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Ourworldismadeupofpatternsandsequences.They'reallaroundus.Daybecomesnight.Animalstravelacrosstheearthinever-changingformations.Landscapesareconstantlyaltering.Oneofthereasonsmathematicsbeganwasbecauseweneededtofindawayofmakingsenseofthesenaturalpatterns.Themostbasicconceptsofmaths-spaceandquantityarehard-wiredintoourbrains.Evenanimalshaveasenseofdistanceandnumber,assessingwhentheirpackisoutnumbered,andwhethertofightorfly,calculatingwhethertheirpreyiswithinstrikingdistance.Understandingmathsisthedifferencebetweenlifeanddeath.Butitwasmanwhotookthesebasicconceptsandstartedtobuilduponthesefoundations.Atsomepoint,humansstartedtospotpatterns,tomakeconnections,tocountandtoordertheworldaroundthem.Withthis,awholenewmathematicaluniversebegantoemerge.我们的世界由模式和序列组成，他们就在我们身边，白昼变成黑夜，动物迁徙的路线年年不变，地貌不断改变，数学开始的原因之一，由于我们需要找到一个方法，搞清自然模式的含意，数学中最基本的概念-空间和数量是我们大脑固有的属性。即使动物，也有一些距离和数感，当寡不敌众时，评估战斗还是逃走，计算猎物是否在攻击距离之内。理解数学决定生死存亡，但却是人学习了这些基本概念，并开始建立基本原理，某种程度上，人类开始认出模式，建立联系，计算和建立周围世界秩序。至此，一个全新的数学宇宙开始出现。ThisistheRiverNile.It'sbeenthelifelineofEgyptformillennia.it'swheresomeofthefirstsignsofmathematicsasweknowittodayemerged.Peopleabandonednomadiclifeandbegansettlinghereasearlyas6000BC.Theconditionswereperfectforfarming.ThemostimportanteventforEgyptianagricultureeachyearwasthefloodingoftheNile.Sothiswasusedasamarkertostarteachnewyear.Egyptiansdidrecordwhatwasgoingonoverperiodsoftime,soinordertoestablishacalendarlikethis,youneedtocounthowmanydays,forexample,happenedin-betweenlunarphases,orhowmanydayshappenedin-betweentwofloodingsoftheNile.Recordingthepatternsfortheseasonswasessential,notonlytotheirmanagementoftheland,butalsotheirreligion.TheancientEgyptianswhosettledontheNilebanksbelieveditwastherivergod,Hapy,whofloodedtherivereachyear.Andinreturnforthelife-givingwater,thecitizensofferedaportionoftheyieldasathanksgiving.Assettlementsgrewlarger,itbecamenecessarytofindwaystoadministerthem.Areasoflandneededtobecalculated,cropyieldspredicted,taxeschargedandcollated.Inshort,peopleneededtocountandmeasure.这里是尼罗河，一千年来，它一直是埃及人的生命源泉，并且是是数学发祥地之一，早在公元前6000年左右，人们就放弃了游牧生活，开始定居于此，肥沃的土壤很适合农耕，每年埃及农业最关心的事件莫过于尼罗河的定期泛滥，这被作为新的一年开始的标志，埃及人记录了事情发生的周期，为了建立这样的日历，你需要计算天数，例如，月相发生的间隔，尼罗河水定期泛滥之间相隔的确切天数，根据天象确定季节成了十分重要的工作，这有利于他们管理国家和教会的事务，在尼罗河两岸，古埃及人定居下来，相信河神--哈比神(Hapy)，掌管着每年尼罗河洪水的泛滥，人们进献一部分农业收益，藉以回报神王的赐福，当定居点日益变大，寻找管理的办法变的很有必要，需要计算土地的面积，农作物的产量预测，征收和管理税收。总之，人民需要计算和测量。TheEgyptiansusedtheirbodiestomeasuretheworld,andit'showtheirunitsofmeasurementsevolved.Apalmwasthewidthofahand,acubitanarmlengthfromelbowtofingertips.Landcubits,stripsoflandmeasuringacubitby100,wereusedbythepharaoh'ssurveyorstocalculateareas.There'saverystronglinkbetweenbureaucracyandthedevelopmentofmathematicsinancientEgypt.Andwecanseethislinkrightfromthebeginning,fromtheinventionofthenumbersystem,throughoutEgyptianhistory,really.FortheOldKingdom,theonlyevidencewehavearemetrologicalsystems,thatismeasurementsforareas,forlength.Thispointstoabureaucraticneedtodevelopsuchthings.Itwasvitaltoknowtheareaofafarmer'slandsohecouldbetaxedaccordingly.OriftheNilerobbedhimofpartofhisland,sohecouldrequestarebate.Itmeantthatthepharaoh'ssurveyorswereoftencalculatingtheareaofirregularparcelsofland.Itwastheneedtosolvesuchpracticalproblemsthatmadethemtheearliestmathematicalinnovators.TheEgyptiansneededsomewaytorecordtheresultsoftheircalculations.AmongstallthehieroglyphsthatcoverthetouristsouvenirsscatteredaroundCairo,TheEgyptianswereusingadecimalsystem,motivatedbythe10fingersonourhands.Thesignforonewasastroke,10,aheelbone,100,acoilofrope,and1,000,aLotusplant.HowmuchisthisT-shirt?Er,25.25!Yes!Sothatwouldbe2kneebonesand5strokes.Soyou'renotgonnachargemeanythinguphere?Here,onemillion!Onemillion?MyGod!Thisonemillion.Onemillion,yeah,that'sprettybig!Thehieroglyphsarebeautiful,buttheEgyptiannumbersystemwasfundamentallyflawed.Theyhadnoconceptofaplacevalue,soonestrokecouldonlyrepresentoneunit,not100or1,000.Althoughyoucanwriteamillionwithjustonecharacter,ratherthantheseventhatweuse,ifyouwanttowriteamillionminusone,thenthepooroldEgyptianscribehasgottowriteninestrokes,nineheelbones,ninecoilsofrope,andsoon,atotalof54characters.Despitethedrawbackofthisnumbersystem,theEgyptianswerebrilliantproblemsolvers.Weknowthisbecauseofthefewrecordsthathavesurvived.TheEgyptianscribesusedsheetsofpapyrustorecordtheirmathematicaldiscoveries.Thisdelicatematerialmadefromreedsdecayedovertimeandmanysecretsperishedwithit.Butthere'sonerevealingdocumentthathassurvived.TheRhindMathematicalPapyrusisthemostimportantdocumentwehavetodayforEgyptianmathematics.WegetagoodoverviewofwhattypesofproblemstheEgyptianswouldhavedealtwithintheirmathematics.Wealsogetexplicitlystatedhowmultiplicationsanddivisionswerecarriedout.Thepapyrishowhowtomultiplytwolargenumberstogether.Buttoillustratethemethod,let'staketwosmallernumbers.Let'sdothreetimessix.Thescribewouldtakethefirstnumber,three,andputitinonecolumn.Inthesecondcolumn,hewouldplacethenumberone.Thenhewoulddoublethenumbersineachcolumn,sothreebecomessixandsixwouldbecome12.Andtheninthesecondcolumn,onewouldbecometwo,andtwobecomesfour.No