Въведение
Althoughwehaveenteredtheageofelectroniccomputers,lookingattheancientChineseabacus,wecan’thelpbutadmirethegreatwisdomofourancestors.Thegeneralabacusismostlymadeofwood(orplasticproducts).Astringofequalnumbersofabacusbeadsarrangedinarectangularwoodenframeiscalledafile.Abeamdividesthebeadsintoupperandlowerparts.Eachabacusintheupperhalfrepresents5,Eachbeadinthelowerhalfrepresents1.Fromrighttoleft,eachbeadrepresentsone,ten,hundred,thousand,andtenthousanddigitsindecimal.Withtheadditionofsoftware-asetofcalculationformulasforfingerdialingrules,variouscomplexcalculationscanbesolved,andevenmultipleprescriptionscanbemade.TheabacusisthepredecessorofmoderncomputersandthesymbolofancientChinesecomputingtechnology.
Theabacus shape system
Thenewshapeoftheabacusisarectanglewithawoodenframeonthecircumferenceandastraightcolumninside,commonlyknownas"file".Generallyfrom9to15gears,thebeamisusedinthemiddleofthegear,twobeadsonthebeam,eachbeadcountsfive,andfivebeadsunderthebeam,eachbeadcountsone.Afterpositioning,thebeadscanbeusedforcalculation,whichcanbeadded,subtracted,multipliedanddivided.Andotheralgorithms.
Theexistingabacushasdifferentshapesandmaterials.Thegeneralabacusismostlymadeofwood(orplasticproducts).Theabacusconsistsofaseriesofabacusbeadsarrangedinarectangularwoodenframeforseveraldays.Abeamdividesthebeadsintoupperandlowerparts,andtheabacusrunsthroughastraightcolumn.Commonlyknownas"gear",itisgenerally9gears,11gearsor13gears.Inthemiddleofthefile,thereisabeam,with1beadonthebeam,andthisbeadis5;andthereare5beadsunderthebeam,andeachbeadis1.
Основни категории
ItisworthnotingthatthetermabacusdoesnotspecificallyrefertoChineseabacus.Judgingfromtheexistingliterature,manyancientcivilizationshadtheirowncalculationtoolssimilartotheabacus.VarioustypesofabacusinancientandmodernChinaandabroadcanberoughlydividedintothreecategories:sandtabletype,abacustype,andabacustype.
Thesandtableiscoveredwithfinesandonthetabletop,stoneslab,etc.Peopleusewoodenstickstowrite,drawpicturesandcalculateonthefinesand.Later,insteadoflayingsand,severalparallellineswerecarvedontheboard,andsmallstones(called"operators")wereplacedontheboardtocountandcalculate.Thisistheabacus.Aone-meter-longmarbleabacusfoundinSalamis,Greece,inthemiddleofthe19thcentury,istheancientGreekabacus,anditisnowintheAthensMuseum.TheabacushasalwaysbeenanimportantcalculationtoolintheMiddleAgesinEurope,buttherearebigdifferencesinform.Thelinesarestraightandhorizontal,theoperatorsareroundorflat,andsometimestheyareconical(similartocheckers),andtheyarealsomarkedwithnumbers.WearingabacusreferstoChineseabacus,JapaneseabacusandRussianabacus.TheJapaneseabacusiscalled"TenLupan".ThedifferencefromtheChineseabacusisthatthelongitudinalsectionoftheabacusisnotanoblatebutarhombus,withasmallersizeandalargernumberofgrades.TheRussianabacushasanumberofcurvedwoodenstripsinlaidhorizontallyinawoodenframe,eachwearing10abacusbeads.Amongthevariousancientabacusintheworld,theChineseabacusisthemostadvancedabacustool.
