Arc - Urb - Cost (Mag.)(ord. 270) - MI (1217) ARCHITETTURA E DISEGNO URBANO - ARCHITECTURE AND URBAN DESIGN

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099899 - APPLIED MATHEMATICS FOR ARCHITECTURE

Obiettivi dell'insegnamento

The goal of the Course is to provide students who have an interest in applications of mathematical ideas to Architecture with a compact overview of the tools and technique which are used or are of inspiration in some areas, such as computational design. Knowledge and understanding of mathematical concepts which go beyond what is traditionally taught in basic courses of Architectural Schools are now needed for some sophisticated applications, and this course aims to help students to be aware of and acquire such knowledge, according to their interests.

Risultati di apprendimento attesi

Students are expected to become aware of some key mathematical ideas which are behind technicques used in contemporary architecture. Students are expected to be able to apply such ideas in an investigation of a topic of their interest.

Argomenti trattati

Mathematical tools for descriptive and computational modelling of surfaces will be introduced (such as n-order Bezier curves and surfaces, NURBS, Coon pathces). Properties of minimal surfaces and their use in some contemporary architectural projects will be investigated, together with some connections to the mechanical properties of membranes.

A rigorous derivation of the Euler model for elaqstic rod will be provided.

Tasseletions of the plane will be introduced, with some of their applications in arts and architecture, and their classification through the notion of "symmetry group". Students will be invited to search for appropriate examples among the monuments and builidings in the Milan region.

The idea of "fractality" has acquired some importance in Architectural theory, together with "L-systems", for some contemporary applications.

Students will be invited to provide ideas and proposals of topics of their interest where some connections bewteen Architecture and Mathematics are relevant.

The approach of the course will not be strictly mathematical and, in view of this, some software tools typical of modern Architectural Design will be used.

Main Topics:

Curves. Curvature. Bezier Curves. Torsion and curvature. Mean and total curvature of a surface and their properties. Algorithms for the creation of parametric curves and surfaces. Freeform Surfaces. NURBS. Mechanics of membranes and minimal surfaces. Fractal sets and L-systems. Deformations and Algorithmic manipulation of curves and surfaces. Examples and applications of the modelling software "Grasshopper"

A basic knowledge of Calculus and Linear Algebra is required. Some ideas about curves and surfaces will be useful.

Prerequisiti

Modalità di valutazione

Evaluation and grading will be based on a project of mathematics applied to Computational Design and Architecture, chosen by the students according to their interests, among the topics suggested by the teacher during the Course. Students will also have the possibility of suggesting fields or themes of their own choice, taken from their previous experience.