Here you will find a comprehensive list, including abstracts, of my publications and conference submissions.
For a copy of the papers, please send an email mentioning the title(s) you are interested in. They can be sent to you in .PDF format, which can be read using Acrobat Reader.
Transfert de 2-D en
3-D des contraintes géométriques de l'Opus 84 de Hans
Hinterreiter (M.Sc.A.
Université
de Montréal, 1997)
Extrait du sommaire: Le parallèle entre les structures des mondes 2-D et 3-D est un concept qui a depuis longtemps été pris pour acquis. La question peut se poser, pourtant, sur la façon dont cela se traduit dans le monde pratique, particulièrement dans le domaine de la conception formelle. En effet, quelle forme pourront rendre le ou les objets 3-D régis par les mêmes relations dans l’espace qu’obéit un objet 2-D dans son propre environnement...
Life after Escher:
a (young) artist's journey (in
M.C.Escher's Legacy, A Centennial Celebration, Emmer, M. and
Schattschneider, D., Editors, Springer-Verlag,
Heidelberg, 2002)
Book description: "One of the most popular artists of the
20th century, M. C. Escher, leaves a rich legacy. The centennial
celebration of his birth, held in Rome and Ravello in 1998, gave
testimony to the keen interest and new insight into his work, and
showcased a number of contemporary artists and scientists whose
work is directly inspired by that of Escher.
Developing a Procedure
to Transfer Geometrical Constraints from the Plane into Space
(Journal
for Geometry and Graphics, 1998)
Abstract: Topology teaches us that the two dimensional plane
and three dimensional space have a comparable structure. In fact,
this apparent parallel is deeply rooted in our consciousness and
is applied in many domains, including various fields in the design
industry, through the use of such tools as descriptive geometry
and perspective drawing. From the particular point of view of the
designer, however, this parallel in structure has often been simplified
to plans, sections and elevations i.e. 2-D slices through a 3-D
object. It has therefore not been an integral part of the design
process, but rather a tool of representation of the design process.
Barn-Raising an Endo-Pentakis-Icosi-Dodecahedron
(with Simon Morgan, Bridges
Conference Proceedings, 1999)
Abstract: The workshop is planned as the raising of an endo-pentakis-icosi-dodecahedron with a 1 meter edge length. This collective experience will give the participants new insights about polyhedra in general, and deltahedra in particular. The specific method of construction applied here, using kite technology and the snowflake layout allows for a perspective entirely different from that found in the construction of hand-held models or the observation of computer animations. In the present case, the participants will be able to pace the area of the flat shape and physically enter the space defined by the polyhedron.
From the circle to the
icosahedron (Bridges
Conference Proceedings, 2000)
Abstract: The following exercise is based on experiments conducted in circular Origami. This type of paper folding allows for a completely different geometry than the square type since it lends itself very easily to the creation of shapes based on 30-60-90 degree angles. This allows for experimentation with shapes made up of equilateral triangles such as deltahedra. The results of this research were used in Annenberg sponsored activities conducted in a progressive middle school in Houston TX, as well as a workshop presented at the 1999 Bridges Conference in Winfield, KS. Not including preparatory and follow up work by the teacher, the activities in Houston were composed of two main parts, the collaborative construction of a three-yard-across, eighty-faced regular deltahedron (the Endo-Pentakis Icosi-dodecahedron) and the following exercise. The barn-raising was presented last year in Winfield, and the paper folding is the topic of this paper.
Polyhedra, Learning
by Building: Design and Use of a Math-Ed. Tool (with
Simon Morgan, Bridges
Conference Proceedings, 2000)
Abstract: This is a preliminary report on design features
of large,light-weight,modular equilateral triangles and classroom
activities developed for using them.They facilitate the fast teaching
of three dimensional geometry together with basic math skills,and
create a lasting motivational impact on low achievers and their
subsequent performance in math and science.
Decomposing Deltahedra
(ISAMA
Conference Proceedings, 2000)
Abstract: Deltahedra are polyhedra with all equilateral
triangular faces of the same size. We consider a class of we will
call 'regular' deltahedra which possess the icosahedral rotational
symmetry group and have either six or five triangles meeting at
each vertex. Some, but not all of this class can be generated using
operations of subdivision, stellation and truncation on the platonic
solids. We develop a method of generating and classifying all deltahedra
in this class using the idea of a generating vector on a triangular
grid that is made into the net of the deltahedron.
