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1、MagicsquareInrecreationalmathematics,amagicsquareisanar-worksofart.Inmoderntimestheyhavebeengeneralizedrangementofdistinctnumbers(i.e.eachnumberisusedanumberofways,includingusingextraordifferentcon-once),usuallyintegers,inasquaregrid,wherethenum-straints,multiplyinginsteadofaddingcells,usingalte
2、r-bersineachrow,andineachcolumn,andthenumbersinnateshapesormorethantwodimensions,andreplacingthemainandsecondarydiagonals,alladduptothesamenumberswithshapesandadditionwithgeometricopera-number.Amagicsquarehasthesamenumberofrowstions.asithascolumns,andinconventionalmathnotation,"n"standsforthenu
3、mberofrows(andcolumns)ithas.Thus,amagicsquarealwayscontainsn2numbers,anditssize1History(thenumberofrows[andcolumns]ithas)isdescribedasbeing“ofordern".*[1]Amagicsquarethatcontainstheintegersfrom1ton2iscalledanormalmagicsquare.(Theterm“magicsquare”isalsosometimesusedtorefertoanyofvarioustypesofwo
4、rdsquares.)Normalmagicsquaresofallsizesexcept2×2(thatis,wheren=2)canbeconstructed.The1×1magicsquare,withonlyonecellcontainingthenumber1,istrivial.Thesmallest(anduniqueuptorotationandreflection)non-trivialcase,3×3,isshownbelow.Ironplatewithanorder6magicsquareinArabicnumbersfromChina,datingtotheYu
5、anDynasty(1271–1368).MagicsquareswereknowntoChinesemathematiciansasearlyas650BC,*[2]andtoArabmathematicianspossi-blyasearlyastheseventhcenturyAD.Thefirstmagicsquaresoforder5and6appearinanencyclopediafromBaghdadcirca983,theEncyclopediaoftheBrethrenofAnymagicsquarecanberotatedandreflectedtoproduceP
6、urity(Rasa'ilIhkwanal-Safa);simplermagicsquares8triviallydistinctsquares.Inmagicsquaretheoryallof*wereknowntoseveralearlierArabmathematicians.[2]thesearegenerallydeemedequivalentandtheninesuchSomeofthesesquareswerelaterusedinconjunctionwithsquaresaresaidtocompriseasingleequivalenceclass.magicle
7、tters,asin(ShamsAl-ma'arif),toassistArabTheconstantthatisthesumofeveryrow,columnandillusionistsandmagicians.*[3]diagonaliscalledthemagicconstantormagicsum,M.Everynormalmagicsquarehasaconstantdependentonn,calculatedbytheformulaM=[n
