Geometry

Code:

G102

Acronym:

G

Keywords
Classification	Keyword
CNAEF	Fine Arts

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Desenho
Course/CS Responsible:	Fine Arts

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
AP	101	Plano de estudos de LAP_publicaçao em DR de 24/05/2021	1	-	3	30	81

Teaching language

Suitable for English-speaking students

Objectives

With the study of the science of Geometry, we want:
- to encourage the logical and deductive abilities of the student, building an analytic attitude and strengthening the synthetical thinking on the world of objects and spaces. It all starts from the conscience of the body in space.

Assuming Geometry as the structure of the Drawing, students should:
- to acquire knowledge that would enable them to use the projective geometry's systems of linear representation as the based for the knowledge and understanding of shapes.

Learning outcomes and competences

The student should acquire, and make it operative, the geometric knowledge that allow him to:

- understand his position and his relationship with and within the spaces;
- understand the formal structures of spaces and objects;
- use the linear systems of projection which structure the evocations of reality achieved by Drawing.

Thus, the students will be able to assume Geometry as the structure of the drawing and as a structure of their rational thinking.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The previous knowledge on basics Descriptive Geometry and/or Drawing is advisable.

Program

1. Approaches on the contribution of Geometry to Drawing.
2. Reflection on the concept of projection: the principles of projective geometry and its relationship with perceptions of reality.
3. Projection systems: the need, applicability, and intercommunication.
4. Presentation of the linear perspective and axonometric projection systems, reflecting the different origins and applicability.
5. Theoretical concepts on the systems: - Bases of the systems; - Representation of the primitives of geometrical drawing; - Representation of objects and spaces; - Auxiliary geometrical methods; - Theory of the reflexes, in plane mirrors; - Theory of the shadows.
6. Practice of the two projection systems as instruments to knowledge and understanding of space and objects in space.
7. Practice of the two systems as operators of changes in objects and spaces.

Mandatory literature

Daniel Jacques; Géométrie spatiale. ISBN: 978-2-88074-945-3
Guilherme Ricca; Geometria descritiva. ISBN: 972-31-0547-0
Javier Navarro de Zuvillaga; Forma y representación. ISBN: 978-84-460-2018-9
Jean Aubert; Axonométrie. ISBN: 2-903539-38-3
João Pedro Xavier; Perspectiva, perspectiva acelerada e contraperspectiva. ISBN: 972-9483-25-6
Lino Cabezas Gelabert; Análisis gráfico y representación geométrica. ISBN: 84-8338-294-6
Reiner Thomae; Perspectiva y axonometría

Complementary Bibliography

Armando Cardoso; Sombras e perspectivas
Cláudia Amandi; Ver, fazer, pensar, editar. ISBN: 978-989-746-035-7
Erwin Panofsky; A^perspectiva como forma simbólica. ISBN: 972-44-0886-8
Fernando Izquierdo Asensi; Geometria descriptiva. ISBN: 84-604-7480-1
Javier Navarro de Zuvillaga; Imágenes de la perspectiva. ISBN: 84-7844-174-3
Javier Navarro de Zuvillaga; Mirando a través. ISBN: 84-7628-291-5
Jurgis Baltrusaitis; Anamorphoses au thaumaturgus opticus. ISBN: 2-08-012604-0
Kirsti Andersen; The geometry of an art. ISBN: 0-387-25961-9
Lawrence Wright; Perspective in perspective. ISBN: 0-7100-0791-4
Philippe Comar; La^perspective en jeu. ISBN: 2-07-53185-6
R. L. Gregory; A^psicologia da visão
Rudolf Arnheim; Arte e percepção visual

Teaching methods and learning activities

The methodology main goal consists of providing the student's ability to integrate the acquired knowledge in practical drawing, it is therefore to explore the relationship between representation and understanding: to represent to comprehend and understand to represent.
The individual working capacity of the student, his organizational aptitudes, and his systematic work, are methodology goals.

The estimated hours for this semester (HTS) is organized as follows.
(HCS):
- presentation and explanation of the subjects;
- theoretical and practical work for implementation, development and operation of the exercises;
- critical analysis and results evaluation, as a process of progression towards greater autonomy, leading to implementation of a project of representation and intervention in a space used by the students.
(HTS):
- Development of the contents as well as its study and discussion, and development of the practice involved in it delivered from specific proposals.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Trabalho prático ou de projeto	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de projeto	30,00
Frequência das aulas	30,00
Estudo autónomo	21,00
Total:	81,00

Eligibility for exams

The teaching/learning/evaluation process will focus on the progress revealed by the student on the development of his performances on working proposals which will be presented.

The student's attendance (75%) is an essentially prerequisite to enable ongoing evaluation inherent to the nature of this theoretical-practical course.

Calculation formula of final grade

The evaluation main criteria consist of assessing the student's ability to integrate the acquired knowledge in practical drawing.
The student's working capacity, his organizational skills and systematic work are also assessment topics.

The evaluation components will be:
- Project work - 60%;
- Theoretical-practical work - 40%.

The existence of elements of assessment for the two components is mandatory.

Internship work/project

Students are going to lead their debate with the theoretical contents. After that, it will be deepened in class under teacher guidance. Students will deliver its exploration by performing a drawing project of representation of space. To this end, the logical-deductive skills will enable the student to:
- understand the formal structures of spaces and object;
- understand the position of his body in space;
- master the representation systems based on the geometric model for Drawing.

The activity of a space representation project will gradually start from the classroom to the student's autonomous work. This methodological strategy aims to stimulate the student's autonomy, organization, and systematization of work.

Special assessment (TE, DA, ...)

Students with special status or condition must establish with the teachers a Distributed Assessment plan for the component of study and work related to the Contact Hours, in a way equivalent to that of the other UC’s students, but in accordance with their conveniences.

Classification improvement

In accordance with the provisions of the Faculty Evaluation Regulation, it is settled the improvement of classification in this UC can be achieved by frequency in the following edition of the UC in the course.

Observations

Geometry is a science, so it provides knowledge to its students. Geometry science’s main role is to scaffold the understanding, representation and creation of shapes and spaces. Thus, geometric literacy is determinant, both for the analytical process and for the creative process.
In the context of undergraduate studies in Fine Arts and Design at FBAUP, Geometry and Drawing are associated as areas of knowledge that promote the development of spatial, formal, and visual thinking.
Therefore, and based on the assumption of Geometry as the structure of Drawing, the programme contents will be studied in a holistic way and from real problems of representation, involving the body and space in a tangible way. Problem solving will summon scientific contents that will lead cognition to drawing, as Joaquim Vieira (2007) has so well emphasized.