2004_HiMCM_Outstanding_Papers

Number88ISSN0889-5392Spring/Summer2005CONSORTIUMTheNewsletteroftheConsortiumforMathematicsandItsApplicationsCONSORTIUMTheNewsletteroftheConsortiumforMathematicsandItsApplicationsPage2FromtheEditor’sDesk:LookingAheadPage3MathToday:MathematicsHelpsSortOutOurGenesPage6Geometer’sCorner:WhatisaRegularPolygon?Page11Henry’sNotes:DrawingaTrianglePage13Everybody’sProblems:TheGasStationProblemPull-OutSection:WakeUpandSmelltheCoffeeHiMCMOutstandingPapersPage19HistoricalNotes:AMathematicalParadise(TheWorldofInfinity)PartIWelcometoour7thannualHiMCMissue!WehopethatourreaderswillenjoyreadingtheworkoftheyoungmodelerswhosepapersachievedNationalOutstandingstatus—andweareconfidentthatourreaderswillenjoythelatestcontributionsfromourtalentedpanelofmodeler-educators.ThereareseveraldevelopingCOMAPprojectsthatwewanttocalltoourreaders’attention.TheTechMAPproject,whichdevelopedmodulesintechnicalapplicationsforthehighschoollevel,reachedcompletionin2004.Eachmoduleiscomprisedoftwoorthreelessonsbuiltaroundactivitiesandexercises.ExamplesoftitlesareOntheBotpath,whichtreatscoordinategeometryinaroboticscontext,andOvertheLimit,whichtreatsinequalitiesderivedfromlimitstatementsinbuildingcodes.All22modulesareavailableinPDFformatonasingleCD-ROM.Additionalinformation,includingadownloadablesample,canbefoundat—it’squiteabargain!❏2CONSORTIUMFromtheEditor’sDesk1-800-772-6627TOLLFREETOORDER1-800-772-6627CONSORTIUMConsortiumisaquarterlynewsletteroftheConsortiumforMathematicsandItsApplications,Inc.(COMAP),butitisalsomuchmore.EachissuebringslessonsandideasthatdemonstratewhatCOMAPbelievesisanexcitingwaytoteachandlearnmathematics.ThecenterPull-OutSectionoftheissueisaclassroomlessonreadytobephotocopiedanddistributedtoyourstudents.IfyouareinterestedinreceivingConsortium,call1-800-772-6627forinformationaboutCOMAPmembership.ThismaterialisdevelopedbyCOMAP,Inc.Anyfindings,conclusions,orrecommendationsexpressedarethoseoftheauthorsanddonotnecessarilyreflecttheviewsofCOMAP,thecooperatingsocieties,ortheeditorialboard.SubmissionsshouldbesenttoConsortiumEditor,COMAP,Inc.ortotheindividualdepartmenteditors.(COMAP),Inc.,Suite210,57BedfordStreet,Lexington,MA02420.[phone].:GaryFroelichDepartmentEditorsGeometer’sCorner:JonathanChoateHiMCMNotes:WilliamP.FoxHistoricalNotes:RichardL.FrancisEverybody’sProblems:DotDoyleDanTeagueMathToday:PaulKehleJosephMalkevitchHenry’sNotes:HenryPollakHiMAPPull-OutSection:FloydVestMarshaDavisPatTaylorRosalieDanceJamesSandefurGARYFROELICHLOOKINGAHEADIntroductionOneareaofintensecontemporaryactivityinappliedmathematicsismathematicalbiology.Advancesinthestudyofmanybranchesofbiologyaregeneratingbothbetterunderstandingsoflifeandnewchallengingproblems.Someoftheseproblemshaveadefinitequantitativeorgeometricalcharacter,andbiologistshavesuccessfullycollaboratedwithmathematiciansinapplyingmathematicsinsolvingthem.Thiscollaborationhasbeensofruitfulthattheinterdisciplinaryfieldofmathematicalbiology,andtherelatedfieldofbioinformaticsaregrowingquickly.Inresponsetothevastquantitiesofgeneticinformationbeingmadeavailablebygenomesequencingprojects,workwithpatternsintheformofsequencesofnucleotides(adenine,cytosine,guanine,andthyminethatareusuallyabbreviatedwiththecapitallettersA,C,G,andT)thatmakeupstrandsofDNAisahighpriority.Workingwithnon-numericalpatternsmightnotseemasmathematicaltomanystudentsasdoesworkwithnumbersorgeometricshapes,butmathematicsisoftendefinedinpartasthesearchfor,andstudyofpatterns—nomatterwheretheyarefound.Inthiscolumn,we’llsurveysomeofthemostchallengingproblemsarisingfromworkwithnucleotidesequences,forexample:GATACAATCGG.SurveyofMathematicalBiologyTosituatethecontemporarymathematicsthatwewillseelat