HYPERSEEING - International Society for the Arts, Mathematics, and ...

HYPERSEEINGThe Journal of the International Society of the Arts, Mathematics, and Architecture November 2006www.isama.orgArticlesExhibitsResourcesCartoonsBooksISAMA’07atTexas A&MMay 18-212007NewsIlustrationsAnnouncementsCommunicationsFor four daysTexas A&Mwill beTexas Arts and Mathematics

HYPERSEEINGEditors. Ergun Akleman, Nat Friedman.Associate Editors. Javier Barrallo, Anna Campbell Bliss, Claude Bruter, Benigna Chilla, MichaelField, Slavik Jablan, Steve Luecking, Elizabeth Whiteley.November, 2006Cover Photo: Robert Longhurst’s Arabesque 29, Bubinga, 12”h x 10 ½ “w x 9½ “d.ArticlesRobert Longhurst:Arabesque 29. Nat FriedmanBasketball is an Octahedron: Intriguing Structures ofBalls, Ergun AklemanTwo Americans in Paris: George Rickey and KennethSnelson, Claude BruterSpace, Nat FriedmanCartoonsCartoons from Flatland by Friedman & AklemanCartoons by Tayfun AkgulNewsJournal of Mathematics and the Arts, Gary Greenfield.A Coxeter ColloquiumAnnouncementsISAMA’07ExhibitionsAn Exhibition of Mathematical Art, Claude Bruter.CommunicationsBooksIllustrationsIllustrations by Robert KauffmannResources____________________________________________Article SubmissionFor inclusion in Hyperseeing, members of ISAMA areinvited to email material for the preceding categoriesto hyperseeing@gmail.comNote that articles should be a maximum of threepages.Joint Meeting of the MAA and the AMS.Mathematics and Culture, 2007.Bridges 2007.Nexus V11 2008.

Robert Longhurst’sArabesque 29.Nat FriedmanRobert Longhurst isa sculptor who livesin Chestertown, NYabout a 1½ hour drivenorth of Albany. I haveknown Bob for aboutfifteen years. He carvesabsolutely beautifulwood sculptures generallyin Bubinga wood.These sculptures areextremely thin surfacesthat often have hyperbolicgeometry. The cover sculpture Arabesque 29is an example. This sculpture is actually based on anEnneper’s Surface. The computer image of the usualposition of an Enneper surface is shown below.Three Views of Robert Longhurst, Arabesque 29, Bubinga, 12”h x 10½ “w x 9½” d.Bob has rotated the usual position ¼ turn counterclockwiseto obtain the position in the center photoabove. In this case the sculpture is mounted on avisible rod that is inserted into a thickened edge. Ifthe sculpture in the center photo is rotated on the rodabout a 1/8th turn to the right, the view in the rightphoto is obtained. Another 1/8th turn to the rightwill result in the view in the left photo, which is quitestriking and would correspond to the Top view of theusual position. Another ¼ turn to the right will returnto the center view. Thus ½ turn to the right returnsthe sculpture back to its initial view, which impliesthe sculpture has ½ turn symmetry from above. Thiscan be seen in the computer image of the top view ofEnneper’s surface corresponding to the above photos.see all the possible front views.Note that the left photo has 1/3 turn rotational symmetry.This implies that rotating the Usual Position 1/3turn horizontally results in hyperseeing the sculpturecompletely in the Usual Position. Additional photos ofLonghurst sculptures can be seen atwww.robertlonghurst.com.Computer images are from the excellent websitersp.math.brandeis.edu/3D-XplorMath/Surface/gallery_m.html•Alfred Enneper is a German mathematician who earned his PhDfrom the Georg-August-Universität Göttingen in 1856 for his dissertationabout functions with complex arguments. He studied minimalsurfaces and parametrized Enneper’s minimal surfaces in 1863. Acontemporary of Karl Weierstrass, the two created a whole class ofparameterizations.From WkipediaThe top view has ½ turn rotational symmetry. Thisimplies that for any front view, as in the above photos,the view is identical to the view directly opposite (1/2way around). That is, if we consider any of the threephotos as a front view, then the back view will be thesame. Thus the half-turn symmetry of the top viewhelps to hypersee the sculpture. In particular, we onlyneed to rotate the sculpture ½ turn on the rod to hyper-Usual PositionTop ViewComputer Generated Enneper’s Surface

