Revision of elementary geometry.
Elements of Projective Geometry.
Orthogonal Projections.
Central Projection.
Perspective. Perspective through Orthogonal Projections.
Elements of Perspective Restitution.
Axonometry.
Parallel Perspective.
Aterini B., Introduzione ai metodi di rappresentazione della Geometria Descrittiva, Alinea Ed., Firenze 2009
Aterini B., Il Metodo delle Proiezioni Ortogonali Applicazioni, Alinea Ed., Firenze 2007
Aterini B. – Pero Nullo A., Il Metodo della Proiezione Centrale Applicazioni, Alinea Ed., Firenze 2003
Aterini B., Appunti dalle lezioni del corso di Fond. ed Appl. della Geometria Descrittiva, Alinea Ed., Firenze 2000
Aterini B., La Prospettiva Parallela, Alinea Ed., Firenze 1995
Aterini B., Restituzione Prospettica, Alinea Ed., Firenze.
For seminar topics will be provided by the teacher an annotated bibliography.
Aterini B., Introduzione ai metodi di rappresentazione della Geometria Descrittiva, Alinea Ed.,
Firenze 2009
Aterini B., Il Metodo delle Proiezioni Ortogonali Applicazioni, Alinea Ed., Firenze 2007
Aterini B. – Pero Nullo A., Il Metodo della Proiezione Centrale Applicazioni, Alinea Ed., Firenze
2003
Aterini B., Appunti dalle lezioni del corso di Fondamenti ed Applicazioni della Geometria
Descrittiva, Alinea Ed., Firenze 2000
Aterini B., La Prospettiva Parallela, Alinea Ed., Firenze 1995
Learning Objectives - Last names A-D
The drawing (‘Disegno’) is not only a language to communicate ideas, but it is a study tool, analysis, which educates the understanding of reality, and in this sense becomes an integral part of the cognitive process of space. In particular for the architect it is essential to know how to graph the project idea and thus "materialize". Indeed, it is through design that the designer to check the shape of the object that proposes to realize, but to do so must be provided with appropriate methodologies and techniques. It is the descriptive geometry that develops the ability to think in three-dimensional space and allows, thanks to the methods of representation, to draw on a flat surface shapes of objects that surround us.
The course is set so as to clarify the students which are the methods for representing the three-dimensional reality on the drawing sheet, that is, to obtain the two-dimensional representation of the space that surrounds us. The classes are organized starting from the most commonly used method, that of Orthogonal projections, which serve to illustrate the object in the right relationship and such that it is still measurable. Following are treated the Central Projection and in particular the Perspective, useful for an overview of project ideas, as well as the Axonometry and Parallel Perspective. In addition the course also aims to understand how these methods are, among them, closely related and, after all, indispensable to the architect.
Learning Objectives - Last names N-Z
The course aims to educate the student to consider the design, in particular the architectural design,
as a language to communicate ideas, an instrument of study and analysis for the
understanding of the real. In particular, for the architect, the design becomes an integral part of the
cognitive process of space, fundamental in order to be able to represent the idea graphically
design and its materialization: in fact it is through the design that the designer controls the
form of the object that it is proposed to achieve, evidently placing methodologies and
appropriate techniques. In this regard, descriptive geometry develops the ability to think in
three-dimensional space and allows, thanks to the methods of representation, to draw on one
flat surface the shapes of the objects that surround us.
The course is therefore designed to show students the methods to represent reality
three-dimensional on the drawing sheet, ie to obtain the two-dimensional representation of the
space that surrounds us. The lessons are articulated starting from the most commonly used method, that
of orthogonal projections, which serve to illustrate the object in the right ratio and such
however measurable. The central projection and in particular the projection are discussed below
perspective, useful for an overview of design ideas, as well as axonometric and
parallel perspective. In addition, the course also aims to show how these methods are, between
they are closely linked and, all in all, indispensable to the architect.
Prerequisites - Last names A-D
Knowledge of plane geometry.
Prerequisites - Last names N-Z
Basic knowledge on:
Basic geometric bodies: point, straight line, plane
Angles: definitions and operations with angular measurements
Polygons
Triangles: heights, bisectors, medians and axes
Characteristics and criteria of congruence of the triangles
Characteristics and classification of quadrilaterals
Rotations and translations
Area of regular polygons
Pythagorean theorem
Circumference and circle
Similarity criteria and Euclid's theorems
Lines and planes in space
Solid bodies: the polyhedra, sphere.
Teaching Methods - Last names A-D
Lessons on the chalkboard drawings with colored chalk.
Ex-tempore verification after each topic.
Ppoint to illustrate the research-related applications.
Teaching Methods - Last names N-Z
The teacher guides learning in a coordinated course of theoretical lessons and practical exercises. The teaching activity is divided into:
basic theoretical concepts;
individual practices to be held in the classroom;
individual reviews.
Students are therefore required to carry out graphic exercises and the final elaboration of three tables, the topic of which will be agreed upon with the teacher.
Further information - Last names A-D
Through the topics of the seminar, proposed during the course, you can
experiment the applications of geometry to the field of scientific
research.
These are, for example, the study of the painted architecture, the
anamorphosis two or three dimensional, the gnomonic instruments such
as sundials, armillary spheres and astrolabes.
Further information - Last names N-Z
The individual student requires his own work equipment.
Type of Assessment - Last names A-D
The exam is held by an individual written exam, an oral exam and
evaluation of the graphics tablets (A2) presented.
Type of Assessment - Last names N-Z
The exam takes place through an individual written exam, which the student can access after completing all the required graphic works. Passing the graphic test will allow him access to the final oral exam.