Произходът на развитието
TheabacusisatraditionalChinesecalculationtool.IthasgraduallyevolvedfromacalculationthathasbeencommonlyusedasearlyastheSpringandAutumnPeriod.ItisnotonlyanancientChineseitemAnimportantinvention,anditisacalculationtoolthatwaswidelyusedbypeoplebeforetheappearanceofArabicnumerals.Chinaisthehometownoftheabacus.Today,whencomputersarewidelyused,theancientabacushasnotbeenabandoned,butisstillfavoredbymanypeoplebecauseofitsflexibilityandaccuracy.Therefore,peopleoftencomparetheinventionoftheabacuswiththefourgreatinventionsofancientChina,andbelievethattheabacusisalsoamajorcontributionoftheChinesenationtomankind.However,whendidChinastarttohaveanabacus?SincetheQingDynasty,manymathematicianshavestudiedthisissue,andJapanesescholarshavealsoputalotofenergyintoit.However,duetothelackofsufficientevidence,theissueoftheoriginoftheabacusisstilldividedtoday.
TheQingDynastymathematicianMeiQizhaoandothersbelievethattheabacusoriginatedinmycountryduringtheEasternHanandSouthernandNorthernDynasties.ThebasisisthattheEasternHanmathematicianXuYueoncewrotea"SuccessofMathematics",inwhich14kindsofalgorithmsaredescribed,the13thiscalled"AbacusCalculation",andsaid:"Abacuscalculation,controlbeltfouro'clock,longitudeandlatitudethreetalents."Later,themathematicianZhenLuanoftheNorthernZhouDynastymadeacommentonthispassage:"Thestereotypeisthreepoints,theupperandlowertwopointsareusedtostopthebead,andthemiddlepointisusedtodeterminetheposition.Eachhasfivebeads,andtheupperoneandthelowerfourbeadsaredifferentincolor.,Thebeadsofdifferentcolorsonthetoparefive,fourbeadsonthebottom,andonebeadeach.Tothenextfourbeadsareled,sothe'cloudbeltfouro'clock'.Itsbeadsswiminthethreedirections,sothecloud'sthreelatitudesandlongitudesarealso"Thesewordsareconsideredtobetheearliestrecordsofabacusinourcountry.However,somescholarsinmoderntimesbelievethattheabacusdescribedin"ShushuJiyi"isatbestacountingtoolorasimplearithmeticboardthatcanonlybeusedforadditionandsubtraction,whichisnotthesameastheabacusthatappearedlater.
QianDating,ascholarintheQingDynasty,andothersbelievedthattheabacusappearedinthemiddleoftheYuanDynastyandwaswidelyusedbytheendoftheYuanDynastyandthebeginningoftheMingDynasty.ThebasisisthatTaoZongyioftheYuanDynastyquotedtheproverbofthetimein"TheWellBeads"inthe29thvolumeof"NancunShuoGenglu":Dialautomatically;forawhile,theJapaneseabacusbeads,andthedialwillmove;afteralongtime,theBuddhawilltopthebeads,andthespeechwillremaincalmthroughouttheday,evenifdialed,itwillnotmove."Latergenerationscalledthis"threebeaddrama."Comparingveteranservantsandmaidstoanabacusbead,flickingandflicking,thisshowsthattheabacuswasverypopularamongthepeopleatthattime.AttheendoftheSongDynastyandthebeginningoftheYuanDynasty,LiuYinalsohadafive-characterquatraintitled"Abacus"inthebook"Mr.Howhardisit?”ThisisalsoastrongproofthattheabacusappearedintheYuanDynasty.Inaddition,inthesection"PangJutuMisplacedNextLifeDebts"in"YuanquXuan",itwasalsomentionedthat"Gototheabacusandsetasidemyage".IntheMingDynasty,inthe"LubanWoodenScriptures"compiledduringtheYongleperiod,therewerealreadyspecificationsanddimensionsformanufacturingabacus:"Abacustype:onefootandtwoincheslong,fourinchesandtwocentsbig.Theframeissixminutesthick,nineminutesbig,...Onlinetwosons,oneinchonepoint;offlinefivesons,threeinchonepoint.Lengthandsize,youcandoitforyou.”Inaddition,XuXinlu's"AbacusAlgorithm",ChengDawei's"DirectPointAlgorithm",ThereisnodoubtthattheabacushasbeenwidelyusedintheMingDynasty,suchasKeShangqian's"TongrailofMathematics"andZhuZaiyu's"NewTheoryofArithmetic".
