Chipcountingmethod
Inthechipcountingmethod,thenumberofunitsisexpressedintwoarrangementsofverticalandhorizontal,amongwhich1-5arearrangedinaverticalandhorizontalmanner.Itisexpressedbychips,6-9isexpressedbytheabovecountingchipsplusthecorrespondingcountingchipsbelow.Whenexpressingmultipledigits,theonesdigitisvertical,thetensdigitishorizontal,thehundredsdigitisvertical,thousandsishorizontal,andsoon,anditisleftblankwhenitencounterszero.Thiscountingmethodfollowstheone-hundred-digitsystem.Accordingtotherecordsof"SunTzuSuanJing",theruleofcountingandcountingis:Everymethodofcountingistoknowitspositionfirst."XiayangHouSuanJing"says:sixormore,fiveatthetop.Sixdoesnotaccumulate,fiveisnotaleaflet.
Invention
Theinventionofcountingchipsisgraduallyproducedinthehistoricaldevelopmentofthesecountingmethods.Whenitfirstappeared,itisnolongeravailable,butatthelatestintheSpringandAutumnPeriodandtheWarringStatesPeriod;theuseofcountingchipsisalreadyverycommon.Asmentionedearlier,countingchipsaresmallsticksofthesamelengthandthickness,sohowdoyouusethesesmallstickstoexpressvariousnumbers?
Pendulum
Sowhyaretheretwodifferentpendulums,verticalandhorizontal?Thisisbecauseoftheneedofthedecimalsystem.Theso-calleddecimalsystem,alsoknownasthedecimalvaluesystem,hastwomeanings.Oneisthe"decimalsystem",thatis,oneunitisenteredforeveryfullnumberofdecimals,tenisenteredasten,tenisenteredasahundred,andtenhundredisenteredasathousand...Thesecondisthe"placevaluesystem,thatis,eachnumberThevalueindicatednotonlydependsonthenumberitself,butalsodependsonitspositioninthecounting.Ifitisalsoanumber"2",itmeans2intheonesplace,and20inthetensplace.,Placedonthehundredsplacemeans200,placedonthethousandsplacemeans2000...InthewordcountingsystemoftheShangDynastyinourcountry,thedecimalvaluesystemhassprouted,andwhenitcomestocounting,countingandcomputing,It’seventhestandarddecimalvaluesystem.
Asearlyasmorethantwothousandyearsago,theancientworkingpeopleinChinainventedthecalculationmethodofmultiplication.However,themethodatthattimewasdifferentfromthecurrentone.Countingchipsareusedforcalculations.Countingchipsaresmallsticksmadeofbambooorothermaterials.Atthattime,thereweretwomethodsofusingsmallstickstorepresentnumbers,horizontalandvertical.Useverticaltype,horizontaltypefortensplace,verticaltypeforhundredsplace,horizontaltypeforthousandsplace,andsoon.Ifitiszero,itwillbeleftblank),asshowninFigure1.
Useacalculatortoperformmultiplicationcalculations.,Putthemultiplieronthetop,andthenputthemultiplicandonthebottom,andalignthefirstdigitoftheuppernumberwiththelastdigitofthelowernumber,andmultiplythelowerdigitswiththefirstdigitoftheuppernumberintheorderfromlefttoright,andmultiplytheresultTheproductisplacedinthemiddleoftheupperandlowernumbers,thenthefirstdigitoftheuppernumberisremoved,thelowernumberismovedoneplacetotheright,andtheseconddigitoftheuppernumberismultipliedbythelowerdigits,andthemiddleproductisadded,andtheseconddigitoftheuppernumberisremoved.Afteryoufinishcounting,thenumberinthemiddleistheresult.Let’stake183×26asanexampletoexplainindetail:
1.Putthemultiplier26onthetop,andthemultiplicand183onthebottom,andbemultiplied.Theonesplaceofthenumberisalignedwiththetensplaceofthemultiplier,leavingspaceinthemiddle,readytoplacetheproductobtainedbymultiplication(Figure2inFigure2);
2.Multiplyfromthehighpositionandmultiplybydozens2timesthemultiplicand183ontheposition,get3660,placedinthemiddle,andthedigitsoftheproductarealignedwiththemultiplicand(asshowninFigure3inFigure2,theunitdigit0oftheproductisrepresentedbyaspace);
3.Removethenumber2inthetensofdigitsthathavebeenmultiplied,andmovetheunitdigit6ofthemultipliertothepositionalignedwiththeunitsdigitofthemultiplicand(Figure4inFigure3);
4.Multiplythemultiplicand183bythemultiplierunitdigit6,andaddtheproductto3660,andthefinalproductis4758(Figure5inFigure3).