asketball is an octahedron:intriguing structures of ballsErgun aklemanEach sport has its own easilyidentifiable ball. The major differencebetween the balls comes notfrom their sizes or colors but fromtheir mesh structures. Each sport’sball consists of a set of sphericalpolygons. For instance, the currentmesh structure of a soccer ball isa spherical version of a truncatedicosahedron that came from BuckminsterFuller’s famous geodesicdome designs. Soccer balls consistof 12 spherical pentagons and 20spherical hexagons. At each vertex,three polygons meet. This particulardesign of a soccer ball was firstmarketed in the 1950’s and usedin the 1970 world cup. Before the1950’s, soccer balls were simplyspherical versions of the footballused in American Football. For adetailed history of soccer balls seewww.soccerballworld.com/.Good understanding of mesh structuresof the balls is important forillustrators. Any student of illustrationmust learn geometry to be ableto observe the structures that existin nature. Unfortunately, geometryis not a subject that is taught in artschools. In fact, geometry is noteven really taught in engineeringschools. In 1978, I was a professionalcartoonist for Girgir magazineand I was also an engineeringstudents. I had already taken coursesin calculus, linear algebra, ordinaryand partial differential equations,discrete mathematics andeven engineering drawing, but I didnot know anything about platonicsolids. I clearly remember that oneweek I had to draw a soccer ball forDodecahedral ball2004 European Cup official ballSoccerball with honecomb texturea cartoon. I knew that there had tobe some pentagonal patches. Thatwas all I knew. I drew a soccer ballbut that soccer ball looked strange.The cartoon was published butI could not figure out what waswrong with my drawing. Duringmy PhD on Computer Graphics,I had a minor in mathematics butnone of the courses I took dealtwith geometry. It is interesting thatI learned geometry by myself whenI worked on my thesis.I first realized the importance ofmesh structures of balls during ourvisit to Germany in the Summer2004. We stayed with my wife’ssister. It was the time of the EuropeanSoccer Cup and as a rabidsoccer fan I loved watching soccerevery night with my brother in-lawwho was was an amateur soccercoach. Naturally, in their backyardthere were a wide variety of soccerballs. I realized that some of themwere unusual. So, I took the photographsof these unusual soccerballs. A soccer ball in the backyardwas particularly interesting to meas a researcher. In this soccer ball,the designers drew hexagons on thesurfaces. Obviously, they thoughtthat if they drew hexagons smallenough, they can cover a sphereusing only hexagons. Interestinglyenough, I had just written apaper on pentagonal subdivision(a remeshing algorithm that canconvert any given mesh to a pentagonalmesh) and showed thata pentagonal subdivision is theonly one beyond quadrilateral andtriangular subdivisions. Using theEuler-Poincare equation it is easyto prove that a hexagonal subdivisiondoes not exist. In other words,it is not possible to cover a spherewith even non-regular hexagonsregardless of how small they are.Ian Stewart had a very nice articleon this subject. Obviously, thedesigners of that ball did not know