Withthediscoveryofnewhistoricalmaterials,someexpertsbelievethattheabacusshouldoriginateintheTangDynastyandbepopularintheSongDynasty.ThebasisisthatthereisamedicineshopinthefamouspaintingoftheSongDynasty"ARiverontheQingmingFestival",andthereisanabacusonthefrontcounter.TheabacusexpertsinChinaandJapanhavemagnifiedthepictureandconfirmedthattheobjectsinthepaintingareusedinmoderntimes.Theabacusissimilartothestringabacus.Moreover,in1921,awoodenabacusfromtheoldhouseoftheSongpeoplewasunearthedinJuluCounty,Hebei,mycountry.Althoughithasbeensubmergedbywaterandsoilfor800years,itcanstillbeseenintheshapeofadrumwithaholeinthemiddle.Theabacusisthesame.
Inaddition,thosewhoholdthisviewalsobelievethatthereisanine-fileabacusinthetextbook"NewCompilationofRelativeFourCharacters"intheearlyYuanDynasty.Itcanbeseenthattheabacuswasalreadyanordinarythingatthattime,anditsappearancecanbepusheduptotheSongDynastyatleast.Moreover,LiuYinwhowrotethepoem"Abacus"wasalsoapersonfromthelateSongDynastyandtheearlyYuanDynasty.HispoemsarenotsomuchdescribingthingsintheYuanDynastyastheyreflectthingsintheSongDynastymoreaccurately.Similarly,TaoZongyi’s"ThreeBeadsinDrama"hastheabacusbeadsintheproverbsoftheYuanpeople,whichalsoreflectsthat"thelawprevailedintheSongDynasty".
ButifitisbelievedthattheabacusoriginatedintheSongDynasty,thereseemstobedoubt.Becauseintermsofformandsystem,theabacusoftheSongDynastyhasbeenrelativelymature,anditdoesnothavetheclumsyorroughnessthatnewthingsoftenhave.Therefore,manyarithmeticscholarsbelievethatthebirthoftheabacuscanbepushedbacktotheTangDynasty.BecauseofthecontinuouswarsintheFiveDynastiesandTenKingdomsperiodbeforetheSongDynasty,thedevelopmentofscienceandtechnologyculturewasrelativelyslow,anditislesslikelythattheabacuswasbornatthistime.TheTangDynastywasaprosperouserainChinesehistory,andtheeconomyandculturewererelativelydeveloped,andnewcalculationtoolswereneeded.Therefore,thecalculationsusedin2000weretransformedintoabacuscalculations.ItisverylikelythattheabacuswasinventedintheTangDynasty.
Мантра
AdditionМантра
Explanation:Abacusadditionmantraisatextsummaryusedtoguidethemovementofdialingbeadsandperformcalculations.Inordertohaveaclearerunderstandingofthecontentoftheformula,firstbrieflydescribethemeaningoftherelevanttermsintheadditionformulaasfollows:
„Шанг“ означава да наберете мънистото върху гредата.
„Надолу“ се отнася за преместване на горната перла към гредата.
„Върви“ означава да преместиш мънистата на абакус от лъча настрани.
„Напред“ означава добавяне на номер към предната позиция (първата предавка отляво).
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobeadded,andthelastwordindicatesthenumbertobemovedbythebead.
Формули за изваждане
Explanation:Thereare26sentencesintheabacussubtractionformulas,whicharedividedintofourtypes:directsubtraction,breakingfivesubtraction,retreatingtensubtractionandretreatingtenreplenishingfivesubtraction.Themeaningoftherelevanttermsinthesubtractionformula:
"Up"referstodialingdownthepearlandrelyingonthebeam.
„Надолу“ означава да преместите долното перло отстрани на гредата.
"Go"meanstomovetheabacusbeadsthatleanonthebeamandmovetothesideofthebeam.
„Напред“ означава добавяне на номер към предната позиция (първата предавка отляво).
