Geometry and Architecture

Code:

30308B3

Acronym:

30308B3

Instance: 2010/2011 - 1S

Active?	Yes
Responsible unit:	Desenho (D)
Course/CS Responsible:	Integrated Master Degree in Architecture

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIARQ	38	MIARQ	3	-	3	-

Teaching language

Portuguese

Objectives

This unit will discuss some Geometry topics implied in the drawing and characterization of architectural space, using examples that clearly reveal this relationship. The student should be able to:

_Develop the heuristic, visual and analytic thinking, in 2D and 3D space;
_Know the role of geometrical concepts while using Geometry in the architectural drawing;
_Establish relationships between Geometry and other graphic and technical knowledge indispensable to the architect apprenticeship;
_Know the basic techniques coming from different geometries in order to model situations for a creative exploration.

Program

1. GEOMETRIES
Geometries: Metric, Conform, Affine and Projective; Topology. Non Euclidean Geometries. Fractal Geometry. The evolution of Geometry and the transformation of the idea of space.
2. SYMMETRY
Isometries. Symmetry groups. Object symmetries. Plane symmetry groups: punctual or Leonardo groups, frieze groups, wallpaper groups. Tridimensional space symmetry groups: punctual groups, crystallographic groups, other groups.
3. PROPORTION
Ratio and proportion. Proportional systems; arithmetic, geometric and harmonic means; musical theory and architecture; dynamic structures; gnomonic growth.
4. FRACTALS
Architecture and Nature. Fractal dimension; irregularity; infinitude; complexity; initial conditions; self similarity; interactivity; recursivity. Fractal architecture and fractal cities hypothesis.
5. TOPOLOGY AND GRAPHS
Surfaces: two sided and one sided surfaces. Surface genus. Topological transformations. Graphs. Plane graphs. Paths. Jordan curve. Polygonal graphs. Euler formula. Regular polyhedron. Graphs and functional organization. Space syntax.
6. REPRESENTATION
Representation and Architecture. Projection and project ideas. Ortographic projections, perspective and axonometry, topographic projections; digital simulation.

Mandatory literature

Critchlow Keith; Order in space
Marcolli Attilio; Teoria del campo
Norberg-Schulz Christian; Intenciones en arquitectura. ISBN: 84-252-1750-4
Veloso Eduardo; Geometria. ISBN: 973-8353-26-X
Camerota Filippo; La prospettiva del renascimento. ISBN: 88-370-2119-4
Katz Victor J.; A history of mathematics. ISBN: 0-321-01618-1
Hagen Margaret A.; Varieties of realism
Nexus – Architecture and Mathematics. , Kim Williams, 1996_2008
Nexus Network Journal – Architecture and Mathematics. , Kim Williams, 1999_2008
March Lionel; Architectonics of humanism. ISBN: 0-471-97754-3
WILLIAMS, Kim; "La simmetria in architettura". In Matematica e Cultura 2001., Springer Verlag, 2001. ISBN: 88-470-0141-2
Pérez-Gómez Alberto; Architectural representation and perpective hinge. ISBN: 0-262-66113-6
Quaroni Ludovico; Proyectar un edificio. ISBN: 84-85434-09-9
Le Corbusier; Le modulor. ISBN: 2-904-833-01-3
Pedoe Dan; La geometria en el arte. ISBN: 84-252-0900-5
CABEZAS GELABERT, Lino; El dibujo como invención. Idear, construir, dibujar, Ediciones Cátedra, 2008
Fonatti Franco; Principios elementales de la forma en arquitectura. ISBN: 84-252-1349-5
Kappraff Jay; Connections. ISBN: 981-02-4585-8
Calter Paul A.; Squaring the circle
Mandelbrot Benoit B.; The fractal geometry of nature. ISBN: 978-0-7167-1186-5
Blackwell William; Geometry in architecture. ISBN: 1-55953-018-9

Teaching methods and learning activities

The syllabus will be developed weekly in 17 units of 3 hours each. Each lesson will consist on a first part to explain the subjects – with visual and audiovisual support, models or other resources – and a second part for presentation and discussion.

keywords

Physical sciences > Mathematics > Geometry
Technological sciences > Architecture

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	54,00
	Total:	-	0,00

Eligibility for exams

To be approved, the student must attend a minimum of 75% of the estimated classes, and get a minimum mark of 9,5 resulting from his participation in the class and the accomplishment of the individual assignment.

Calculation formula of final grade

The final classification will be the average calculation of participation in class (20%) and individual work (80%).

Classification improvement

There is the possibility to improve the final work until 15 days after the publication of its classification.

Observations

Optional unit of the 1st semester; without mandatory class precedents.