空间几何体求解平面投影的分类与总结

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(11710072),,(a),x,y,z,F(x,y,z)=0G(x,y,z)=0,FG(x,y)z,xoyFG(x,y)=0z=0(b),,(1):,,,,,(2)(2):,,,1::0za2-x2-y2x2+y2ax(a0)xoyxoz1:,(1)xoy:(b)(1):(1ABCD):z=a2-x2-y2x2+y2-ax=0z,x2+y2-ax=0xoyxoyz=0,x2+y2-ax=0z=0,x2+y2-ax0z=093Vol15,No11Mar.,2002STUDIESINCOLLEGEMATHEMATICSX:2001-10-29©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2)xoz:(1),:z=a2-x2-y2x2+y2=ax(x0)yz=a2-axx0,0za2-axx0,y=0xoz(2MN),(b)(2)xoz:2:0za2-x2-y2y=0:0za2-x2:x2+y2axy=0:x2ax,0xax2+z2a2z0,x0,y=0,22z=x2+y2z2=2x3:(1)xoy:z=x2+y2z=0zø+2=2x3x2-2x+y2=0z=0,x2+y2-2x0z=0(2)zoy:z22-12+y21x=0(b)(1),(3)zox:z2=2xy,4,(2),:z=x2+y2y=0zx2=ûxûz2=2x,0z2x,:xz2xx0,4,,,,,,04STUDIESINCOLLEGEMATHEMATICSVol15,No11Mar.,2002