about it.The most interesting soccer ballin the backyard was a hand-sewndodecahedral ball. Although a dodecahedronis not as good approximationof a sphere as a truncatedicosahedron, the sole existence ofthis ball suggested to me that thedodecahedral structure have beenused for soccer balls until BuckminsterFuller’s design won overany other rival structure.Another observation from the tripwas the design of the official ball ofthe 2004 European Cup. Obviously,the designers of the ball wanted tomake the ball more interesting anddrew brush strokes that create anoctahedral structure on the surface.They did not complete the trianglesbut the octahedral structurewas clearly visible from the brushstrokes. So, I wondered what areother mesh structures on the surfacesof balls that are used in sports.When I returned back to the US,I started to look at other balls. Abasketball turned out to be themost interesting one. Basketballwas originally played with brownsoccer balls. In the 1950’s, thelegendary basketball coach TonyHinkle invented the current orangeball to make it more visible to bothplayers and spectators. The meshstructure of the current basketballturned out to be an octahedron. Itconsists of 8 identical spherical trianglesand 4 triangles meet in eachvertex. It is really hard to see thesetriangles. So, I cut an old basketballto see the shapes of triangles.As you can see in the images, eachspherical triangle consists of twolong and one short curved edges.Although, these triangles do notlook aesthetic themselves, theSpherical Triangle of BasketballTwo Spherical TrianglesHemisphere with four Spherical TrianglesBasketball: Four triangles at each vertexVolleyball: Can you find hexagons?basketball has its own beauty. So,this is a clear example of the wholebeing more than its parts.Another interesting shape turnedout to be the tennis ball. It is notknown who designed the tennisball, but, Charles Goodyear’svulcanization process allowed massproduction of rubber balls in the1850’s. I do not know how similarthose balls in the 1850’s were withtoday’s tennis balls. However, thecurrent tennis ball consists of twospherical polygons drawn on thesphere as if they are 3D yin andyang symbols. I also cut a tennisball to clearly see the shapes ofthese 3D yin and yang symbols.Since the ball is pressurized, it wasvery hard to cut it, but it is reallyworth it to see the shapes. A baseballshares the same mesh structurewith the tennis ball.On the other hand, a volleyballseems to be the most uninterestingball. But, if you look at one carefullyyou will see 6 quadrilateralsand 12 hexagons. Can you findthem? Note that you have to countthe number of vertices to determinethe type. This particular structurewas briefly used in soccer ballsbefore 1950. I could not find outthe history of a volleyball but thecurrent mesh structure of volleyballsmust have been adapted fromthe early soccer balls.Since a football is not sphericalI do not call it a ball, but, thereare many other balls. For instance,table tennis balls or billiardballs have only one surfaceand no edge. If you know anyother sports ball with an interestingmesh structure, write to us. •

Two Americans in Paris: GeorgeRickey and Kenneth SnelsonClaude P. Bruter“Two Americans in Paris” is a sculpture exhibitionshowing the work of the eminent sculptors KennethSnelson and George Rickey.The exhibition is at the Gardens of the PalaisRoyal in Paris, October 24- December 15, 2006.Kenneth Snelson (1927-) is the inventor oftensegrity and his informative website is www.kennethsnelson.net/ George Rickey (1907-2002)is considered the leading modern kinetic sculptor.Kenneth Snelson, Four mobile Piece, 1968, foreground,George Rickey, Two Planes Vertical Horizontal IV, 1974, background.At the bottom of the Avenue of the Opera, two stepsaway from the Louvre, along the Comédie Francaise,the Gardens of the Palais Royal presently welcomeworks by the eminent American sculptors GeorgeRickey and Kenneth Snelson. George Rickey (1907-2002) is considered the leading modern kinetic sculptorand Kenneth Snelson (1927-) is the inventor oftensegrity sculpture. This exhibition was inauguratedon October 23, 2006 by the French Minister forCulture and Communication, Renaud Donnedieu deVabres, and will close December 15, 2006. (All photographsby C.P.Bruter.)That these sculptors are American expresses the currentstate of our global society whose movement isstill influenced by the strong vitality of the nation ofthe star spangled banner. These are definitely works ofthe present time as seen in their design, material, andform. They are based on engineering principals andreflect a stage of the artistic evolution of humanity.The sculptures of Rickey and Snelson both reflect asimplicity of basic forms. Rickey’s kinetic sculpturesare based on rectangles moving with the wind. Themovement is not frantic but rather slow and quitehypnotic. Rickey has constructed these kinetic sculpturesso that they convey a wonderful choreographyof simple geometric shapes. There is also the play ofreflected light on the polished surfaces.George Rickey, Four Rectangles Oblique, 1979, foreground,Kenneth Snelson, Indexer, 2000, E.C. Column, 1969-81, background.Snelson’s tensegrity sculptures consist of compositionsof metal tubes individually suspended in spacedue to the tension on the connecting cables. When firstseen, the constructions do not seem possible. Each

Kenneth Snelson, Sleeping Dragon, 2002-3, detail.Kenneth Snelson, Sleeping Dragon, 2002-3linear tube is like an individual musical note in spaceand the sculptures are compositions of these linearnotes. Snelson displays both horizontal and verticalsculptures of impressive size.The works of Rickey and Snelson are undoubtedlycharacteristic works of our time. They are impressiveworks that have evolved from ingenious fundamentalideas.Kenneth Snelson’s website www.kennethsnelson.comis rich in information. In particular, the discussion inthe section Structure and Tensegrity is excellent. •Kenneth Snelson, E.C. Column, 2002-3, detail.

