University of Albany, New York, juin 1992

Topologie
structurale
* 20 * Structural
Topology
* 1993
University of Albany, New York,juin 1992
a rencontre Arts and Mathematics
s’est tenue a 1’Universite SUNY a
Albany, etat de New York, en juin
1992. Cette rencontre a ete realisee sous
I’initiative et grace a l’organisation de
Nathaniel Friedman, mathematicien et
sculpteur du Departement de mathematiques a SUNY.
Les activites comprenaient des conferences, des films, des presentations sur
ordinateur et des expositions. L’etalage de
modeles, jouets, materiel pedagogique,
trousses de modelisation, produits industriels et commerciaux, a largement contrihue au succes de cette rencontre. La conference d’ouverture Ctait sous la responsabilite de Arthur Loeb. La clarte et le
dynamisme de sa presentation intitulee
Polyhedral Models (modeles polyedriques)
a assure une excellente amorce pour
l’evenement.
Meme si, lors de la rencontre, les
conferences et expositions n’etaient pas
regroupees selon des themes, pour ce
compte rendu, les sujets seront partages
en six categories.
1. Sculptures giiom&iques,
gf5ombies
sculptutales
Nous avons pu voir les plus recentes realisations des chefs de file de ce champ :
Charles 0. Perry, Robinson Fredenthal,
et Arthur Silverman S’il existait une
description generale pour caracteriser les
styles hautement individuels de ces trois
sculpteurs, ce pourrait btre la suivante : de
leurs compositions se degage un processus creatif ordonne qui est inspire, plutot
que restreint, par une veritable geometric
tridimensionnelle.
Une equation algebrique choisie est d’abord affichee en projection sur un &ran
d’ordinateur, puis le logiciel controle point
par point la quantite de Pierre qu’il faut
tailler pour la retirer. Les coupes reelles
met-rent parfois a des resultats non souhaites, auquel cas ces informations sont
retransmises a l’ordinateur qui met a jour
la geometric precedente dans un mode
continu.
2. Explorations des troisi&me et
quatrikme dimensions
Magnus Wenninger presentait ses derniers modeles issus de son univers exceptionnel: les polyedres Ctoiles. La conference de Harsh Lalvani, Higher Dimensional Structures (Structures de dimensions superieures), constituait un delice
autant pour l’esprit que pour les yeux.
L’architecture quasicristalline de ‘Ibny
Robbin (Quasi Cr+stul AvckitectMre) est
une exploration visuelle intuitive des
dimensions superieures.
4. Art- Gkombieeducation
Le remarquable ouvrage de Jay Kappmf’f
Connectrons- the Geometric Bridge between
Art and Science, constitue en effet un pont
important entre les deux mondes. Sa conference nous assurait de son inter&t marque pour l’education.
Doris Schattschneider
nous a montre
Geometeu’sSketckpud, un logiciel developpi:
par son Cquipe. I1 s’agit d’un outil innovateur pour l’enseignement et l’apprentissage avec plaisir de la geometric. Nous
avons eu une bonne discussion avec
Marion Walter, la didacticienne qui explore les facons d’enseigner la geometric
aux tout jeunes.
3. Nouvelles technologies
Stewart Dickson presentait une fascinante technologie, nommee stereolithographie, qui permet de produire des surfaces algebriques complexes, que nul oeil
humain n’avait pu voir avant, sous forme
de modeles plastiques. Un faisceau laser
ultraviolet guide par ordinateur parcourt
la surface d’un liquide photosensible,
solidifiant les surfaces exposees. Les superbes sculptures sur Pierre presentees
par Helaman Fergusson ont Cte produites par la combinaison dun logiciel
interactif et d’un tour de main artistique.
6. Systkmes de modt?lisation structurale
C’est avec plaisir qu’on a rencontre
Caspar Schwabe de Zurich. Son sempiternel gros Porte-documents Ctait plein de
surprises geometriques superbement
realisees, dont un bon nombre Ctaient
fondees sur des result&s tres recents de
recherche geometrique. Man: Pelletier
est arrive avec une trousse toute nouvelle
presentee pour la premiere fois : Zometool
(Biocystal, Boulder, CO). Elle est fondee
sur le systeme structural 31-zone propose
par Steve Bauer. A l’aide de Zometool,
l’utilisateur affi-anchi peut explorer la geo-
metric des charpentes spatiales, les
quasicristaux et les hyperespaces.
6. Production artistique co mmerciale
Deux attrayantes expositions ont attire
l’attention des participants. Les oeuvres
d’ebenisterie de Jane Greenberg
(Woodwovkings and Fumrture Design,
Boston, MA) nous rappela l’art oublie de
la renaissance florentine : la marqueterie.
Bill Greenlaw (Mosuica, Worchester, MA)
exposait des tuiles de ceramique presentant des motifs de pavage intrigants. Ces
exemples nous ramenaient Cgalement a
une source de la renaissance (Francesco
Quinterio : Maiolica NelllAvckitectum del
Rmascimento Italian0 1440-1520, Cantini,
Firenze, 1992).
