Introduction
Althoughwehaveenteredtheageofelectroniccomputers,lookingattheancientChineseabacus,wecan’thelpbutadmirethegreatwisdomofourancestors.Thegeneralabacusismostlymadeofwood(orplasticproducts).Astringofequalnumbersofabacusbeadsarrangedinarectangularwoodenframeiscalledafile.Abeamdividesthebeadsintoupperandlowerparts.Eachabacusintheupperhalfrepresents5,Eachbeadinthelowerhalfrepresents1.Fromrighttoleft,eachbeadrepresentsone,ten,hundred,thousand,andtenthousanddigitsindecimal.Withtheadditionofsoftware-asetofcalculationformulasforfingerdialingrules,variouscomplexcalculationscanbesolved,andevenmultipleprescriptionscanbemade.TheabacusisthepredecessorofmoderncomputersandthesymbolofancientChinesecomputingtechnology.
Theabacusshapesystem
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.
Maincategories
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.
Theoriginofdevelopment
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.
Mantra
AdditionMantra
Explanation:Abacusadditionmantraisatextsummaryusedtoguidethemovementofdialingbeadsandperformcalculations.Inordertohaveaclearerunderstandingofthecontentoftheformula,firstbrieflydescribethemeaningoftherelevanttermsintheadditionformulaasfollows:
"Shang"meanstodialthebeadtorelyonthebeam.
"Down"referstoshiftingtheupperpearltothebeam.
"Go"meanstomovetheabacusbeadsbythebeamtotheside.
"Advance"meansaddinganumbertothefrontposition(thefirstgearfromtheleft).
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobeadded,andthelastwordindicatesthenumbertobemovedbythebead.
Subtractionformulas
Explanation:Thereare26sentencesintheabacussubtractionformulas,whicharedividedintofourtypes:directsubtraction,breakingfivesubtraction,retreatingtensubtractionandretreatingtenreplenishingfivesubtraction.Themeaningoftherelevanttermsinthesubtractionformula:
"Up"referstodialingdownthepearlandrelyingonthebeam.
"Down"meanstomovethelowerbeadtothesideofthebeam.
"Go"meanstomovetheabacusbeadsthatleanonthebeamandmovetothesideofthebeam.
"Advance"meansaddinganumbertothefrontposition(thefirstgearfromtheleft).
"Retreat"meanstodecrementthenumberfromthepreviousposition(thefirstgearfromtheleft).
"Return"meansthatthenumbershouldbeaddedtothedigitafterthefirstdigitisremoved.
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobesubtracted,andthenextwordindicatesthenumberofbeadstobemoved.
Multiplicationformula
oneone01onetwo02onethree03onefour04onefive05onesix06oneseven07oneeight08onenine09
Twoone02twotwo04twothree06twofour08twofive10twosix12twoseven14twoeight16twonine18
threeone03threetwo06threethree09threefour12threefive15threeSix18threeseven21threeeight24threenine27
fourone04fourtwo08fourthree12fourfour16fourfive20foursix24fourseven28foureight32fournine36
Fiveone05fivetwo10fivethree15fivefour20fivefive25fivesix30fiveseven35fiveeight40fivenine45
6one06sixtwo12sixthree18sixfour24sixfive30sixsix36sixseven42sixeight48sixnine54
sevenone07seventwo14seventhree21sevenfour28sevenfive35sevensix42sevenseven49seveneight56sevennine63
Augustone08eighttwo16eightthree24eightfour32eightfive40eightsix48eightseven56eighteight64eightnine72
nineone09ninetwo18ninethree27ninefour36NineFive45NineSix54NineSeven63NineEight72NineNine81
Explanation:Eachsentenceofthemultiplicationformulaconsistsoffournumbers,thefirsttwoareChinesecharacters,andthelasttwoareArabicnumbers.Thefirstnumberreferstothemultiplier,thesecondnumberreferstothemultiplicand,andthethirdandfourthnumbersrefertotheproduct.
Inordertopreventthewrongtipfromaddingtheproductinthecalculation,theproductiscomposedoftwodigits.Eveniftheproducthasonlyonesignificantdigit,itmustbereadbyadding0beforetheproduct,suchas6x1,andtheformulaisreadasonesix06.
Ninereturnformula
Onereturn(divideby1):enteroneateveryone,entertwoateverysecond,enterthreeateverythree,enterfourateveryfour,enterfiveateveryfive,Everysixenterssix,everysevenentersseven,everyeightenterseight,andeverynineentersnine.
Tworeturn(divideby2):enteroneeverytwo,entertwoeveryfour,enterthreeeverysix,enterfoureveryeight,andaddfiveeverytwo.
Sangui(divideby3):enteroneeverythree,entertwoeverysix,enterthreeeverynine,threeonethreemorethanone,threetwosixmorethantwo.
Fourreturn(divideby4):enteroneeveryfour,entertwoeveryeight,addfiveafterfourtwo,fouronetwomorethantwo,fourthreesevenmorethantwo.
Fivereturn(divideby5):everyfiveentersone,fivetimesmakestwo,fivetimesmakesfour,fivetimesmakessix,fivetimesmakeseight.