spaceNat FriedmanA major development of twentieth century sculpturewas the introduction of space so that a sculpture becamea composition of both form and space. Examplesare works of Barbara Hepworth and Henry Moore.Actually form and space were appreciated much earlierin so-called Asian scholar’s rocks that were naturalrocks found in rivers that had spaces carved out bythe effects of time and water. In these sculptures theappreciation of the form-space compositions is mainlyvisual as the spaces are not large enough to enter. Inparticular, photographs can partially convey the visualexperience of these sculptures.There are two ways to appreciate a landscape formspacesculpture like the Grand Canyon. One way is tostand at the rim and appreciate it visually. A secondway is to enter the canyon and move through it eitherby hiking or rafting. In this case there is the body experienceof being in the canyon, as well as the visualexperience. There are the same two ways of appreciatingcertain architectural sculpture.The significance of large spaces that one can enter isof utmost importance in major contemporary sculpture.For example, Richard Serra’s torqued ellipses arelarge steel shells enclosing a space whose mathematicalshape corresponds to an elliptical cross-sectionthat rotates as the height of the cross-section increases.These are spaces that theobserver can enter and walkaround in and therefore experiencethe shape of the space.Thus the emphasis here ison the body experience of amathematical space. Serraconsiders the visual experienceof the steel shell assecondary to the body experience.Thus he does not feelthat photographs can conveythe main body experience ofthe torqued ellipses. Serrahas also created sculpturesthat consist of long steel walls that one can walk between.These walls may be conical sections that leanin and out as well as sections with positive and negativecurvature. Positive curvature corresponds to sectionsof spheres and negative curvature corresponds tosections of saddle shapes. Walking through the spacesbetween these walls can be a rather disorienting bodyexperience. Thus appreciating these sculptural mathematicalspaces is also mainly through body experiencerather than visual experience. There is a permanentexhibit of eight of Serra’s sculptures, The Matterof Time, at the Guggenheim Art Museum in Bilbao,Spain, which will be visited during this years BridgesDonostia (see below). These sculptures are describedas “gigantic exercises in topology”, The Guardian,June 22, 2005, Man of Steel, http://arts.guardian.co.uk/features/story/0,11710,1511714,00.html Alsosee the links at the end of the article.There are also the space sculptures of Anish Kapoorthat are hugh topological spaces enclosed by shellsof plastic fabric supported by cables. These are notspaces that one could walk through, although one canimagine being a bird and flying through them. A majorexample is Marsyas, 2002, constructed for the TurbineHall at the Tate Modern, www.tate.org.uk/modern/exhibitions/kapoor/.Marsyas has round openings at eachend, as well as a central opening that one could seePhoto from Grand Canyon National Park Service Archive

into from a central viewing platform. The emphasishere was on the visual experience of the light in thespace, as well as the extant of the shell form. Anotherexample is Melancholia, which consists of a spacewith a circular opening at one end and a rectangularopening at the other end. This example is suggestedby a mathematical string model in the British ScienceMuseum in London, which consists of circleand square ends with equal numbers of holes throughwhich string is threaded between the circle and thesquare. Thus one can see shapes that morph from acircle to a square. This mathematical model led HenryMoore and Barbara Hepworth to create string sculptures.Naum Gabo later developed quite refined stringsculptures. Thus it is interesting that Anish Kapoorextended this mathematical idea to monumental size.A third example is Taratantara,1999, www.commissionsnorth.org/showcase/portfolio/102which is aspace with rectangular openings at each end. Thereare books available on Taratantara and Marsyas, seeBooks section. •CArtoons from flatlandNat Friedman&Ergun AklemanCArtoonstayfun akguL

