Handbook of the Mathematics of the Arts and Sciences PDF
Preview Handbook of the Mathematics of the Arts and Sciences
Bharath Sriraman Editor Handbook of the Mathematics of the Arts and Sciences Handbook of the Mathematics of the Arts and Sciences Bharath Sriraman Handbook of the Mathematics of the Arts and Sciences Volume 1 With1473Figuresand74Tables 123 Editor BharathSriraman DepartmentofMathematicalSciences, UniversityofMontana, Missoula,MT,USA ISBN978-3-319-57071-6 ISBN978-3-319-57072-3(eBook) ISBN978-3-319-57073-0(printandelectronicbundle) https://doi.org/10.1007/978-3-319-57072-3 ©SpringerNatureSwitzerlandAG2021 AllrightsarereservedbythePublisher,whetherthewholeorpartofthematerialisconcerned,specif- icallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Thisworkisdedicatedto:MymotherSwarna –initiumAuream&Claire–Luxvitaemeae Foreword ThefirsteditionoftheHandbookoftheMathematicsoftheArtsandSciencesisa 5-year undertaking that has culminated in a scholarly product consisting of 100+ chapters, which address the ubiquity of mathematics in the arts and sciences. The handbookconsistsofsevenpartswithchaptersthataddress(1)mathematics,artand aesthetics;(2)mathematics,humanitiesandthelanguagearts;(3)mathematicsand architecture; (4) mathematics in society; (5) mathematics, science and dynamical systems;(6)mathematics,historyandphilosophy;and(7)mathematicalinfluences andnewdirections. Thepartsincludecontributionsfromresearchersthathavebothanappreciationas wellasanunderstandingofthemathematicsthatinteractswiththeirparticulartopic. Each part also has a separate introduction written by the section editors that sum- marizesthecontentsandscopeoftheirrespectivesections.Thesectioneditors/co- editors of this handbook are Michael Ostwald (mathematics and architecture); KyeonghwaLee(mathematics,artandaesthetics);TorstenLindström(mathematics, science and dynamical systems); Gizem Karaali (mathematics, humanities and language arts) and Ken Valente (mathematical influences and new directions). In addition,threeconsultingeditors,AlexandreBorovik,DainaTaimina,andNathalie Sinclair,werepartoftheeditorialteam. Thegoalofthishandbookwastobecomeanauthoritativesourcewithchapters that show the origins, unification, and points of similarity between different disci- plinesandmathematics.Somechaptersalsoshowbifurcationsandthedevelopment ofdisciplineswhichgrowtotakeonalifeoftheirown.Scienceandartareusedas umbrellatermstoencompassthephysicalandnaturalsciences,aswellasthevisual and performing arts. Numerous chapters in the book explore these connections. Someofthequestionsthatprovokedthishandbookwere: • Whataretheoriginsofinterdisciplinarityinmathematics? • Whatarecross-culturalcomponentsofinterdisciplinaritylinkedtomathematics? • Whatarecontemporaryinterdisciplinarytrends? Thechaptersinthisbookrevealthatmathematicsisbothaconcretehumanactivity, thatis,presentinnumerousartistic,building,exploratory,andrhetoricalendeavors as well as an abstract activity as evidenced in its presence in uncanny situations andcontextsbothmicroandmacro.Theoriginsoftheintentionalorunintentional vii viii Foreword use of mathematics abound in the artistic and architectural splendors of the world since time immemorial whereas modern artistic, computational, and scientific forays into the digital world reveal this ubiquity all over again. In the natural and physical sciences, newer connections are continuously being made. For instance, at the microscopic level, notions from topology, a very abstract mathematical discipline, find relevance in cellular biology whereas at the macroscopic level, ergodic theory, another abstract mathematical discipline, forms the theoretical backbone for modeling dynamical systems all around us. Rhetorical endeavors are understood here in their Aristotelian sense – namely ethos, logos, and pathos. Indeed, mathematics is a very persuasive language that has stood the test of time. Numerous chapters also reveal cross-cultural aspects of interdisciplinarity linked to mathematics. This is especially evident in the parts Mathematics, History, and Philosophy and Mathematical Influences and New Directions. In these two parts, cross-cultural aspects ofinterdisciplinarity, bothancient andmodern, areexplored in familiar and unfamiliar contexts. Finally, contemporary interdisciplinary trends manifest themselves in the sheer range of topics covered in this handbook, which moreorlessruntheentiregamutofthealphabet.Theinterestedreadercanuncover thiswhenperusingthetableofcontents. No preface is complete without acknowledging those who were integral to this project. Clemens Heine (Birkhauser) was the initial sounding board for this idea who helped me crystalize the impossible into something workable. Thomas Hempfling and Michael Hermann gave their logistical expertise and publishing experience.LucaSidler(Birkhauser),RuthLefevre,andEleanorGaffneyprovided invaluableproductionsupportduringdifferentphasesofthisbookprojectforwhich I am most grateful. Last but not least, my family played a major role in their enthusiasticquestionsandnoiselevelsinmotivatingmetocompletethisbook. BharathSriraman Contents Volume1 PartI Mathematics,Art,andAesthetics ......................... 