelti finora per la prima parte del corso:

1) M. Reynolds From Pentagon to Eptagon: a Discovery on the Generation of the regular Eptagon from the Equilateral Triangle and the Pentagon Volume 3 (2), pp 139-146 (2001) Abstract:Geometer Marcus the Marinite presents a construction for the heptagon that is within an incredibly small percent deviation from the ideal. The relationship between the incircle and excircle of the regular pentagon is the key to this construction, and their ratio is 2 : ϕ. In other words, the golden section plays the critical role in the establishment of this extremely closeto-ideal heptagon construction. Keywords: vesica piscis architecture and mathematics constructing regular polygons with compass and straightedge plane geometry golden secion regular heptagon

 2) Buthayna H.Eilouti, Amer M. Al-Jokhadar A Generative System for Madrasa Form-Making Nexus N Journ  Volume 9 (1), pp7-30 (2007)
Abstract: In this paper, a parametric shape grammar for the derivation of the floor plans of educational buildings (madrasas) in Mamluk architecture is presented. The grammar is constructed using a corpus of sixteen Mamluk madrasas that were built in Egypt, Syria, and Palestine during the Mamluk period. Based on an epistemological premise of structuralism, the morphology of Mamluk madrasas is analyzed to deduce commonalities of the formal and compositional aspects among them. The set of underlying common lexical and syntactic elements that are shared by the study cases is listed. The shape rule schemata to derive Mamluk madrasa floor plans are formulated. The sets of lexical elements and syntactic rules are systematized to form a linguistic framework. The theoretical framework for the formal language of Mamluk architecture is structured to establish a basis for a computerized model for the automatic derivation of Mamluk madrasa floor plans.
3) P.Calter How to Construct a Logarithmic Rosette (without even knowing it) Nexus N Journ  Volume 2 (1-2), pp25-32 (2000)
Abstract: Paul Calter explains what a logarithmic rosette is and gives some examples of their occurrence in pavements. Then he gives a simple construction method which is totally geometric and requires no calculation. He then proves that it gives a logarithmic rosette, with the exception that the spirals are made up of straight-line segments rather than curved ones.

4) M. Reynolds A Comparative Geometric Anlysis of the Height and Basis of the Great Pyramid of Khufu and the Pyramid of the Sun at Teotihuacan Nexus N Journ  Volume 1 (1-2), pp23-42 (1999) Abstract: Mark Reynolds examines the Pyramid of the Sun at Teotihuacan and the Great Pyramid of Khufu from the point of view of geometry, uncovering similarities between them and their relationships to the Golden Section and π.

5) C. Bovil The Doric Order as Fractal  Nexus N Journ  Volume 10 (2), pp283-290 (2008) Abstract: Owen Jones in The Grammar of Ornament clearly states that ornament comes from a deep observation of nature. He emphasizes the importance of the harmony of the parts and the subordination of one part to another. This subordination and harmony between the parts is what fractal geometry explores as self-similarity and self-affinity. An iterated function system (IFS) is a digital method of producing fractals. An IFS in the shape of columns holding up a lintel produced an attractor displaying fluted columns with capitals and an entablature with the proper number and spacing of triglyphs and mutules. Thus, fractal geometry, through the use of iterated function systems, provides a new insight into the intention of Doric ornament design.

6) G. Canévet “Localizzazione auditiva di suoni nello spazio” in: Spazi Sonori della musica,  a cura di G.Giuriati, L. Tedeschini Lalli, L’Epos, 2010, pp53-78
7) W. Bergeron-Mirskj, J. Lim, J. Gulliford, A. Patel “Architectural Acoustics for Practitioners” in: Advances in Architectural Geometry 2012 pp. 129-136 Abstract: While much ink has been spilled over the benefits of intelligent models, information flow in the design process and the authoring of data sets there has been, in our opinion, little impact on the day-to-day practice of most architects. This paper discusses work by a team of graduate researchers to develop acoustic software tools that embody engineering fundamentals in support of the architectural design process.
8) T.Kiser, M. Eigensatz M. Man Nguyen, P. Bompass, M. Paulj “Architectural Caustics – Controlling Light with Geometry” in Advances in Architectural Geometry 2010 pp. 91-106 Abstract: Caustics are captivating light patterns created by materials bundling or diverting light by refraction or reflection. We know caustics as random side effects, appearing, for example, at the bottom of a swimming pool. In this paper we show that it is possible to control caustic patterns to form almost any desired shape by optimizing the geometry o f the reflective or refractive surface generating the caustic. We demonstrate how this surprising result offers a new perspective on light control and the use of caustics as an inspiring architectural design element. Several produced prototypes illustrate that physical realizations of such optimized geometry are feasible.

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tutorial del software Mathematica con esempi 08112014