NewsJournal of Mathematics and the ArtsDue to the energy of Gary Greenfield, the art-mathtribe now has the Journal of Mathematics and the Arts(JMA). Gary Greenfield is the editor and JMA will bepublished by Taylor and Francis of England. JMA isa peer - reviewed journal that focuses on connectionsbetween mathematics and the arts.Editorial BoardEditor:Gary Greenfield - Mathematics & Computer Science,University of Richmond, Richmond VA 23173, USAAssociate Editors:Aims & ScopeThe Journal of Mathematics and the Arts is a peerreviewed journal that focuses on connections betweenmathematics and the arts. It publishes articles of interestfor readers who are engaged in using mathematicsin the creation of works of art, who seek to understandart arising from mathematical or scientific endeavors,or who strive to explore the mathematical implicationsof artistic works. The term ”art” is intended to include,but not be limited to, two and three dimensional visualart, architecture, drama (stage, screen, or television),prose, poetry, and music. The Journal welcomes mathematicsand arts contributions where technology orelectronic media serve as a primary means of expressionor are integral in the analysis or synthesis of artisticworks. The following list, while not exhaustive,indicates a range of topics that fall within the scope ofthe Journal:• Artist’s descriptions providing mathematical context,analysis, or insight about their work.• The exposition of mathematics intended for interdisciplinarymathematics and arts educators and classroomuse.• Mathematical techniques and methodologies of interestto practice-based artists.• Critical analysis or insight concerning mathematicsand art in historical and cultural settings.Donald Crowe - University of Wisconsin-MadisonMike Field - University of HoustonGwen Fisher - California Polytechnic State University,Richard J. Krantz - Metropolitan State College ofDenverNat Friedman - University at Albany, SUNYGeorge W. Hart - Stony Brook UniversityCraig S. Kaplan - University of WaterlooRobert Krawczyk - Illinois Institute of TechnologyReza Sarhangi - Towson UniversityJohn Sharp - WatfordJohn Sullivan - Technical University of BerlinDaylene Zielinski - Bellarmine UniversityPapers for consideration should be sent to the Editor atthe address below:Gary Greenfield - Mathematics & Computer Science,University of Richmond, Richmond VA 23173, USA;Email: ggreenfi@richmond.edu.For information, seewww.tandf.co.uk/journals/titles/17513472.aspThe Journal also features exhibition reviews, bookreviews, and correspondence relevant to mathematicsand the arts.

NewsA Coxeter ColloquiumOn November 3, 2006, A Coxeter Colloquium washeld at Princeton University, in honor of H.S.M. (Donald) Coxeter (1907-2003), who was considered thefather of modern geometry. In particular, a dedicationceremony for John Conway’s 4-dimensional dodecahedronsculpture by Marc Pelletier took place at QuarkPark. The sculpture is a copy of one that was presentedby an anonymous donor to the Fields Mathematical Institutein Toronto to honor the 95th birthday of H.S.M.Coxeter in February, 2002. The same donor presentedthis sculpture to the Princeton University MathematicsDepartment in honor of Professor John H. Conway. Anarticle by Ivars Peterson on Quark Park is atwww.sciencenews.org/articles/20061111/mathtrek.aspThe schedule of the talks follows. Siobhan Roberts isthe author of King of Infinite Space, a recent book onH.S.M. Coxeter. For a detailed summary of the Colloquium,seewww.georgehart.com/CoxeterProgramme.pdfSession OneJ.R.Gott III, Welcome.Siobhan Roberts on “Unfashionable Pursuits”, an excerptfrom King of Infinite Space.Freeman Dyson on “How Polyhedra Fit Into EachOther”Michael Longuet-Higgins on “Snub Polyhedra andOrganic Growth”George Hart on “The Geometric Aesthetic”Doris Schattschneider on “Coxeter and the Artists”Marjorie Senechal on “Coxeter, the Verb”Session Two.Neil Sloane on “The Music of Quadratic Forms”John Conway on “The Four Dimensional Polytopes”Tony Robbin on “ Coxeter, Hyper-tessellations, andQuasicrystals”Marc Pelletier on “ Coxeter’s Model Maker, PaulDonchian”Roe Goodman on “ Alice Through Looking Glassafter Looking Glass”J.R.Gott III on “ Regular Skew Polyhedra and theSponge-Like Topology of the Large Scale Structureof the Universe”Siobhan Roberts on “JeffWeek’s Dodecahedral Universe”,a computer-animatedexcerpt from King of InfiniteSpace, with 3D glasses. •

announcementsISAMA’07 in College StationTexas A&M University, May 18-21, 2007.Thank you much to Ergun Akleman for arranging forTexas A&M University, College Station, Texas tohost ISAMA’07 at the College of Architecture, May18-21. There will be a Proceedings with an electronicsubmission process and an exhibit. There is a hotelon campus, as well as dorm facilities. There is also anairport in College Station serviced by several airlines.Relevant information will be on the website http://archone.tamu.edu/isama07/For four days Texas A&M will be Texas Arts andMathematics!!Joint Meeting of the MAA and AMS in New Orleans.The annual joint meeting of the MAA and AMS willbe held in New Orleans January 4-8, 2007. Fortunately,New Orleans is the home of the sculptor Arthur Silvermanwhose work is based on the tetrahedral form.Arthur has spoken at several of the Art-Mathematicsconferences in Albany, Berkeley, and San Sebastian.Here is the announcement concerning Arthur’s talkand studio visit.Arthur Silverman: Tetrahedral Variations.Arthur Silverman graduated from Tulane MedicalSchool in 1947 and pursued a highly successful careeras a surgeon in New Orleans. He retired from his medicalpractice while in his fifties in order to concentrateon an earlier passion for sculpture. He was attractedto geometric sculpture and became infatuated with thetetrahedron. He has produced more than 300 sculpturesbased on the tetrahedron, predominately in stainlesssteel or aluminum (see www.artsilverman.com).His signature work is a pair of tetrahedrons, each 10ft by 60 ft in front of the Energy Center in downtownNew Orleans (see cover page). There are twenty ofhis sculptures in public buildings and outdoor areas inNew Orleans. A map showing locations of the sculptureswill be available at the Art Exhibit. Arthur Silvermanwill be giving a talk Tetrahedral Variations onSaturday at 6 pm at the Marriott. A studio visit is alsobeing planned for Sunday at 6 pm. If you plan to visitthe studio, please contact Nat Friedman: artmath@math.albany.eduMathematics and CultureMathematics and Culture-Convegno “ Mathematicaand Cultura 2007”, Venice, Italy, March, 2007, organizedby Michelle Emmer. Information will appear atwww.mat.uniroma1.it/venezia2007.Bridges DonostiaMucho congratulations to Reza for the tenth annualBridges Conference, Bridges Donostia, to be held atthe University of the Basque Country in San Sebastian,Spain, July 24-27, 2007. Donostia is the Basquename for San Sebastian. Javier Barrallo will be themain organizer in San Sebastian. Javier has alreadyorganized two wonderful conferences in San Sebastian.Namely Mathematics and Design in 1998 andISAMA 99 in 1999. San Sebastian is a beautiful cityon the northern coast of Spain in the Basque country.Dorm rooms with private bath will be available at avery reasonable cost that includes breakfast. Therewill be an excursion to Bilbao to see the GuggenheimArt Museum, as well as an excursion to Zabalaga, thesculpture park of Eduardo Chillida, outside San Sebastian.This conference will differ from the 1998 and1999 conferences in that you will NOT have your ownbottle of wine at lunch. Thus the afternoon sessionsare expected to be better attended!! Alas, some confereeswill no doubt end up asleep on the beach. Watchthe Bridges website for information.Nexus V11, 2008Nexus V11: Relationships between Architecture andMathematics is organized by Kim Williams and willbe held in June, 2008. For information, see www.nexusjournal.com

