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©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:abc=2009(a+b+c)(a,b,c).()2.1,ABC,BAC=90,1EABCBC(A),AEEC.ECF,EAC=CAF,BFD,ED,DEFO.:ACO.()3.,{P1,P2,,P4n+1}={(x,y)|xy,|x|n,|y|n,xy=0},,nN+.(P1P2)2+(P2P3)2++(P4nP4n+1)2+(P4n+1P1)2.()4.n(n4)V1,V2,,Vn,,.1,2,,nnn,.n:,;,.n,,k(k=1,2,,n)Vk,.,.()5.xyz1.:(x2-2x+2)(y2-2y+2)(z2-2z+2)(xyz)2-2xyz+2.()26.2,12S,2AB1C,MAB(S),MMNAB,N.1r.:ACCB=2rMN.()7.10104n11,n,n().n.()8.an=n5-n5.a1,a2,,a2009,,xx.()1.:abc.03©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=2009(a+b+c)6027c]ab6027.,(a,b),cabcabc=2009(a+b+c).c(ab-2009)=2009(a+b),(a,b),cabcabc=2009(a+b+c).,abc.2..33,AEFACP,PEPF.EAC=FAC,,AEPF.PEF=PFE=EAP]PE=PF]EPF=180-2EAP.EDAB,BDE=EAB=90-EAC=90-EAP.BDE=12EPF.PPEP.EFP.,DP.PDEF.,PO,AEFOAC.3..s1s2sm,f(s1,s2,,sm)=min(t1,t2,,tm){|t1-t2|2+|t2-t3|2++|tm-1-tm|2+|tm-t1|2},,(t1,t2,,tm)(s1,s2,,sm).f(s1,s2,,sm)f(s2,s3,,sm)+2(s1-s2)(s1-s3).:t1=s1.|t1-t2|2+|t2-t3|2++|tm-1-tm|2+|tm-t1|2=|t2-t3|2++|tm-1-tm|2+|tm-t2|2+(|t1-t2|2+|tm-t1|2-|tm-t2|2)=|t2-t3|2++|tm-1-tm|2+|tm-t2|2+2(t1-t2)(t1-tm)f(s2,s3,,sm)+2(s1-s2)(s1-s3)..Pi=(xi,yi)(i=1,2,,4n+2),,P4n+2=P1.4n+1i=1PiP2i+1=4n+1i=1[(xi-xi+1)2+(yi-yi+1)2].4n+1i=1PiP2i+12f(n,,1,,-1,,-n)2f(n-1,,1,,-1,,1-n)+162f(1,,-1)+16(n-1)=16n-8.P1,P2,,P4n+1(2,0),(4,0),,(n,0),,(3,0),(1,0),(0,2),(0,4),,(0,n),,(0,3),(0,1),(-2,0),(-4,0),,(-n,0),,(-3,0),(-1,0),(0,-2),(0,-4),,(0,-n),,(0,-3),(0,-1),(0,0),4n+1i=1PiP2i+1=16n-8.,16n-8.4.n+1.,n,:(1)V1,V2,,Vn,;13200911©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2)V1,V2,,Vn,.(1),V1.V1.,Vi.,VjV1.,ViVj,V1,.,V11,,.,.(2),.,ViVj,ViVj,,Vij,,,;,ViVi+1(i=1,2,,n,Vn+1=V1).,,,ViVi+1,Vi+1Vi(i=1,2,,n),,V1V213,,,.,ViVi+1(i=1,2,,n,Vn+1=V1),Vn-1V1,.,,.M1:ViVi+1(i=1,2,,n).M2:ViVi+1(i=1,2,,n-2),Vn-1V1,Vn.:k(1kn),,1,2,,kV1,V2,,Vk.k=1,1Vi.n-i+1M11V1.,1,2,,kV1,V2,,Vk,k+1Vr(k+1rn).n-rM1,r-k-1M2,k+1M1,1,2,,k+1V1,V2,,Vk+1.,,kVk(k=1,2,,n).,.,,n+1.5.x1,y1.(x2-2x+2)(y2-2y+2)-[(xy)2-2xy+2]=(-2y+2)x2+(6y-2y2-4)x+(2y2-4y+2)=-2(y-1)[x2+(y-2)x+1-y]=-2(y-1)(x-1)(x+y-1)0.(x2-2x+2)(y2-2y+2)(xy)2-2xy+2.4,xy1,z1,,[(xy)2-2xy+2](z2-2z+2)(xyz)2-2xyz+2.,.6.1:4,12O1O2,rR.,MNO2,NAB.12S,,23©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=(AN-CN)(AN+CN)=AN2-CN2.AO2.AN2=R2-(R-MN)2=2RMN-MN2.CN2=O1O22-O1D2=(R-r)2-(r+MN-R)2=2(R-r)MN-MN2.ACCB=AN2-CN2=2[R-(R-r)]MN=2rMN.52:5,1CD.S12,,CM,SCM.ACCB=SCCM.RtSCDRtNMC,SCCM=CDMN=2rMN.7.AB.:n.661010.A4,,B.n,nA;nB,.,n.n=2,A7.B.7,n4.8n=4.88.b0=0,b1=1,bn=4bn-2+bn-1(n2).bn=(2+5)n-(2-5)n25.,b6=1292,b7=5473.k(k=1,2,,5473),xkyk,1292k=xk+5473yk(1xk5473).(1292,5473)=1,,x1,x2,,x54731,2,,5473,{yk}y1y2y5473=1291.,f(x)=x-[x].,f(xk5)=f((1292k-5473yk)5)=f(2+5)6-(2-5)62k-(2+5)7-(2-5)72yk=f(-(2-5)6k+(2-5)7yk).0(2-5)6k-(2-5)7yk5473(2-5)6-1291(2-5)71,f(xk5)=1-(2-5)6k+(2-5)7yk.x1=1292,x5473=5473,x5472=4181,x5471=2889,x5470=1597,a1292,a1597.()33200911