Circular Origami: a
Survey of Recent Results (Origami3,
AK
Peters Publishers, 2002)
Book description: "The book contains papers from the proceedings of the 3rd International Meeting of Origami Science, Math, and Education, sponsored by OrigamiUSA. They cover topics ranging from the mathematics of origami using polygon constructions and geometric projections, applications, and science of origami, and the use of origami in education."
From a Subdivided Tetrahedron
to the Dodecahedron: Exploring Regular Colorings (Bridges
Conference Proceedings, 2002)
Abstract: The following paper recounts the stages of a stroll through symmetry relationships between the regular tetrahedron whose faces were subdivided into symmetrical kites and the regular dodecahedron. I will use transformations such as stretching edges and faces and splitting vertices. The simplest non-adjacent regular coloring , which illustrates inherent symmetry properties of regular solids, will help to keep track of the transformations and reveal underlying relationships between the polyhedra. In the conclusion, we will make observations about the handedness of the various stages, and discuss the possibility of applying the process to other regular polyhedra.
Preliminary Field Explorations
in K-6 Math-Ed: the Giant Triangles as Classroom Manipulatives
(with Simon Morgan, Bridges
Conference Proceedings, 2002)
Abstract: The present paper reports on children's investigations
using the giant equilateral triangles from the Geraldine Project.
It took place at the De Zavala Elementary School as the initial
stage of a project in mathematics education. The triangles are a
part of a modular construction kit made using kite technology. Their
size, sturdiness and light weight make them ideal for in-class activities
with children of all ages and stages of development.
Finding the Dual of
the Tetrahedral-Octahedral Space Filler, an Excursion through Geometry
and Crystallography
(with Simon Morgan, Bridges
Conference Proceedings, 2003)
Abstract: The goal of this paper is to illustrate how octahedra and tetrahedra pack together to fill space, and to identify and visualize the dual to this packing. First, we examine a progression of 2-D and 3-D space-filling packings that relate the tetrahedral-octahedral space-filling packing to the packing of 2-D space by squares. The process will use a combination of stretching, truncation and 2-D to 3-D topological correspondence. Through slicing, we will also relate certain stages of the process back to simple 2-D packings such as the triangular grid and the 3,6,3,6 Archimedean tiling of the plane. Second, we will illustrate the meaning of duality as it relates to polygons, polyhedra and 2-D and 3-D packings. At a later stage, we will reason out the dual packing of the tetrahedral-octahedral packing. Finally, we will demonstrate that it is indeed a 3-D space filler in its own right by showing different construction methods.
Experiencing Research
Practice in Pure Mathematics in a Teacher Training Context.
(with Paul Ernest and Simon Morgan, Psychology
of Mathematics Education-23, Proceedings of the 23rd conference,
Bergen, Norway, 2004)
Abstract: This paper presents the early results of an experiment involving a class of elementary student teachers within the context of their mathematics preparation. The motivation of the exercise centred on giving them an experience with mathematical research a their own level and ascertaining its impact on their attitudes and beliefs. The students spent the first month working on open-ended geometrical topics. In the second month, working alone or in groups of up to four, they chose one or more of these topics then worked on a problem of their own design. The students spent the class time developing their ideas using strategies such as generating examples and non-examples, generalising, etc. Reference to books was not accepted as a research tool, but the instruction team monitored student progress and was available for questions.
Discussing the Challenge
of Categorising Mathematical Knowledge in Mathematics Research Situations
(with Cécile Ouvrier-Buffet,
Fourth Congress of the European Society for Research in Mathematics
Education, 2005)
Abstract: Starting with a quotation describing mathematical research, this paper presents the beginning of an imaginary dialogue between a practicing mathematician and a didactician about ways of providing students with adequate experiences in mathematical research. The conversation begins with a discussion of the benefits and implications for the students of such experiences, followed by a more detailed discussion of what forms these experiences might take, including two examples. Later, the didactical goals of the experimented situations are elaborated from a more theoretical perspective. The last section includes two proposed hierarchies of knowledge, and concludes with an illustration of how one goes about fostering these hierarchies of knowledge through an experience in mathematical research. |