AdvancesinTheoreticalandAppliedMathematics(ATAM)，ISSN07934554，Vol.7,№4,2012,pp.425431AProofoftheKepler’sConjectureZhangTianshuNanhaiwestoilcorporation,ChinaoffshorePetroleum,Zhanjiangcity,Guangdongprovince,P.R.ChinaEmail:friend_zhang888@sina.comAbstractHeaptogetherequivalentspheresintoacubeuptomostpossible,thenvariantgeneralvolumesofequivalentspheresinsidethecubedependonvariantarrangementsofequivalentspheresfundamentally.Thisπ/√18whichtheKepler’sconjecturementionsistheratioofthegeneralvolumeofequivalentspheresunderthemaximumtothevolumeofthecube.Wewilldoacloserarrangementofequivalentspheresinsideacube.Furtherletageneralvolumeofequivalentspherestogettinggreaterandgreater,uptotendupwardsthesuperlimit,inpacewithwhicheachofequivalentspheresisgettingsmallerandsmaller,andtheiramountisgettingmoreandmore.WewillprovetheKepler’sconjecturebysuchawayinthisarticle.KeywordsEquivalentspheres,rearrangements,cube,cuboid,square,rectangle,sphericalcenter,volume,differentialcubes,pointlikespheres,superlimit,infinity,Ratio,π/√18.BasicConceptsFirstletusreviewfollowingafewofbasicconceptsoncemore,fortheyrelatingtotheproof.TheKepler’sconjecturestatesthatheaptogetherequivalentspheresintoacube,then,aratioofanygeneralvolumeofequivalentspheresinsidethecubetothevolumeofthecubeisnotgreaterthanπ/√18always.Supposethatthelengthofeachedgeofacubeisα,thenthevolumeof1thecubeisα3,andthevolumeofinternaltangentsphereofthecubeisequaltoπα3/6.Theratioofthevolumeofinternaltangentsphereofacubetothevolumeofthecubeisequaltoπ/6.Supposethatthelengthofedgesofacuboidisα,βandγrespectively,thenthevolumeofthecuboidisαβγ.Supposethatthelengthofarectangleisα,anditsbreadthisβ，thenitsareaisαβ.Supposethatthelengthofeachsideofasquareisα,thenitsareaisα2.Aforementionedα,βandγarerealnumbers.Hereweneedtostressabitthatyoucangetalinesegmentwherebyanyrealnumbermeasuresfromthenumberaxistoactasanedgeofrectangularparallelopipedoradiameterofsphere.TheProofS