外文翻译-某城市博物馆建筑方案设计8

广西科技大学毕业设计（论文）外文翻译课题名称ARCHITECTURE,PATTERNS,ANDMATHEMATICS结构形态数学模数学院土木建筑工程学院专业建筑学班级建筑091班学号姓名指导教师2014年3月24日原文ARCHITECTURE,PATTERNS,ANDMATHEMATICSNIKOSSALINGAROSPOSITSTHEIMPORTANCEOFARCHITECTURALPATTERNINMANSINTELLECTUALDEVELOPMENT,EXAMININGHOWTWENTIETHCENTURYARCHITECTURALATTITUDESTOWARDSDECORATIONANDPATTERNHAVEIMPOVERISHEDMANSEXPERIENCEOFBOTHMATHEMATICSANDTHEBUILTENVIRONMENTINTRODUCTIONTHETRADITIONALLYINTIMATERELATIONSHIPBETWEENARCHITECTUREANDMATHEMATICSCHANGEDINTHETWENTIETHCENTURYARCHITECTURESTUDENTSARENOLONGERREQUIREDTOHAVEAMATHEMATICALBACKGROUNDWHILEAPROBLEMINITSELF,AFARMORESERIOUSPOSSIBILITYISTHATCONTEMPORARYARCHITECTUREANDDESIGNMAYBEPROMOTINGANANTIMATHEMATICALMINDSETTHEMODERNISTMOVEMENTSUPPRESSESPATTERNINARCHITECTURE,ANDTHISHASPROFOUNDIMPLICATIONSFORSOCIETYASAWHOLEMATHEMATICSISASCIENCEOFPATTERNS,ANDTHEPRESENCEORABSENCEOFPATTERNSINOURSURROUNDINGSINFLUENCESHOWEASILYONEISABLETOGRASPCONCEPTSTHATRELYONPATTERNSELIMINATINGPATTERNSFROMTWENTIETHCENTURYARCHITECTUREAFFECTSOURCAPACITYTOPROCESSANDINTERPRETPATTERNSINTHOUGHTMATHEMATICS,ANDTHEINTELLECTUALPATTERNSITEMBODIES,LIEOUTSIDEOURCONTEMPORARY,EXPLICITLYANTIPATTERNARCHITECTURALWORLDVIEWMATHEMATICSTEACHERSAREBEMOANINGTHEFACTTHATTHEREISLESSANDLESSINTERESTINMATHEMATICS,WHICHHASRESULTEDINADECLININGMATHEMATICALCAPACITYAMONGSTUDENTSTHISSTANDSINSHARPCONTRASTINDEEDACONTRADICTIONWITHTHEINCREASINGTECHNOLOGICALADVANCESWEAREWITNESSINGINOURTIMESHERE,ITISPROPOSEDTHATANENVIRONMENTALFACTORMIGHTCONTRIBUTETOTHEOVERALLDECLINEOFMATHEMATICSINOURSOCIETYTHISTHEORYAROSEFROMTHEAUTHORSINTERESTINTHETHEORETICALBASISBEHINDARCHITECTURALSTYLESFROMDIFFERENTPERIODSANDREGIONSITHASRECENTLYBEENSHOWNHOWTRADITIONALARCHITECTURESOBEYRULESTHATAREINTRINSICALLYMATHEMATICALTHOSERULESLEADTOBUILDINGSTHAT,WHATEVERTHEIRFORM,ENCAPSULATETOAGREATERORLESSEREXTENTMULTIPLEMATHEMATICALQUALITIESANDINFORMATIONTHEARCHITECTUREOFTHETWENTIETHCENTURYHASACHIEVEDNOVELTY,ANDABREAKWITHTHEPAST,PRECISELYBYELIMINATINGTHOSEQUALITIESINTHISPAPER,THEWORD“PATTERN”DENOTESAREGULARITYINSOMEDIMENSIONTHESIMPLESTEXAMPLESAREREPEATEDVISUALUNITSORDEREDWITHTRANSLATIONALLINEARORROTATIONALSYMMETRYPATTERNSALSOEXISTINASCALINGDIMENSION,WHERESIMILARFORMSOCCURATDIFFERENTMAGNIFICATIONWHENGEOMETRICSELFSIMILARITYISDEFINEDONAHIERARCHYOFSCALES,ASELFSIMILARFRACTALISCREATEDTHECONCEPTOFAPATTERNALSOEXTENDSTOSOLUTIONSPACE,INTHATSOLUTIONSTOSIMILARPROBLEMSARETHEMSELVESRELATEDANDDEFINEASINGLETEMPLATETHATREPEATSWITHSOMEVARIATIONEVERYTIMESUCHAPROBLEMISSOLVEDTHEUNDERLYINGIDEAISTOREUSEINFORMATIONWHETHERINREPEATINGAUNITTOGENERATEATWODIMENSIONALTILINGDESIGN,ORINREUSINGTHEGENERALSOLUTIONTOACLASSOFDIFFERENTIALEQUATIONSENVIRONMENTALPSYCHOLOGISTSKNOWTHATOURSURROUNDINGSINFLUENCENOTONLYTHEWAYWETHINK,BUTALSOOURINTELLECTUALDEVELOPMENTORDEREDMATHEMATICALINFORMATIONINTHEENVIRONMENTGENERATESPOSITIVEEMOTIONALRESPONSESIFWEARERAISEDINANENVIRONMENTTHATISIMPLICITLYANTIMATHEMATICAL,THATADVERSELYAFFECTSOURINTERESTINMATHEMATICSPOSSIBLYEVENOURABILITYTOGRASPMATHEMATICALCONCEPTSDOESSPENDINGONESWHOLELIFEINAPATTERNLESSWORLDWEAKENOREVENDESTROYTHECRUCIALCAPACITYTOFORMPATTERNSEVENTHOUGHTHEDEFINITIVEANSWERTOTHISQUESTIONISNOTKNOWN,ITSIMPLICATIONSAREALARMINGWHILETHEREISVERYSTRONGCRITICISMOFCONTEMPORARYARCHITECTUREFORITSLACKOFHUMANQUALITIES,THEPRESENTCRITICISMGOESFARDEEPERTHISISNOTANARGUMENTABOUTDESIGNPREFERENCESORSTYLESITCONCERNSTHETRAINEDFUNCTIONALITYOFTHEHUMANMINDASCIENCEOFPATTERNSMATHEMATICSISASCIENCEOFPATTERNSTHEMINDPERCEIVESCONNECTIONSANDINTERRELATIONSBETWEENCONCEPTSANDIDEAS,THENLINKSTHEMTOGETHERTHEABILITYTOCREATEPATTERNSISACONSEQUENCEOFOURNEURALDEVELOPMENTINRESPONDINGTOOURENVIRONMENTMATHEMATICALTHEORIESEXPLAINTHERELATIONSAMONGPATTERNSTHATARISEWITHINORDERED,LOGICALSTRUCTURESPATTERNSINTHEMINDMIMICPATTERNSINNATUREASWELLASMANMADEPATTERNS,WHICHISPROBABLYHOWHUMANBEINGSEVOLVEDSOASTOBEABLETODOMATHEMATICSMANKINDGENERATESPATTERNSOUTOFSOMEBASICINNERNEEDITEXTERNALIZESCONNECTIVESTRUCTURESGENERATEDINTHEMINDVIATHEPROCESSOFTHINKING,WHICHEXPLAINSTHEUBIQUITOUSNESSOFVISUALPATTERNSINTHETRADITIONALARTANDARCHITECTUREOFMANKINDPATTERNSINTIMEAREALSOESSENTIALTOHUMANINTELLECTUALDEVELOPMENTDAILYACTIVITYISORGANIZEDAROUNDNATURALRHYTHMSANNUALEVENTSBECOMEASOCIETYSFIXEDPOINTSMOREOVER,THESEOFTENLINKSOCIETYTOANEMERGINGSCIENTIFICUNDERSTANDINGOFPERIODICNATURALPHENOMENASUCHASSEASONSANDTHEIREFFECTSMATHEMATICSITSELFAROSEOUTOFTHENEEDTOCHRONICLEOBSERVEDPATTERNSINSPACEANDTIMEONSMALLERSCALES,REPEATINGGESTURESBECOMETHEATERANDDANCE,ANDAREINCORPORATEDINTOMYTH,RITUAL,ANDRELIGIONTHEDEVELOPMENTOFVOICEANDMUSICRESPONDSTOTHENEEDTOENCAPSULATERHYTHMICPATTERNSANDMESSAGESALLOFTHESEACTIVITIESOCCURASPATTERNSONTHEHUMANRANGEOFTIMESCALESCOMPLEXPHYSICALANDCHEMICALSYSTEMSAREKNOWNTOGENERATEPATTERNSINSPACEORTIME,ASARESULTOFSELFORGANIZATIONTHESYSTEMSORGANIZEDCOMPLEXITYISMANIFESTEDONAMACROSCOPICSCALEASPERCEIVABLEPATTERNSTHISISNOTONLYTRUEFORTHEINNUMERABLESTATICPATTERNSFOUNDINNATUREPATTERNSALSOREPRESENTCOLLECTIVEMOTIONSOROTHERFORMSOFORGANIZED,DISSIPATIVEBEHAVIORTHEOBSERVATIONOFSTEADYSTATEPATTERNSINDYNAMICSYSTEMSISOFTENINDICATIVEOFTHESYSTEMASSUMINGANOPTIMALSTATEFORENERGYTRANSFEREXAMPLESINCLUDECONVECTIONCELLS,OCEANCURRENTS,ANDWHIRLPOOLSINRIVERSBYCONTRAST,THEREISVERYLITTLEGOINGONINAHOMOGENEOUSSTATEBEFORETHEERAOFMASSEDUCATION,ANDFORAGREATMANYPEOPLESTILLTODAY,ARCHITECTURALPATTERNSREPRESENTONEOFTHEFEWPRIMARYCONTACTSWITHMATHEMATICSTILINGSANDVISUALPATTERNSAREA“VISIBLETIP”OFMATHEMATICS,WHICHOTHERWISEREQUIRESLEARNINGASPECIALLANGUAGETOUNDERSTANDANDAPPRECIATEPATTERNSMANIFESTTHEINNATECREATIVEABILITYANDTALENTTHATALLHUMANBEINGSHAVEFORMATHEMATICSTHENECESSITYFORPATTERNSINTHEVISUALENVIRONMENTOFADEVELOPINGCHILDISACKNOWLEDGEDBYCHILDPSYCHOLOGISTSASBEINGHIGHLYINSTRUMENTALONESPECIFICINSTANCEOFTRADITIONALMATERIALCULTURE,ORIENTALCARPETS,REPRESENTASEVERALMILLENNIAOLDDISCIPLINEOFCREATINGANDREPRODUCINGVISUALPATTERNSACLOSELINKEXISTSBETWEENCARPETDESIGNSANDMATHEMATICALRULESFORORGANIZINGCOMPLEXITYASECONDEXAMPLE,FLOORPAVEMENTSINWESTERNARCHITECTURE,ISNOWAPPRECIATEDASBEINGAREPOSITORYHENCE,ATYPEOFTEXTBOOKFORITSTIMEOFMATHEMATICALINFORMATIONALEXANDRINEPATTERNSASINHERITEDARCHITECTURALSOLUTIONSANEFFORTTODEFINEPATTERNSINSOLUTIONSPACEWASMADEBYCHRISTOPHERALEXANDERANDHISASSOCIATES,BYCOLLECTINGARCHITECTURALANDURBANSOLUTIONSINTOTHEPATTERNLANGUAGETHESEDISTILLTIMELESSARCHETYPESSUCHASTHENEEDFORLIGHTFROMTWOSIDESOFAROOMAWELLDEFINEDENTRANCEINTERACTIONOFFOOTPATHSANDCARROADSHIERARCHYOFPRIVACYINTHEDIFFERENTROOMSOFAHOUSE,ETCTHEVALUEOFALEXANDERSPATTERNLANGUAGEISTHATITISNOTABOUTSPECIFICBUILDINGTYPES,BUTABOUTBUILDINGBLOCKSTHATCANBECOMBINEDINANINFINITENUMBEROFWAYSTHISIMPLIESAMOREMATHEMATICAL,COMBINATORICAPPROACHTODESIGNINGENERALUNFORTUNATELY,THISBOOKISNOTYETUSEDFORAREQUIREDCOURSEINARCHITECTURESCHOOLSALEXANDRINEPATTERNSREPRESENTSOLUTIONSREPEATEDINTIMEANDSPACE,ANDARETHUSAKINTOVISUALPATTERNSTRANSPOSEDINTOOTHERDIMENSIONSEVERYSERIOUSDISCIPLINECOLLECTSDISCOVEREDREGULARITIESINTOACORPUSOFSOLUTIONSTHATFORMSITSFOUNDATIONSCIENCEANDASARESULT,MANKINDHASADVANCEDBYCATALOGUINGREGULARITIESOBSERVEDINNATURALPROCESSES,TOCREATEDIFFERENTSUBJECTSOFORDEREDKNOWLEDGETHEELIMINATIONOFVISUALPATTERNS,ASDISCUSSEDLATER,CREATESAMINDSETTHATVALUESONLYUNIQUE,IRREPRODUCIBLECASESTHATHASTHECONSEQUENCEOFELIMINATINGALLPATTERNS,VISUALONESASWELLASTHOSEOCCURRINGINSOLUTIONSPACEFORTUNATELY,THESTRUCTURALSOLUTIONSTHATARCHITECTSDEPENDUPONREMAINPARTOFENGINEERING,WHICHPRESERVESITSACCUMULATEDKNOWLEDGEFORREUSEBASICLAWSFORGENERATINGCOHERENTBUILDINGSFOLLOWALEXANDERSMORERECENTWORKSUCCESSFULBUILDINGSOBEYTHESAMESYSTEMLAWSASACOMPLEXORGANISMANDANEFFICIENTCOMPUTERPROGRAMTHISAUTHORSTHEORETICALRESULTS,WHICHSUPPORTTHEEFFORTSOFALEXANDER,MAYEVENTUALLYBECOMEPARTOFACOREBODYOFARCHITECTURALKNOWLEDGETHEDESIGNOFCOMMONBUILDINGSISALREADYBEINGTAKENOVERBYTHEUSERSTHEMSELVESINTHECASEOFRESIDENTIALBUILDINGS,ORBYTHECONTRACTORSOFCOMMERCIALBUILDINGSBUILDERSHAVEDEVELOPEDTHEIROWNREPERTOIREOFUSUALLYVERYPOORARCHITECTURALPATTERNS,MOTIVATEDBYTHEDESIRETOMINIMIZECOSTANDSTANDARDIZECOMPONENTSRATHERTHANTOOPTIMIZEUSABILITYARCHITECTSINCREASINGLYDESIGNONLY“SHOWCASE”BUILDINGS,WHICHAREFEATUREDINTHEARCHITECTURALMAGAZINES,BUTREPRESENTAVANISHINGPERCENTAGEOFWHATISACTUALLYBUILTTODAYARCHITECTURALEDUCATIONTENDSTOFOCUSONTRYINGTODEVELOP“CREATIVITY”ASTUDENTISURGEDTOINVENTNEWDESIGNSWITHTHESEVERECONSTRAINTNOTTOBEINFLUENCEDBYANYTHINGFROMTHEPASTBUTISNOTTAUGHTHOWTOVERIFYIFTHEYARESOLUTIONSTHISAPPROACHIGNORESANDSUPPRESSESPATTERNSINSOLUTIONSPACECONTEMPORARYARCHITECTURALTHEORYCANONLYVALIDATEDESIGNSBYHOWCLOSELYTHEYCONFORMTOSOMEARBITRARYSTYLISTICDICTATETHEONLYWAYTOAVOIDCOMINGBACKTOTRADITIONALARCHITECTURALPATTERNSWHICHWORKSOWELLISTOBLOCKTHEDEDUCTIVEPROCESSTHATRELATESANEFFECTWITHITSCAUSEBYDELIBERATELYIGNORINGTHECONSEQUENCESOFDESIGNDECISIONS,ARCHITECTURALANDURBANMISTAKESAREREPEATEDOVERANDOVERAGAIN,WITHTHESAMEDISASTROUSCONSEQUENCESEACHTIMEMATHEMATICSANDARCHITECTUREHISTORICALLY,ARCHITECTUREWASPARTOFMATHEMATICS,ANDINMANYPERIODSOFTHEPAST,THETWODISCIPLINESWEREINDISTINGUISHABLEINTHEANCIENTWORLD,MATHEMATICIANSWEREARCHITECTSWHOSECONSTRUCTIONSTHEPYRAMIDS,ZIGGURATS,TEMPLES,STADIA,ANDIRRIGATIONPROJECTSWEMARVELATTODAYINCLASSICALGREECEANDANCIENTROME,ARCHITECTSWEREREQUIREDTOALSOBEMATHEMATICIANSWHENTHEBYZANTINEEMPERORJUSTINIANWANTEDANARCHITECTTOBUILDTHEHAGIASOPHIAASABUILDINGTHATSURPASSEDEVERYTHINGEVERBUILTBEFORE,HETURNEDTOTWOPROFESSORSOFMATHEMATICSGEOMETERS,ISIDOROSANDANTHEMIOS,TODOTHEJOBTHISTRADITIONCONTINUEDINTOTHEISLAMICCIVILIZATIONISLAMICARCHITECTSCREATEDAWEALTHOFTWODIMENSIONALTILINGPATTERNSCENTURIESBEFOREWESTERNMATHEMATICIANSGAVEACOMPLETECLASSIFICATIONMEDIEVALMASONSHADASTRONGGRASPOFGEOMETRY,WHICHENABLEDTHEMTOCONSTRUCTTHEGREATCATHEDRALSACCORDINGTOMATHEMATICALPRINCIPLESITISNOTENTIRELYFAIRTODISMISSTHEMIDDLEAGESASBEINGWITHOUTMATHEMATICSTHEIRMATHEMATICSISBUILTINTOSTRUCTURESINSTEADOFBEINGWRITTENDOWNTHEREGRETTABLELOSSOFLITERACYDURINGTHOSECENTURIESWASMOSTEMPHATICALLYNOTACCOMPANIEDBYACOMMENSURATELOSSOFVISUALORARCHITECTURALPATTERNS,BECAUSEPATTERNSASOPPOSEDTOTHEABSTRACTREPRESENTATIONSOFAWRITTENSCRIPTREFLECTPROCESSESTHATAREINHERENTINTHEHUMANMINDWEAREINTERESTEDHEREINWHATHAPPENEDINTHETWENTIETHCENTURYTHEAUSTRIANARCHITECTADOLFLOOSBANNEDORNAMENTFROMARCHITECTUREIN1908WITH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VELSOFSCALEINNOVATIVEARCHITECTSMAYWISHTOGENERATEFRACTALRHYTHMSINORDERTOEXPLORECOMPLEXITYATTHEINTERFACEBETWEENORGANIZATIONANDCHAOS,ANDTOLINKITTOMUSICALRHYTHMSTHECOMPLEXITYOFSUCHPATTERNSWILLNECESSARILYDEPARTFROMSIMPLEREPETITIONINTHISAUTHORSOPINION,PATTERNSAREESSENTIALTOARCHITECTURALFORMMATHEMATICALCHAOSISTHESTUDYOFHIDDENPATTERNSINSYSTEMSTHATAREONLYAPPARENTLYCHAOTICTHEREISNOCHANGEINTHEFUNDAMENTALAIMOFMATHEMATICSWHICHISTODISCOVERPATTERNSINGOINGFROMNEWTONIANTOCHAOTICMODELSDESPITETHEENORMOUSPOSSIBILITIESOFAPPLYINGFRACTALSTOBUILTFORMSINANINNOVATIVEMANNER,DECONSTRUCTIVISTBUILDINGSHAVEONLYLEDTORANDOMNESSBUILTEXAMPLESJUMPFROMONEEXTREMETOANOTHERFROMTHEEMPTYMODERNISTMODELSTRAIGHTINTORANDOMFORMSANYDECORATIONAPPEARINGONCONTEMPORARYBUILDINGSISEITHERSOMINIMALASTOBEHARDLYVISIBLE,ORITISINTENTIONALLYDISARRAYEDANDBROKENSOTHATITISINCOHERENTCONCLUSIONDOESARCHITECTUREINFLUENCEOURCIVILIZATIONQUITEDEFINITELYTOEVALUATETHISEFFECTINEARNEST,WESHOULDBEINVESTIGATINGTHERELATIONSHIPBETWEENARCHITECTUREANDMATHEMATICSINTHEPAST,THECONNECTIONWASTWOWAY,REINFORCING,ANDMUTUALLYBENEFICIALTHEREAREINDICATIONSTHATARCHITECTUREHASSEPARATEDITSELFFROMMATHEMATICSINAKEYASPECT,FIRSTUNDERTHEINFLUENCEOFTHEOVERLYSIMPLISTIC,POLITICALLYDRIVENMODERNISTSOCIALIDEOLOGY,ANDNOWEVENFURTHERBYFOLLOWINGTHEANTISCIENTIFICDECONSTRUCTIVISTPHILOSOPHERSASARCHITECTUREISUBIQUITOUS,THEIDEASITEMBODIESINFLUENCEOUREVERYDAYLIFEANDWAYOFTHINKINGTOAREMARKABLEEXTENTWECANNOTAFFORDTOIGNORETHISINFLUENCEONOURCULTURE,ESPECIALLYBECAUSEOFTHESTRONGPOSSIBILITYTHATITMAYALREADYHAVEHADNEGATIVECONSEQUENCESWEHAVETRAINEDPEOPLETOREJECTMATHEMATICALINFORMATIONINTHEBUILTENVIRONMENTTHISREVERSALOFMATHEMATICALVALUESNOTONLYAPPLIESTOBUILDINGSANDURBANREGIONSITDEFINESAPERVASIVEAESTHETIC译文结构形态数学模数尼克斯扎林格尔斯认定建筑架构在人的智力发展上的重要性，分析了20世纪建筑装饰和建筑模式方面人们毕生的研究态度。介绍在20世纪，传统的建筑和数学之间的关系发生了实质性的改变。建筑学系的学生不在要求需要有数学背景。然而着自身就有问题，更加严重的问题在于当代建筑和设计可能促进了一个反数学模数的心态。现代主义运动抑制了模式架构，这对整个社会具有深远的影响。数学是一门科学的模式，模式的存在与否是由于环境的影响如何能够让一个人轻松的理解依赖于模式的概念。从20世纪的建筑设计中消除了影响我们处理能力和解释模式。数学，它所承载的只是模式，展现出来，我们的同时代的，明确的反模数架构的世界观。数学老师叹息在现实当中越来越少数学的趣味了，这也导致学生的数学能力有所下降。这种鲜明的对比，反驳了一个我们正在见证这个时代的技术进步。这里提出了一个可能导致数学在我们社会中总体下降的环境因素。这一理论源于作者对不同时期和地区的建筑风格理论基础的兴趣。最近表明了传统架构服从于数学规则的本质。这些规则引领的建筑，他们的各种形式，都囊括在或大或小的线性数学性能和信息中。二十世纪创造了新奇的体系结构，并且通过消除这些性能，结束了过去的体系结构。在本文中，“模式”这个词在某些维数代表一种规律。最简单的例子是在重复的视觉单位下令线性或者旋转无题对称。在扩展维度的模式中也存在类似的形式出现在不同程度上有所放大。集合相似性定义的层次结构尺度上与自身相似时，就创造了一个自身相似的分型。模式还延伸到解空间的概念，在解决类似的问题上，是与自定义相关的一个模板，每一次的重复，其实都是在变化中解决同一个问题。无论是在重复单元生成二维花砖设计，还是重用一类微分方程的一般解基础的想法是最重要的信息。环境心理学家知道，环境不仅影响我们的思维方式，而且影响我们的智力发展，安排好的数学信息环境对我们产生积极的情绪反应。如果我们生长在一个隐式的反数学的环境之中，不利于影响我们的兴趣用在数学上，甚至我们没有掌握数学概念的能力。如果一个人一生都生活在一个缺失模式，甚至是破坏至关重要的能力的世界里，是否会削弱其形成模式的能力呢尽管这个问题的最终答案是不知道，但是对人的影响是惊人的。虽然有很强烈的声音在批评当代建筑很大程度上缺少人类的品质所在。这不是涉及到饿偏好或者是风格有关，担忧的是人类思维训练的功能。科学的模式数学是一个科学的模式。是大脑感知之间的互相联系与概念和想法相互联系在一起。能够创建模式是我们的神经发育的结果在应对我们所在的环境。数学理论解释出现在命令，逻辑结构之间的关系模式。心里模式模仿自然界以及人为的模式，这是人类如何进化，能做数学的原因。人类生成模式的一些基本的内在需要，外化连接结构生成心里通过四维的过程，这就解释了无处不在的视觉模式在传统的人类艺术和建筑中。模式对人类的智力发展也是至关重要的。日常的活动是围绕自然的节奏，年度事件成为了社会的不动点，此外，这些经常联系社会的新型科学研究周期性季节等自然现象及其影响。数学本身需要在基础上产生记录，空间和时