The final evaluation will derive from those recognized in the presented papers, and graphic and oral tests.
Course program - Last names A-D
APPLICAZIONI DELLA GEOMETRIA DESCRITTIVA
Prof. Barbara Aterini – Corso A CFU 8
1. Objectives
The design (‘Disegno’) is not only a language to communicate ideas, but it is a study tool, analysis, which educates to the understanding of reality, and in this sense becomes an integral part of the cognitive process of space. In particular for the architect it is essential to know how to graph the project idea and thus "materialize". Indeed, it is through design that the designer to check the shape of the object that proposes to realize, but to do so must be provided with appropriate methodologies and techniques. It is the Descriptive Geometry that develops the ability to think in three-dimensional space and allows, thanks to the methods of representation, to draw on a flat surface shapes of objects that surround us.
The course is set so as to clarify the students which are the methods for representing the three-dimensional reality on the drawing sheet, that is, to obtain the two-dimensional representation of the space that surrounds us. The classes are organized starting from the most commonly used method, that of Orthogonal projections, which serve to illustrate the object in the right relationship and such that it is still measurable. Following are treated the Central Projection and in particular the Perspective, useful for an overview of project ideas, as well as the Axonometry and Parallel Perspective. In addition the course also aims to understand how these methods are, among them, closely related and, after all, indispensable to the architect.
2. Topics
- Elements of elementary geometry. the plane geometry: basic geometric entities, part aura of a segment, construction of regular polygons, conic. geometry of space: cones and cylinders, sphere, geodetic.
- Elements of Projective Geometry; Central and parallel projection; rollover of plan, perspectivity; Polarity and Antipolarity.
- Correspondence between the real object and its projection.
- Orthogonal Projections: Reference items. Conditions of belonging, parallelism, squareness. Change of the second plane of projection. Overturning of a projecting floor and a generic plan. measurement problems. Homology akin orthogonal. Representations of plane figures and solids with relative shadows. Polyhedra, cones, cylinders, sphere.
- Central Projection: Reference items. Change of the representation of a point. Conditions of belonging, parallelism, squareness. Overturning of a projecting floor and a generic plan. Tipping homology. measurement problems. Perspective. conic sections. Prospect of plane figures and solids with relative shadows. Perspective through Orthogonal. Measuring points. Perspective Restitution of nods
- Axonometry: Reference items. Oblique Axonometric, Orthogonal Axonometric. Representation and reversal of generic plane, perpendicularity.
- Parallel Perspective. Reference elements. Representation of architectural elements. Perspective restitution.
Through the topics of the seminar, proposed during the course, you can experiment the applications of geometry to the field of scientific research.
These are, for example, the study of the painted architecture, the anamorphosis two or three dimensional, the gnomonic instruments such as sundials, armillary spheres and astrolabes.
3. Mode of Teaching
The course consists of lessons and exercises on the topics covered.
Lessons are conducted by the teacher at the blackboard through drawings made with colored chalk.
Ex-tempore verification after each topic.
By Ppoint will learn the applications of geometry to scientific research.
The final drawings (format A2) will treat an architectural theme of particular interest (to be agreed with the teacher).
4. Review Mode
The exam is held by an individual written exam, an oral exam and evaluation of the graphics tablets (format A2) presented.
5. Bibliography
- B. Aterini,‘Introduzione ai Metodi di Rappresentazione della Geometria Descrittiva’, Alinea Ed., Firenze, 2009 (I ed. 1997).
- B. Aterini,‘Il Metodo delle Proiezioni Ortogonali. Applicazioni’, Alinea Ed., Firenze, 2007 (I ed. 1992 ).
- B. Aterini, ‘Il Metodo della Proiezione Centrale. Applicazioni’, in coll. con A. Pero Nullo, Alinea Ed., Firenze, 2007, (I ed. 1990)
- B. Aterini,‘Appunti dalle lezioni del Corso di Fondamenti ed Applicazioni della Geometria Descrittiva’, Alinea Ed., Firenze, 2007 (I ed. 2000).
- B. Aterini,‘La Prospettiva Parallela’, Alinea Ed., Firenze, 1995.
- B. Aterini,‘Restituzione Prospettica - Misura di elementi rappresentati in una immagine fotografica per il rilievo di architettura’, Alinea Ed., Firenze, 1997.
For seminar topics we will be provided by the teacher an annotated bibliography.
The Holder of the course
Prof.Arch. Barbara Aterini
Course program - Last names N-Z
- Elementary geometry. Geometry plane: fundamental geometric entities, golden part
of a segment, construction of regular, conical polygons. The geometry of space: cones and cylinders and
sphere, geodesics.
- Elements of projective geometry; central projection and parallel projection; perspectivity;
reversal as a prospect. Polarity and antipathy.
- Orthogonal projections: reference elements. Membership conditions, parallelism,
perpendicularity. Change of the second projection plane. Turnover of a plan
projecting and a generic plan. Measurement problems. Orthogonal homology.
Representations of flat and solid figures with relative shadows. Polyhedra, cones, cylinders, spheres.
- Central projection: reference elements. Change the representation of a point.
Conditions of belonging, parallelism, perpendicularity. Overturning of a projecting plane e
of a generic plan. Rollover homology. Measurement problems. Perspective. Conical sections.
Flat and solid figures with relative shadows. Perspective through the Projections
Orthogonal. Measurement points. Overview of prospective restitution
- Axonometry: reference elements. Oblique axonometry and orthogonal axonometry.
- Overturning the generic plan and perpendicularity.
- Parallel perspective. Reference elements. Representation of architectural elements.
Perspective restitution.