1 1 Mathematics,Art,andAesthetics:AnIntroduction ............ 3 BharathSriramanandKyeonghwaLee 2 TheArtofModernHomoHabilisMathematicus,or:What WouldJonBorweinDo?.................................... 7 ScottB.Lindstrom 3 TheBeautyofBlaschkeProducts ............................ 45 UlrichDaepp,PamelaGorkin,GunterSemmler,andEliasWegert 4 LookingThroughtheGlass ................................. 79 AnnalisaCrannell 5 DesigningBinaryTrees..................................... 105 VincentJ.Matsko 6 HomeomorphismsBetweentheCircularDiscandtheSquare.... 123 ChamberlainFong 7 AVisualOverviewofCoprimeNumbers...................... 149 Benjamín A. Itzá-Ortiz, Roberto López-Hernández, and PedroMiramontes 8 AlmostAllSurfacesAreMadeOutofHexagons ............... 169 HyungryulBaik 9 Anamorphosis Reformed: From Optical Illusions to ImmersivePerspectives..................................... 175 AntónioB.Araújo 10 Anamorphosis:BetweenPerspectiveandCatoptrics............ 243 AgostinoDeRosaandAlessioBortot ix x Contents 11 Geometric and Aesthetic Concepts Based on Pentagonal Structures ................................................ 291 CornelieLeopold 12 MathematicsandOrigami:TheArtandScienceofFolds ....... 317 NatalijaBudinski 13 Geometric Strategies in Creating Origami Paper Lampshades:FoldingMiura-ori,Yoshimura,andWaterbomb Tessellations .............................................. 349 JiangmeiWu 14 MathematicalDesignforKnottedTextiles .................... 381 NithikulNimkulratandTuomasNurmi 15 ArtandScienceofRope .................................... 409 AlexanderÅströmandChristofferÅström 16 ASurveyofCellularAutomatainFiberArts .................. 443 JoshuaHoldenandLanaHolden 17 Mathematics and Art: Connecting Mathematicians andArtists................................................ 467 JosephMalkevitch 18 MathematicsandArt:UnifyingPerspectives .................. 497 HeatherM.RussellandRadmilaSazdanovic 19 SphericalPerspective ...................................... 527 AntónioB.Araújo 20 AHiddenOrder:RevealingtheBondsBetweenMusicand GeometricArt–PartOne .................................. 589 SamaMaraandLeeWestwood 21 AHiddenOrder:RevealingtheBondsBetweenMusicand GeometricArt–PartTwo .................................. 627 LeeWestwoodandSamaMara 22 KoreanTraditionalPatterns:FriezeandWallpaper ............ 649 HyunyongShin,ShillaSheen,HyeyounKwon,andTaeseonMun 23 ProjectionsofKnotsandLinks .............................. 665 AlexanderÅströmandChristofferÅström 24 ComparativeTempleGeometries ............................ 697 KellyMcGonigal 25 WasanGeometry .......................................... 711 HiroshiOkumura Contents xi 26 GeometriesofLightandShadows,fromPierodellaFrancesca toJamesTurrell ........................................... 763 AgostinoDeRosaandFrancescoBergamo 27 TONDtoTOND:Self-SimilarityofPersianTONDPatterns, ThroughtheLogicoftheX-Tiles ............................ 801 Jean-MarcCastera 28 ArtisticManifestationsofTopicsinStringTheory ............. 841 NadavDrukker 29 Cutting,Gluing,Squeezing,andTwisting:VisualDesignof RealAlgebraicSurfaces .................................... 863 StephanKlaus 30 DoubleLayeredPolyhedra.................................. 879 RinusRoelofs Volume2 PartII Mathematics,Humanities,andtheLanguageArts.......... 961 31 Mathematics, Humanities, and the Language Arts: An Introduction .............................................. 963 GizemKaraaliandBharathSriraman 32 MathematicsandPoetry:ArtsoftheHeart ................... 967 GizemKaraaliandLawrenceM.Lesser 33 “Elegance in Design”: Mathematics and the Works ofTedChiang............................................. 981 JessicaK.Sklar 34 RunninginShackles:TheInformation-TheoreticParadoxes ofPoetry ................................................. 1001 DmitriManin 35 Metaphor: A Key Element of Beauty in Poetry andMathematics .......................................... 1015 SânzianaCaramanandLoreleiCaraman 36 PoemsStructuredbyMathematics........................... 1045 DanielMay 37 LewisCarroll’sDefenseofEuclid:ParallelsorContrariwise .... 1093 NatalieSchulerEvers
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