Download from the 3D reality to the 2D plane

Central Perspective from the 3D reality to the 2D plane
Project Overview
Learning Areas
Levels
Objectives
Mathematics, Cultural History, Fine Art, Physics
15 – 18 years old (gymnasium)
•To describe and analyze the central perspective as a model for perception
•To be able to draw a picture according to the central perspective and
document the process
•To understand how the mathematical idea history and the cultural history lead
to the visual concept of the central perspective
Description
Software
Keywords
Authors
Documents
The project is about the central perspective, how the three dimensional reality
is projected at the two dimensional picture plane. We have created a room
were we have constructed a coordinate system in the middle of the room with
strings stretched over a wooden frame. The project is part of a collaboration
among all the mathematic teachers at Tensta Gymnasium.
Windows Movie Maker, Windows Media player, MS PowerPoint, MS Word
central perspective, vanishing point, horizon line, picture plane, projection,
orthogonal, parallel, distance, infinity, optic, understanding of space
Anna Stenkvist, Tensta Gymnasium, Stockholm, Sweden
Woodcut from the first book about the central
perspective. It has been used as a schoolbook in geometry. Albrecht Dürer (1471 –
1528)
Central Perspective from the 3D reality to the 2D plane
Teacher Planning and Management
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A room is equipped with a stilleben and a
frame with strings streched over it to represent
a coordinate system and a picture plane. (Fine
Art: 1-3 lessons)
The historical background is presented: the
connection between the understanding of space
through history and the mathematical idea
history. The students learn that, according to the
central perspective, all lines orthogonal to the
picture plane will join at the vannishing point.
(Mathematics, Cultural history: 1-3 lessons)
A discussion about the development of the
central perspective. (Mathematics, Cultural
History, Fine Art: 1-2 lessons)
The students draw according to the central
perspective and learn about related geometrical
concepts such as orthogonal, parallel etc. They
also learn how to use the camera and the
related software to make the film.
(Mathematics, Fine Art: 1-2 lessons)
The students work two by two. One draw
according to the central perspective and the
other one document the process. Then they
change. Finally they cut the film together.
(Mathematics, Fine Art: 4 lessons)
The video is analyzed. Are there deficiencies
compared to what we see? (Mathematics,
Cutural History, Fine Art, Physics: 15-20
minutes per group)
Central Perspective from the 3D reality to the 2D plane
Teaching Resources
For preparation I would like to recommend the book Perspective as
Symbolic Form by Erwin Panofsky, a german art and idea historian. His
theories have inspired to this project. He describes how there is an
resiprocal action between the history of art and the mathematical idea
history in creating the human conception of the universe.
The lexicon Sigma, part one, present an excellent overview over the
mathematical history.
For a short definition of the central perspective klick here.
If you are looking for renaissance paintings you can try the on-line
museum Art Renewal Center or Art Cyklopedia.
The painting of Jan Van Eyck (1390
– 1441) illustrates the central
perspective. In the mirror behind the
couple you can see the artist. All the
lines orthogonal to the picture plane
meet in artist’s eye.
Central Perspective from the 3D reality to the 2D plane
Assessment and Standards
Assessment Rubrics:
Approved
•To be able to explain the concepts: vanishing point, parallel etc.
•To be able to use the central perspective and explain how it works as a
model for perception in terms of the related concepts above
Excellent
•Be able to explain and analyze the shortcomings of the central
perspective as a model for perception
Mapping the Standards: In Sweden we have National Standards for all the
courses at the Gymnasium. In addition to that Tensta Gymnasium have there
own local standards, that are not of course contradicting the national standards,
but adds a similar curriculum as they follow at Ross School. All our teaching is
based on teams consisting of teachers with the same subjects or of teachers in
different subjects. The cultural history is used as a core in all our teaching. We
have formulated the enduring understanding and essential questions that they
should be able to answer for each subject and project.
In mathematics we have a working plan for integration according to the
embedded VCT at this page.
Documents
Central Perspective from the 3D reality to the 2D plane
Teacher and School Information
My name is Anna Stenkvist and I work at Tensta Gymnasium as a teacher in
mathematics, philosophy and computer science. Apart from university studies in
my subjects, I also have an education in fine art. Therefor it is natural for me to
involve art and visualization in my teaching. I can tell that the students like it a lot.
Moreover, it offers an other learning style for the students. This way of teaching
suits me too. I like to learn new things for myself and to use a lot of different
aproaches to involve the students.
Since one year I am dean in mathematics at our school. It means that I am
responsible for the development of mathematics in the pedagogical project, the
Ross Project, a collaboration between Tensta Gymnasium and Ross School at
Long Island. At Tensta Gymnasium the mathematical teachers have devided the
year in four periods of integratrion that correspond to the mathematical main topics:
geometry, algebra/arethmetics, functions and statistics/probalbility. It enables us to
work together and share resources such as different kinds of lecturers for the
teachers and project rooms for the students.
I have participated in the Swedish Mathematics Biennal twice, 2006 och 2008, one
time with a lecture and the other with an exhibition. Both were about integration
beteween mathematics and other school subjects. In 2006 I worked in a project
were we developped a web-based learningtool in mathematics for imigrant
students. Now I am a participant of a project about Internet and the future in
Sweden, at the Royal Swedish Academy of Engineering Sciences. My contribution
to the project is user knowledge from the teaching perspective.
Anna Stenkvist