Sixreturn(divideby6):enteroneeverysix,entertwoeverytwelve,addfivewhensixthree,addfourwhensix,sixtwothreemorethantwo,sixfoursixmorethanfour,Six,five,eight,morethantwo.
Qigui(divideby7):enteroneeveryseven,entertwoeveryfourteen,addthreeunderseven,addsixunderseven,seven,three,four,andtwo,seven,four,five,andfive,Sevenfivesevenmorethanone,sevensixeightmorethanfour.
Bagui(divideby8):Everyeightentersone,eightfouraddsfive,eightaddstwo,eighttwoaddsfour,eightthreeaddssix,eightfivesixremainstwo,Eightsixsevenmorethanfour,eightseveneightmorethansix.
Ninereturn(divideby9):everynineentersone,nineaddone,ninetwoaddtwo,ninethreeaddthree,ninefouraddfour,ninefiveaddfive,Addsixforninety-six,sevenforninety-seven,andeightforninety-eight.
Explanation:Dividingbyasingledigitiscalled"singlereturn";divisionbyadivisoroftwoormoredigitsiscalled"dividing".Thefirstdigitofthedivisoriscalled"gui",andthefollowingdigitsarecalled"division".Forexample,thedivisionofthedivisoris534,whichiscalled"fivereturntothreetofourdivision",thatis,usethefivereturnformulatofindaquotient,andthendivideby34.
Relatedterms
Neutral:Whentheupperandlowerpartsofacertaingeararebothawayfromthebeam,itiscalledneutral.Agapmeansthatthereisnocountinthisposition,oritmeans0.
Emptyplate:Allgearsoftheabacusareempty,whichmeansthatthereisnocountinthewholeplate,whichiscalledanemptyplate.
Innerbeads:Theabacusbeadsthatcountbybeamsarecalledinnerbeads.
Outerbeads:Abacusbeadsthatdonotcountfromthebeamarecalledouterbeads.
Dialup:referstotheloweringofbeadsagainstthebeam.
Dialingdown:referstoputtingtheupperpearlagainstthebeam.
Pullingout:referstopullingtheupperorlowerbeadsawayfromthebeam.
Thisfile:referstothefilethatisabouttobedialedandcounted.
Frontgear:referstothepreviousgearofthisfile,alsocalledtheleftgear(position).
Backgear:referstothenextgearofthisfile,alsocalledtherightgear(position).
Floatingbeads:Theabacusbeadsfloatinginthemiddleofthegearwithoutrelyingonthebeamstobetoolightwhenpullingthebeads.
Beads:Whendialingbeads,bringinoroutthebeadsthatshouldnotbedialedinoroutofthisfileorneighboringfiles.
Realbeads:Abacusbeadsthatrelyonbeamstorepresentpositivenumbers.
Virtualbead:alsocallednegativebead,referstothehangingbeadthatisdialedtoneitherthebeamnortheframe,indicatinganegativenumber.
Setthenumber:alsoteachthenumber,accordingtothecalculationrequirements,dialthenumberintotheabacustoprepareforthecalculation.
Gearposition:Alsocalledgrade,itreferstothepositionofthegear.
Wronggear:Alsocalledmisalignment,itmeansthatthebeadisnotdialedintothegearthatshouldbedialedduringthecalculationprocess.
Interval:Itisalsocalledtheinterval,whichreferstothesecondgear(position)withonegearleftandright.Inintervalmultiplication,twonumbersaremultipliedtogether,andtheunitsplaceoftheproductisplacedontherighttwodigitsofthemultiplicand;inintervaldivision,thequotientoftheintervalreferstothefirsttwoleftdigitsofthedividend.
Carry:Itmeansthatafteraddinganumbertothisfile,itisgreaterthanorequalto10,anditmustbeincreasedby1tothepreviousposition,whichiscalledcarry.
Abdicate:Itmeansthatwhenthisfileissubtractedbyonenumber,thisfileisnotenough,andyoucansubtract1fromthepreviousone,whichiscalledabdication.
Firstplace:Alsocalledthehighestplace,itmeansthatthefirstnon-zerodigitofamulti-digitnumberisthefirstplace.Suchas3in3284and7in0.0726.
Lastdigit:Alsocalledthelowestdigit,itreferstothelastnumberofamulti-digitnumber.Suchas5in3275,0in120,and9in481.29.
Secondplace:Thesecondnumberthatisessentiallyamulti-digitnumber.Enter8in3865and1in0.4178.
Liquidation:Turnofftheabacusbeadsineachstalltomakethewholemarketempty,whichiscalledliquidation.
Comprehensivepractice:Practiceonallthefilesoftheabacus,oronmostofthefiles,andperformcomprehensiveexercisesaccordingtothebasicalgorithm,whichiscalledfullpractice.
Value
Becausetheabacusiseasytomake,cheap,easytoremember,andeasytocalculate,itiswidelyusedinChinaandspreadtoJapan,NorthKorea,theUnitedStatesandSoutheastAsia.Andothercountriesandregions.Today,wehaveenteredtheageofelectroniccomputers,buttheancientabacusstillplaysacertainrole.