"Retreat"meanstodecrementthenumberfromthepreviousposition(thefirstgearfromtheleft).
"Return"meansthatthenumbershouldbeaddedtothedigitafterthefirstdigitisremoved.
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobesubtracted,andthenextwordindicatesthenumberofbeadstobemoved.
Формула за умножение
oneone01onetwo02onethree03onefour04onefive05onesix06oneseven07oneeight08onenine09
Twoone02twotwo04twothree06twofour08twofive10twosix12twoseven14twoeight16twonine18
threeone03threetwo06threethree09threefour12threefive15threeSix18threeseven21threeeight24threenine27
fourone04fourtwo08fourthree12fourfour16fourfive20foursix24fourseven28foureight32fournine36
Fiveone05fivetwo10fivethree15fivefour20fivefive25fivesix30fiveseven35fiveeight40fivenine45
6one06sixtwo12sixthree18sixfour24sixfive30sixsix36sixseven42sixeight48sixnine54
sevenone07seventwo14seventhree21sevenfour28sevenfive35sevensix42sevenseven49seveneight56sevennine63
Augustone08eighttwo16eightthree24eightfour32eightfive40eightsix48eightseven56eighteight64eightnine72
nineone09ninetwo18ninethree27ninefour36NineFive45NineSix54NineSeven63NineEight72NineNine81
Explanation:Eachsentenceofthemultiplicationformulaconsistsoffournumbers,thefirsttwoareChinesecharacters,andthelasttwoareArabicnumbers.Thefirstnumberreferstothemultiplier,thesecondnumberreferstothemultiplicand,andthethirdandfourthnumbersrefertotheproduct.
Inordertopreventthewrongtipfromaddingtheproductinthecalculation,theproductiscomposedoftwodigits.Eveniftheproducthasonlyonesignificantdigit,itmustbereadbyadding0beforetheproduct,suchas6x1,andtheformulaisreadasonesix06.
Девет формула за връщане
Едно връщане (разделяне на 1):въведетевсеки,въведетедванавсяка секунда,въведететривсекитри,въведетечетиривсеки четири,въведетепетвсекипет,Всекишествъведетешест,всекиседемвлезеседем,всекиосемвъведетеосем и всекидеветвлезедевет.
Tworeturn(divideby2):въведетевсеки две,въведетедвевсекичетири,въведететривсекившест,въведетечетиривсяки осем и добавете петнавсяки две.
Sangui(разделяне на3):въведетевсеки три,въведетедвевсекишест,въведететривсекинини,триеднотриповечеотедин,тридвамашестповечедве.
Четири връщане(разделяне на4):въведетевсеки четири,въведетедвевсекиосем,добаветепет след четиридве,четиримрежадве повечеотдве,четвъртитриседемповечеотдве.
Пет връщане (разделяне на 5): всеки пет въвежда едно, пет пъти прави две, пет пъти прави четири, пет пъти прави шест, пет пъти прави осем.
Sixreturn(divideby6):въведетевсекишест,въведетедвевсекидванадесет,добаветепетпришесттри,добаветечетирикогатошест,шестдветриповечеотдве,шестчетиришестповечеотчетири,Шест,пет,осем,повечеотдве.
Qigui(divideby7):въведетевсекиседем,въведетедвевсекичетиринадесет,добавететриподседем,добаветешестподседем,седем,три,четири,идве,седем,четири,пет,ипет,седемпетседемповечеотедин,седемшестосемповечеотчетири.
Баги (разделяне на 8): Всеки осем въвежда едно, осем четири и пет, осем добавя две, осем два добавя четири, осем три добавя шест, осем пет шест остават две, осем шест седем повече от четири, осем седем осем повече от шест.
Devetreturn(divideby9):everyneneentersone,neneaddone,devetnetwoaddtwo,ninethreeaddthree,ninefauraddfour,ninefiveaddfive,Addsixfordevetty-six,sevenfordevetty-sedem,andeightforninety-osem.