444
Comme aspect negatif, on doit attribuer
une mention speciale a la conference de
Rhonda Roland Shearer: Chaos, Fractals,
Art: a Geomety ofa new Frontier. Elle
declarait, lors de sa presentation, que la
geometric euclidienne est sexiste et male,
tandis que la geometric fractale est feminine et constitue ainsi la seule geometric
correcte pour le futur. Elle a presente son
raisonnement mais je n’ai tout simplement pas saisi (just did not get it). Cette
incursion particulibre dans une nouvelle
philosophie mathematique a ete accueillie par un auditoire poli avec un
silence etourdissant.
444
La rencontre Arts and Mathematics 92
a Cte un grand succes et nous Ctions heureux d’apprendre de Nat Friedman qu’il
deviendra un Cvenement annuel, a partir
de juin 1993.
]anos Bavacs
lopologie
structurala?
* 20 * Structural
Topology
* 1993
Conference on “Arts and Mathematics”
University of Albany, New York, June 1992
he “‘Arts and Mathematics” conference was held at the University at
Albany, SUNY in Albany New York
in June 1992. The conference was initiated
and organized by Nathaniel Friedman,
mathematician and sculptor from the
Mathematics Department at SUNY.
The activities included lectures, films,
computer presentations and exhibits, The
displays of models, toys, educational materials, modelling kits, industrial or commercial products largely contributed to
the success of the conference. The keynote lecture was given by Arthur Loeb
on “Polyhedral Models’.’ The clarity and
the dynamism of his presentation provided an excellent beginning of the
events.
Although the lectures and the exhibits
were not grouped into themes, for this
review, the subjects are divided into six
categories.
1. Geometrical sculptures, sculptured
geometries
We saw the most recent realizations by
the leaders of this field: Charles 0.
Perry, Robinson kedenthal,
and
Arthur Silverman. If a common description exists to characterize the highly individual styles of these three sculptors, it
maybe the following: their compositions
reflect an orderly creative process inspired, rather than restrained by a truly
three-dimensional geometry.
equation is displayed by its projection on
a computer screen, then the program
controls point by point the amount of
stone to be cut away. The actual cutting
sometimes yields unwanted results,
which are fed back to the computer and
update the previous geometry in a continuing fashion.
2. Explorations of the third and fourth
dimensions
Magnus Wenninger displayed his latest
models from his unique universe: the
stellated polyhedra. Haresh Lalvani’s
lecture on “Higher Dimensional Structures” was a delight to the mind and the
eyes. lbny Robbin’s “Quasi Crystal Architecture” is an intuitive visual exploration of the higher dimensions,
4. Art-Geometry-Education
Jay Kappraff remarkable book “Connections- the Geometric Bridge between Art
and Science” is indeed an important bridge
between the two worlds. His lecture assured us about his acute interest in education. Doris Schattschneider
showed us
the “Geometer’s Sketchpad”, a computer
program developed by her team. It is an
innovative tool to teach and learn geometry with pleasure. We had good discussion with Marion Walter, the didactician
who explores the ways to teach geometry
to the very young.
3. New technologies
Stewart Dickson presented a fascinating
technology, called stieyeolirhofluphy, to
produce complicated algebraic surfaces,
never seen before by the human eye, as
plastic models. A computer guides ultraviolet laser light beams on the surface of a
photo sensitive liquid, solidifying the
exposed areas. The beautiful stone sculptures shown by Helaman Fergusson
were produced by an interactive computer program combined with a human,
artistic twist. First a chosen algebraic
5. Structural modelling systems
It was a pleasure to meet Caspar
Schwabe from Zurich. His ever present
large briefcase was full of superbly crafted
geometric surprises, quite a few based on
very recent geometrical research results.
Marc Pelletier arrived with a brand new
kit presented the first time: Zometool by
Biocrystal, Boulder, CO. It is based on the
31-zone structural system proposed by
Steve Bauer. With Zometool the initiated
user may explore the geometry of spaceframes, quasicrystals and hyperspaces.
6. Commercial art production
Two very attractive displays caught the
eyes of the participants. The woodworkings by Jane Greenberg (Woodworkings
and Fkmttive Design, Boston, MA)
reminded us the forgotten art of the florentine renaissance: marquetry.
Bill Gmenlaw (Mosaica, Worchester, MA)
displayed ceramic tiles with intriguing
tiling patterns. These examples also reminded us to a renaissance source
(Francesco Quinterio: Ma~olica Nell’
Architectura de1Rinascimento Italian0 1440.
1520. Cantini, Firenze, 1992).
l **
On the negative side, a special mention
should be given to the lecture by Rhonda
Roland Shearer: “Chaos, FYuctuls, Art: a
Geometry of a new F’rontier’l She declared
during her presentation, that Euclidean
geometry is sexist and masculine, while
fractal geometry is feminine and thus it is
the only correct geometry of the future.
She did expose her reasoning but I just did
not get zt. This unique insight into a new
mathematical philosophy was received by
a polite audience with a stunned silence.
l **
The AM 92 conference was highly successful and we were pleased to hear from
Nat Friedman that it will become a yearly
event, beginning in June 1993.
Janos Bavacs