| Code |
15158
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| Year |
2
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| Semester |
S2
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| ECTS Credits |
4
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| Workload |
TP(60H)
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| Scientific area |
Ciências Exatas
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Entry requirements |
-
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Learning outcomes |
It is intended that students:
1. Recognize the aesthetic dimension of Mathematics.
2. Be able to identify, interpret, and explore mathematical models in the context of Architecture.
3. Be able to apply mathematical knowledge to address challenges in Architecture and other fields.
4. Consider Mathematics as an additional source of inspiration and resources for the creation and development of projects.
5. Be able to understand and use Mathematics as a means of communication.
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Syllabus |
1. THE AESTHETIC COMPONENT OF MATHEMATICS
2. PRELIMINARY
2.1. Brief notions of logic, set theory
2.2. Real numbers set
2.3. Trigonometry
3. NUMBERS AND GEOMETRY
3.1. Proportions
3.1.1. Gold number.
3.1.2. Modulor (Le Corbusier).
3.1.3. Thales' theorem
3.2. geometric constructions
4. THE SPACE Rn
4.1. Generalization of topological concepts to Rn
4.2. Sets in R2
4.2.1. Representation of sets in R2
4.2.2. conics
4.3. Representation of sets in R3
4.3.1. Cylinders and quadric surfaces
5. CURVES
5.1. Parametric curves
5.2 Curves in the plane
5.2.1 Bézier curves
5.3. Curves in space
6. SURFACES
6.1. Quadric surfaces
6.2. Ruled surfaces
6.3. Free surfaces
6.4 Bézier surgaces
7. RELATIONSHIPS BETWEEN MATHEMATICS AND ARCHITECTURE
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Main Bibliography |
* Burry, J. & Burry, M. (2010). The new mathematics of architecture. Thames & Hudson.
* Ghyka, M. (1983). Estética de las proporciones en la naturaleza y en las artes. Barcelona: Poseidon.
* Ghyka, M. (2014). The geometry of art and life. New York: Dover Publications.
* Le Corbusier & Sequeira, M. (2010). Modulor. Lisboa: Orfeu Negro.
* Pedoe, D. (2018). Geometry and the visual arts. New York: Dover Publications, Inc.
* Pottmann, H., Asperl, A., Hofer, M., & Bentley, D. (2009). Architectural geometry. Exton: Bentley
Institute Press.
* Stewart, James, Cálculo - Volumes I e II, 7a edição, Cengage Learning, 2014.
Learning, 2014.
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Teaching Methodologies and Assessment Criteria |
Classes are theoretical-practical. In addition to the presentation of contents, discussion, problem solving and the performance and presentation of practical work are promoted.
- The assessment of knowledge during the Teaching-Learning process will consist of 3 individual works (T1, T2 and T3), 1 group work (TG) and 1 written/test (F).
- Graded grades for individual assignments, group assignments and the written test are developed on a 0-20 scale and rounded to the nearest integer. The final Teaching-Learning (CF) classification will be given by rounding to the units of the classification received by the following calculation: CF= F/3+(T1+T2+T3)/9+TG/3.
- To be admitted to the exam, the student must have attended at least two classes or have completed an evaluation period.
- The student who has a Teaching-Learning classification equal to or greater than 10 will be exempt from the final exam.
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Language |
Portuguese. Tutorial support is available in English.
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