1、 23 5 2009 M 9 v ( 1 S )Jour nal of Shandong U niversit y of T echnolog y( Natur al Science Editio n)V ol. 23 N o. 5Sep. 2009l : 2009null03null16T e : ( 1957null) , 3 , q . Enullmail: yunmin gzhou66 yahoo. com. cn c I | : 1672- 6197( 2009) 05- 0040- 03Stew art # bW M 周运明(山东理工大学理学院, 山东淄博 255049)K nul
2、l 1 : 论述了Stew art 定理,并给出了两个推广定理及其在解竞赛题中的应用, 最后将推广定理2移植到了三维空间.1 o M : Stew art定理; 推广定理; 移植定理; 竞赛题 m s | : O124 D S M : AStewart theorem and its application in space transplantationZH OU Yunnullming( Scho ol o f Sciene, Shandong U niv ersity of T echno lo gy , Zibo 255049, China)Abstract: T he Stew ar
3、t theorem is reseached and tw o pr omotion theo rem s w ere g iv en and used tosolv e competition questio ns. T he pro motion theorem 2 w as transplanted to thr eenulldimentionlspace.Key words: Stew art theo rem; transplantation theorem; promo tion theorem; com petition quesnulltionsnull null + : +
4、( Stew art, 1717null1785 M ) 18 W S E , W + a x f + . b w AC, A E !A s L BC E, S BC B , O BS = EC.p AS 2- A E2 = (A B - AC) 2( # w 3 )m 241 5 null null null null null null null null null null null null : Stew art # bW M 4 null A BC , !C = 45, D A C , O AD DC= 2 1, !AD B= 60p : A B BCD M L . ( w 4# ?
5、 )3null M # H ( )a ( )a s Y 8 ( )a= ( )a8 , 5 w 2 bW M 1 null 8 A BCD , A D (BC, V BCT BCE A D EE,5 :S2 BCE = DEA D nullS 2 ABC + A EA D nullS 2 BCD -null 14 BC2 nullA E null DE ( 3)e null m 2,T A F (BC F , A FaEFaDF, AD (BC(X ), A F ( BC BC ( ADF, BC (EF, BC (FD , AFD , w 2 EF2= AF 2 DFA D + FD2 nu
6、ll A EA D - AE null DE ( 4)(4) T 14 BC2, T V . V w :w 5null S ABC = S BCD H , (3) T null null S2 BCE = S 2 ABC - 14 BC2 nullA E null DEw 6null E AD H , (3) T null null S2nullBCE = 12 nullS 2 ABC + 12 nullS2 BCD -null null null 116BC2 null AD2.w 7null BCE s = A - BC - DH , (3) T null null S2 BCE = S
7、ABC null S BCD -null null null 14 BC2 null AE nullDE.w 8null AE: ED= k H , (3) T null null S2 BCE = 1k+ 1null S2 ABC + kk+ 1 nullS2 BCD -null null null 14 k( k+ 1) 2BC2 nullA D2. “ V | 1 5 1 8 . 8 A BCD A D (BC, BCE s = A - BC- D,5 S BCE S ABC null S BCDA 2 8 1 5 , w 7 . I D : 1 . # M . : ,1981. 2 . S tew art bW w J . S , 2007,( 2) : 3null4. 3 r . + M . : F v , 2001.(编辑:刘宝江)42 v (1 S ) 2009 M null