Rules
AccordingtotheancientChinesecountingrules,theexpressionmethodofcountingchipsis:verticalforsingles,horizontalfortens,verticalforhundreds,horizontalforthousands,verticalfortensofthousands,etc.(GotoSogoutocheck)Inthisway,fromrighttoleft,verticalandhorizontal,andsoon,youcanuseacountingchiptoexpressarbitrarilylargenaturalnumbers.Becauseoftheverticalandhorizontaltransformationbetweenitsbits,andeachbithasafixedTherefore,itwillnotbeconfusedormisplaced.Thereisnodoubtthatsuchacountingmethodiscompletelyconsistentwiththemoderndecimalnotation.
十TheCountingChipsoftheCarrySystem
TheCountingChipsoftheDecimalSysteminAncientChina,Isagreatcreationinthehistoryofworldmathematics.Comparingitwiththenotationofotherancientnationsintheworld,itssuperiorityisobvious.TheancientRomannumeralsystemhadnoplacevaluesystem,onlysevenbasicsymbols.Itwouldbequitedifficulttorememberalargernumber.AlthoughtheancientAmericanMayansknewtheplacevaluesystem,theyusedthetwentiethbit;theBabyloniansalsoknewtheplacevaluesystem,buttheyusedthesixtiethbit.Atleast19digitsarerequiredfor20-carryingand59digitsfor60-carrying.Thismakescountingandcalculationsverycomplicated.Itisfarinferiortothedecimalsystem,whichcanrepresentanynaturalnumberwithonly9digits,tobesimpleandconvenient.ThereasonwhyancientChinesemathematicshasmademanyoutstandingachievementsincalculation,toacertainextent,shouldbeattributedtothisarithmeticnotationthatconformstothedecimalsystem.Marxcalledthedecimalnotation"oneofthemostwonderfulinventions"inhis"MathematicsManuscript",ofcourseitisnottoomuch.
Achievementsinancientmathematics
Inthecountingmethod,thenumberofunitsisexpressedintwoarrangements,inwhichthenumberofcalculationsisarrangedverticallyandhorizontally.Itisexpressedbychips,6-9isexpressedbytheabovecountingchipsplusthecorrespondingcountingchipsbelow.Whenexpressingmultipledigits,theonesdigitisvertical,thetensdigitishorizontal,thehundredsdigitisvertical,thousandsishorizontal,andsoon,anditisleftblankwhenitencounterszero.Thiscountingmethodfollowsthedecimalsystem.Thedateoftheappearanceofthecalculationchipsisuntestable,butaccordingtohistoricaldata,thelasttimethecalculationchipsappearedinthelateSpringandAutumnPeriodandtheearlyyearsoftheWarringStatesPeriod(722BCto221BC).
Ourancestorsunderstoodsuchexquisitecalculationsmorethantwothousandyearsago.Itisamazing!Amongthese,arithmeticisindispensable.ItisthemosteffectivecalculationtoolcreatedinChinabeforetheinventionofabacus.TheearlydevelopmentandcontinuousdevelopmentofancientChinesemathematicsbenefitedfromcalculations.