An Exhibition ofMathematical ArtClaude P. BruterA work of art is initially a representation. It carries themark of who has built it. It has a significance.As a representation, a work of art can simply reveal ashare of the intrinsic architecture of the universe. Thisrevelation surprises and delights. It to some extentmakes vibrate, as by resonance, the sensitive cordsof the human being which, as a fragile and temporaryresult of the deployment of this universe, containssome of its fundamental elements, at least in its constitution.It attaches the being with the totality of nature,immerses it in this kind of ocean, which is protectiveand comforting. The work of art is equipped with anemotional capacity.Mathematics as a whole is a representation of structuraland constitutive data of our universe. It has, in anExhibition Places & DatesThe Library of the Poincaré Institute, Jan 24- June 30,05.The Ecole Polytechnique, July 5-Sept 18, 05;IFUM Bonneuil, Jan 4-16, 06;7th Salon des Jeux Mathématiques in Paris, May 25-27, 06;The Media Library of Palaiseau, June 3- Sept 16, 06.The Lycée Alphonse Daudet in Nîmes, Oct 7-14,06,IREM andDept. de Mathematiques,University of Montpellier, Oct 17-24, 06;The Institut Français de Thessaloniki, Greece, Nov 6-25, 06.intrinsic way, the properties of a work of art. Initiallydrawing from the concrete world what it intends torepresent, it forges a symbolic system, which it developsin an apparently autonomous way, whose handlingrequires the acquisition of an increasingly complexand thorough technicality. Thus developing in anincreasingly rich universe but detached also more andmore of the immediate materiality, it becomes less andless accessible to the greatest number, which do notpractice it. It has the appearance of a monster, cold anddisconcerting by its high technicality.However, it is possible to incarnate this universesymbolic system with the play of colors and matter togenerate artistic forms that cause surprise, attract theglance, and arouse curiosity.It is in this preoccupation with communication, exchangeof ideas, and enrichment, which led me to aproject where art would reveal parts of the mathematicalworld, and introduce mathematical ideas in a deferent,delicate, and subtle way. This led to the presentexhibitthat can be seen at http://hermay.org/ARPAM/palaiseau/index.htmlcreated bythe painter Jean Constant.All the principal fields ofgeometry are represented:differential geometry withPatrice Jeener, FrançoisApèry, Jean Constant, andJohn Sullivan; differentialtopology with the last threeand Thomas Banchoff;dynamic topology withMichael Field; hyperbolicgeometry with Irene Rousseauand David Wright;tessellations and polyhedrons with David Austin, BillCasselman and George Binder; fractal geometry withJean Francis Colonna and Nat Friedman. In additionthere are the spheres of Dick Termes and graphics ofBahman Kalantari. •This is a traveling exhibit organized by Claude Bruter. We are sure all the contributing artists join us inthanking Claude Bruter for all of the work he has done in making this exhibition so successful. His email:bruter@univ-paris12.fr

BOOKSAnish Kapoor: Taratantara by Sune Nordgren, MarjorieAllthorp-Guyton, Richard Cork; publisher Actar,2001, ISBN 8495273446.Anish Kapoor: Marsyas by Donna De Salvo andC.Balmond, publisher Tate Gallery, 2003, ISBN1854374419.These two books are described at Amazon but thereare only a few copies, which are expensive. Interlibraryloan is suggested.Art for a House of Mathematics by Anna CampbellBliss, 2004, ISBN 0975491504.an architect in Salt Lake City, Utah. This book documentsa large installation by Anna in the CowlesMathematics Building at the University of Utah in SaltLake City. The installation is multi media and coversthree floors. It is a very impressive installation thatcombines many aspects of mathematics with art andarchitecture. This beautiful book is distributed by theAmerican Mathematics Society, www.ams.org/bookstore.Bradford Hansen-Smith, Folding circle Tetrahedra:Truth in the Geometry of Wholemovement, WholemovementPublications, Chicago IL, 2005 ISBN#0-9766773-0-xAnna has attended many of our conferences. She isillustrationsrobert kauffmann

communicationsThis section is for short communications such as recommendations for artist’s websites, links to articles, queries,answers, etc. For inclusion in HYPERSEEING, members of ISAMA are invited to email material for thecategories outlined on the cover to hyperseeing@gmail.com or Nat Friedman at artmath@math.albnay.edu.a sample of WEB REsources[1] www.kimwilliamsbooks.comKim Williams website for previous Nexus publicationson architecture and mathematics.[2] www.mathartfun.comRobert Fathauer’s website for art-math products includingprevious issues of Bridges.[3] www.mi.sanu.ac.yu/vismath/The electronic journal Vismath, edited by SlavikJablan, is a rich source of interesting articles, exhibits,and information.[4] www.isama.orgA rich source of links to a variety of works. For inclusionin Hyperseeing, members of ISAMA are invitedto email material for the categories outlined in thecontents above to Nat Friedman at artmath@math.albany.edu[9] www.georgehart.comGeorge Hart’s Webpage. One of the best resources.[10] www.cs.berkeley.edu/Carlo Sequin’s webpage on various subjects related toArt, Geometry ans Sculpture.[11] www.ics.uci.edu/~eppstein/junkyard/Geometry Junkyard: David Eppstein’s webpage anythingabout geometry.[12] www.npar.org/Web Site for the International Symposium on Non-Photorealistic Animation and Rendering[13] www.siggraph.org/Website of ACM Siggraph.[5] www.kennethsnelson.comKenneth Snelson’s website which is rich in information.In particular, the discussion in the section Structureand Tensegrity is excellent.[6] www.wholemovement.com/Bradfrod Hansen-Smith’s webpage on circle folding.[7] http://www.bridgesmathart.org/The new webpage of Bridges.[8] www-viz.tamu.edu/faculty/ergun/research/topologyTopological mesh modeling page. You can downloadTopMod.Image by Hernan Molina from Ergun Akleman’s ComputerAided Sculpting Course

isama’07Sixth Interdisciplinary Conference ofThe International Society of the Arts, Mathematics, and ArchitectureCollege Station, Texas, May 18-21, 2007ISAMA’07 will be held at Texas A&M University,College of Architecture, in College Station, Texas. Thepurpose of ISAMA’07 is to provide a forum for thedissemination of new mathematical ideas related tothe arts and architecture. We welcome teachers, artists,mathematicians, architects, scientists, and engineers,as well as all other interested persons. As in previousconferences, the objective is to share informationand discuss common interests. We have seen that newideas and partnerships emerge which can enrich interdisciplinaryresearch and education.FIELDS OF INTERESTThe focus of ISAMA’07 will include the followingfields related to mathematics: Architecture, ComputerDesign and Fabrication in the Arts and Architecture,Geometric Art, Mathematical Visualization, Music,Origami, and Tessellations and Tilings. These fields includegraphics interaction, CAD systems, algorithms,fractals, and graphics within mathematical software.There will also be associated teacher workshops.CALL FOR PAPERSPaper submissions are encouraged in Fields of Intereststated above. In particular, we specify the followingand related topics that either explicitly or implicitlyrefer to mathematics: Painting, Drawing, Animation,Sculpture, Storytelling, Musical Analysis and Synthesis,Photography, Knitting and Weaving, GarmentDesign, Film Making, Dance and Visualization. Artforms may relate to topology, dynamical systems,algebra, differential equations, approximation theory,statistics, probability, graph theory, discrete math,fractals, chaos, generative and algorithmic methods,and visualization.SubmissionAuthors are requested to submit papers in PDF format,not exceeding 5 MB. Papers should be set in ISAMAConference Paper Format and should not exceed 10pages. LaTeX and Word style files are available at:(will be available). Abstracts will not be reviewed.Abstract submission is just for the early identificationof reviewers for papers. The papers will be publishedas the Proceedings of ISAMA’07.For four daysTexas A&M will beTexas Arts and Mathematics!!

IMPORTANT DATESDecember 15, 2006 Submission System OpenJanuary 15, 2007 Paper and Short paper submissiondeadlineFebruary 15, 2007 Notification of acceptance orRejectionMarch 15, 2007 Deadline for camera-ready copiesRELATED EVENTSArt & Architecture ExhibitionThere will be an exhibit whose general objective isto show the usage of mathematics in creating art andarchitecture. Instructions on how to participate will beposted on the conference website.Teacher WorkshopsThere will be teacher workshops whose objective is todemonstrate methods for teaching mathematics usingrelated art forms. Instructions on how to participatewill be posted on the conference website.HISTORYThe International Society of the Arts, Mathematics,and Architecture (ISAMA) was founded in 1998 byNat Friedman, sculptor and professor of mathematicsat SUNY Albany, as an outgrowth of his series of conferenceson Art and Mathematics, held in Albany from1992 through 1997, and in Berkeley in 1998.Previous ISAMA ConferencesISAMA’04, DePaul University, Chicago IllinoisISAMA’03, University of Granada, Granada, SpainISAMA’02, University of Freiburg, Freiburg, GermanyISAMA’00, SUNY-Albany, Albany, NewYorkISAMA’99, University of the Basque Country, SanSebastian, SpainPrevious Conferences on Art and Mathematics (AM)AM’98,University of California, Berkeley, CaliforniaAM’92-AM’97, SUNY-Albany, Albany, NewYorkFor additional ISAMA information, see www.isama.org. In particular, the Directory is a rich source oflinks to works in a variety of fields.Sponsored byCollege of Architecture, Texas A&M UniversityInternational Society of the Arts, Mathematics, and ArchitectureAn illustration by Ergun Akleman, Inspired by Robert Kauffmann’s “One Sided Relationship”. The 3D Escher inspired MoebiusStrip is created by Avneet Kaur in Computer Aided Sculpting course of Ergun Akleman.