Обяснение: Деленето на една цифра се нарича „единично връщане“; деленето на делител на две или повече цифри се нарича „деление“. Първата цифра на делителя се нарича „gui“, а следващите цифри се наричат „деление“. Например, делението на делителя е 534, което се нарича „пет връщане на три на четири деление“, тоест използвайте формулата за връщане на петте 34, за да намерите частно на,
Свързани термини
Neutral:Whentheupperandlowerpartsofacertaingeararebothawayfromthebeam,itiscalledneutral.Agapmeansthatthereisnocountinthisposition,oritmeans0.
Emptyplate:Allgearsoftheabacusareempty,whichmeansthatthereisnocountinthewholeplate,whichiscalledanemptyplate.
Innerbeads:Theabacusbeadsthatcountbybeamsarecalledinnerbeads.
Outerbeads:Abacusbeadsthatdonotcountfromthebeamarecalledouterbeads.
Dialup: се отнася до спускането на мъниста срещу гредата.
Dialingdown:referstoputtingtheupperpearlagainstthebeam.
Pullingout:referstopullingtheupperorlowerbeadsawayfromthebeam.
Thisfile:referstothefilethatisabouttobedialedandcounted.
Предна предавка: отнася се за предишната предавка на този файл, наричана още лява предавка (позиция).
Задна предавка: отнася се за следващата предавка на този файл, наричана още дясна предавка (позиция).
Floatingbeads:Theabacusbeadsfloatinginthemiddleofthegearwithoutrelyingonthebeamstobetoolightwhenpullingthebeads.
Beads:Whendialingbeads,bringinoroutthebeadsthatshouldnotbedialedinoroutofthisfileorneighboringfiles.
Realbeads:Abacusbeadsthatrelyonbeamstorepresentpositivenumbers.
Virtualbead:alsocallednegativebead,referstothehangingbeadthatisdialedtoneitherthebeamnortheframe,indicatinganegativenumber.
Setthenumber:alsoteachthenumber,accordingtothecalculationrequirements,dialthenumberintotheabacustoprepareforthecalculation.
Позиция на предавката: Наричана още степен, отнася се за позицията на предавката.
Wronggear:Alsocalledmisalignment,itmeansthatthebeadisnotdialedintothegearthatshouldbedialedduringthecalculationprocess.
Interval:Itisalsocalledtheinterval,whichreferstothesecondgear(position)withonegearleftandright.Inintervalmultiplication,twonumbersaremultipliedtogether,andtheunitsplaceoftheproductisplacedontherighttwodigitsofthemultiplicand;inintervaldivision,thequotientoftheintervalreferstothefirsttwoleftdigitsofthedividend.
Carry:Itmeansthatafteraddinganumbertothisfile,itisgreaterthanorequalto10,anditmustbeincreasedby1tothepreviousposition,whichiscalledcarry.
Abdicate:Itmeansthatwhenthisfileissubtractedbyonenumber,thisfileisnotenough,andyoucansubtract1fromthepreviousone,whichiscalledabdication.
Първо място: Наричано още най-високото място, това означава, че първата ненулева цифра от многоцифрено число е първото място. Като 3 в 3284 и 7 в 0,0726.
Последна цифра: Наричана още най-ниската цифра, тя се отнася до последния номер от многоцифрено число. Като 5 в 3275, 0 в 120 и 9 в 481.29.
Второ място: Второто число е по същество многоцифрено число. Въведете 8 в 3865 и 1 в 0,4178.
Liquidation:Turnofftheabacusbeadsineachstalltomakethewholemarketempty,whichiscalledliquidation.
Comprehensivepractice:Practiceonallthefilesoftheabacus,oronmostofthefiles,andperformcomprehensiveexercisesaccordingtothebasicalgorithm,whichiscalledfullpractice.
Стойност
Becausetheabacusiseasytomake,cheap,easytoremember,andeasytocalculate,itiswidelyusedinChinaandspreadtoJapan,NorthKorea,theUnitedStatesandSoutheastAsia.Andothercountriesandregions.Today,wehaveenteredtheageofelectroniccomputers,buttheancientabacusstillplaysacertainrole.