Geometry

Code:

100104

Acronym:

100104

Instance: 2010/2011 - A

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	187	MIARQ	1	-	9	-

Teaching language

Portuguese

Objectives

To provide an understanding of the different geometric transformations and their properties as a means for the reading, construction and representation of the space, the territory and the light, in such a way that students can use geometry in the design process.

Program

1. THE DIFFERENT GEOMETRIES
1.1. Geometric Transformations.
1.2. The idea of form and space in topology, in projective geometry, in conformal geometry and in metric geometry. Euclidean and non-Euclidean geometries. Fractal geometry.
2. REPRESENTATION IN PERSPECTIVE
2.1. The central projection as homological transformation.
2.2. Definition and characterization of perspective. Construction methods.
2.3. Vantage point choice and the perception of space.
2.4. Accelerated perspective and counter-perspective. Anamorphoses.
2.5. The position of the light source and the layout of shadow.
3. REPRESENTATION IN AXONOMETRY
3.1. Parallel projection as affine transformation.
3.2. Definition and characterization of axonometry. Construction methods.
3.3. Cross sections and translations.
3.4. Use of transparency and color.
4. REPRESENTATION OF TERRITORY
4.1. Cartography. Cartographic projections and their properties. Aptness of maps.
4.2. The concept of topography. Topographical projections.
4.3. Applications and specificity of the topographic projection system. Representation of surfaces.
5. SOLAR GEOMETRY
5.1. The concept of positional astronomy.
5.2. Construction of protractors, charts and solar clocks.
5.3. Determination of shadows knowing the latitude.
5.4. Orientation and isolation of buildings.

Mandatory literature

Aubert Jean; Axonométrie. ISBN: 2-903539-38-3
Centre Georges Pompidou 340; Cartes et figures de la terra. ISBN: 2-85850-058-4
Critchlow Keith; Order in space
Izquierdo Asensi Fernando; Geometría descriptiva superior y aplicada. ISBN: 84922109-0-7
Izquierdo Asensi Fernando; Geometría Descriptiva
Katz Victor J.; A history of mathematics. ISBN: 0-321-01618-1
Murtinho Vítor; Perspectivas. ISBN: 972-97383-4-3
Nannoni Dante; Geometria prospectiva progetto. ISBN: 88-379-0816-4
Sánchez Gallego Juan Antonio; Geometria descriptiva. ISBN: 84-7653-290-3
Silva Armando Cavaleiro; Geometria da insolação de edificios
Veloso Eduardo; Geometria. ISBN: 973-8353-26-X
Xavier João Pedro; Sobre as origens da perspectiva em Portugal. ISBN: 978-972-9483-79-0
Xavier João Pedro; Perspectiva, perspectiva acelerada e contraperspectiva. ISBN: 972-9483-25-6
Wright Lawrence; Tratado de perspectiva. ISBN: 84-7616-003-8

Teaching methods and learning activities

The Syllabus will be delivered in both theory and practical classes.
Theory classes, of 1,5 hours weekly, are aimed at presenting the course content and, as far as the theoretical bases and examples are concerned, at making known and supporting the exercises to be developed in practical classes, which are of 2 hours duration weekly.
Practical exercises are aimed at:
- the development of the imagination of the ability of perception and synthesis;
- the acquisition of a symbolic language;
- the use of the unifying concept of geometric transformations as a working method;
- an emphasis on group work.
The syllabus will be taught with particular concern for framing knowledge previously acquired by students and the possibility of the use of new technologies for conception and design.

Software

GeoGebra
CaR Metal
Google SketchUp

keywords

Humanities > Arts > Fine arts > Drawing
Physical sciences > Mathematics > Geometry

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Calculation formula of final grade

The final mark will reflect the average of the tests (40%), the exercises done in practical classes (40%) and group work (20%).

Classification improvement

It is possible to sit a remedial tests to improve the score achieved in the regular ones, with a weighting of 40% towards the final mark.

Observations

This is a 1st year subject, therefore no prior courses are required.