Curricular Unit:Code:
Geometry and Topology145GETO
1MasterArchitecture and Urbanism4 ects
Learning Period:Language of Instruction:Total Hours:
Winter SemesterPortuguese/English52
Learning Outcomes of the Curricular Unit:
It is intended with this curricular unit that the student faces and uses Geometry not only as a way of understanding and representing shapes and spaces, but also as an indispensable instrument in the act of making and thinking about Architecture.
Thus, with this curricular unit the student should be able to:
- Perform geometric constructions with accuracy, using the proper execution and representation techniques;
- Select the type of representation most suitable for a given object, whether real or imaginary;
- Use, in an appropriate way, different projection systems;
- Produce rigorous perspectives of objects and built spaces;
- Interpret and use different scales of representation.
- Identify, analyze and understand geometric compositions of designs and constructed buildings.
1. Introduction to geometry
What is Geometry; the visual elements of communication: point, line, plane; notion of horizontality, verticality and obliquity; notion of perpendicularity and orthogonality, relations between lines or segment lines.
2. Geometric constructions
Division of lines and angles (mediatrix, bisector, etc.); polygon design; tangents; spirals; ellipse; arcs.
3. Scales of representation
Linear scale, bar scale or graphic scale; numerical scale; real or “natural” scale; scales of reduction and enlargement.
4. Flat geometric projections
Concept of projection and projection system; multiple orthogonal projection system; sketching volumes through quick perspectives.
5. Standardization
Portuguese standards (NP); European standards (EN); ISO standards; line types; captions, margins and frames; letters and figures; dimensioning of drawings; folding of drawings; drawing scales.
6. Technical shadows
Basic concepts; shadow of a line; shadow of a cube; multiple cubes shadow.
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
After introducing the theme and the main concepts, the student learns rigorous representation processes to perform geometric constructions. The knowledge of several processes allows you to know the rules and logic of geometric constructions, as well as acquire the skills to put them into practice, knowing how to choose the most appropriate method of geometric construction and representation in solving architectural problems. Complementing the knowledge described above with mastery of scales and the notion of existing standards, the student acquires skills to properly perform object representations, as well as the skill to use them in the development of his architectural thoughts.
Teaching Methodologies (Including Evaluation):
Theoretical classes are based mainly on the expository method with ample incentive for debate and discussion. Theoretical-practical and practical classes are based on the expository method, with demonstration of exercises, the same being repeated by the student.
The evaluation consists of two moments of evaluation: theoretical-practical tests, consisting of questions of written development and exercises of geometric representation / construction.
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
The realization of geometric construction exercises allows the student to assimilate the representation processes and norms, as well as to experiment with various methods and techniques of execution. Thus, the student acquires the knowledge of the Curricular Unit and simultaneously develops the critical and analytical spirit to put them into practice in the way that he deems most appropriate throughout his learning path, transversally throughout the course.
[1] ABAJO, F. Javier Rodriguez (1993), “Geometria Descriptiva - Tomo 2: Sistema de planos acotados”, San Sebastian, Editorial Donostiarra SA, 11ªedição.
[2] CARVALHO, Benjamim de A. (1985) “Desenho Geométrico”, Rio de Janeiro, Livro Técnico.
[3] CUNHA, Luís Veiga da (1994) “Desenho Técnico”, Lisboa, Fundação Calouste Gulbenkian.
[4] FERREIRA, Patrícia, (2001) “Desenho de Arquitectura”, Rio de Janeiro, Livro Técnico
[5] IZQUIERDO A., Fernando, (1980) “Geometria Descriptiva”, Madrid, Editorial Dossat, SA.
[6] MAGUIRE, D.E., (1981) “Desenho Técnico”, São Paulo, Hemus.
[7] MORAIS, José M. Simões (1999), “Desenho Técnico Básico 3”, Porto, Porto Editora, 22ª edição.
[8] POTTMAN, H., ASPERL, A., HOFER, M., KILIAN, A. (2007), “Architectural Geometry”, Exton – Pennsylvania USA, Bentley Institute Press.
[9] RICA, Guilherme (2009), “Geometria Descritiva – Método do Monge”, Lisboa, Calouste Gulbenkian/Dinapress, 4ª edição.
Lecturer (* Responsible):
Daniel Félix (