Аналитическая геометрия. Шурыгин В.В. - 33 стр.

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ϕ : V × V → W
a ∈ V V 3 v 7→ ϕ(a, v) ∈ W
V 3 v 7→ ϕ(v, a) ∈ W
2
◦
3
◦
g : V
3
× V
3
3 {a, b} 7→ (a, b) ∈ R.
A
1
A
2
A
3
A
4
• •
•
•
•
•
•
A
1
A
2
A
3
A
4
E
F
A
1
A
3
A
2
A
4
E F r
i
A
i
(r
2
− r
1
)
2
+ (r
3
− r
2
)
2
+ (r
4
− r
3
)
2
+ (r
1
− r
4
)
2
=
= (r
4
− r
2
)
2
+ (r
3
− r
1
)
2
+ 4
(r
1
+ r
3
)
2
−
(r
2
+ r
4
)
2
2
.
M n P =
A
1
A
2
. . . A
n
A
i
A
i+1
n
M A
i
A
i+1
A
i
A
i+1
i = 1, 2, . . . , n n
n ∼ 0 n + 1 ∼ 1 P
   „610; -+36[-;\ ϕ : V × V → W · +070,*M,-\ */70 .30 .3-0[b-7?,-;
O01/03-b6,,-; a ∈ V 16|L-* 0[ -8-+36|*,0M V 3 v 7→ ϕ(a, v) ∈ W \
V 3 v 7→ ϕ(v, a) ∈ W \ 9b79*8/9 70,*M,; =
   s™xw¶ztWxZ ú”Š¦ž” 2 Œ 3 ” Š”Š‰œ¡ŠžŒ ɔŒ”‹Žž‘ ¬Œ‹ŒŽ¦º
                                       ◦           ◦
ŠžŒ ŠžŠ¬»ŽŒ£ g : V × V 3 {a, b} 7→ (a, b) ∈ R.
                                       3           3

ZÊ ˜TWµxTUZ
­7*L2J}0* .30;*3 .-16[b6J8 161 /16793,-* .3-0[b*L*,0* ;-|*8 .30K
;*,98?/9 .30 3*I*,00 36[70),N :*-;*830)*/10N [6L6)=
                                     ðÍwÍñÍ rZ ‚„*-3*;6 “M7*36ƒ= ‡-16K
            A
                   •
                       4
                                  [68?\ )8- /2;;6 1b6L368-b /8-3-, )*K
                         A        83*N2:-7?,016 A A A A 36b,6 /2;K
                                   •
                                           3

           E
                           •
                               •  ;* 1b6L368-b *:- L06:-,67*M 0 2)*8b*K1   2   3       4


                                  3*,,-:- 1b6L3686 36//8-9,09 ;*|L2 /*K
                   •
                   F
     •                            3*L0,6;0 L06:-,67*M=
                                           •

  A  1
            0/
           Ç = =]]          A        àxÿxXWxZ ­;= 30/2,-1 ]]=ˆ+-[,6)0;
                                               2

                                  /*3*L0, L06:-,67*M A A 0 A A \ /-K
-8b*8/8b*,,-\ +21b6;0 E 0 F \ 0 .2/8? r · 36L02/Kb*18-3 b*3I0, A = {          1       3         2   4


[6L6)* 83*+2*8/9 L-16[68?\ )8- 0;**8 ;*/8- /7*L2J}** 36b*,/8b-†
                                                         i                                               i



             (r2 − r1 )2 + (r3 − r2 )2 + (r4 − r3 )2 + (r1 − r4 )2 =
                                                                                2
                                                     (r 1 + r 3 )   (r 2 + r 4 )
                  = (r4 − r2 )2 + (r3 − r1 )2 + 4                 −                 .
                                                          2              2
‡79 L-16[68*7?/8b6 ~8-:- 36b*,/8b6 L-/868-),- 36/138? /1-+10 0 /-+368?
.-L-+,* )7*,=
   ðÍwÍñÍ rrZ „-)16 M 36/.-7-|*,6 b,2830 b.217-:- nK2:-7?,016 P =
             ‡              )
A A . . . A = -16[68?\ 8- ,6ML*8/9 86169 /8-3-,6 A A ~8-:- nK2:-7?,016\
)8- -/,-b6,0* .*3.*,L0127936\-.2}*,,-:- 0[ 8-)10 M ,6 A A 9b79*8/9
 1       2     n                                                   i   i+1


b,283*,,*M 8-)1-M -83*[16 A A =                                                    i       i+1


  àxÿxXWxZ ­;= 30/2,-1 ]Æ= ‡79 2L-+/8b6 -+-[,6)*,0M +2L*; /)0868?\ )8-
                                               i   i+1


0,L*1/ i = 1, 2, . . . , n .3*L/86b79*8 /-+-M -/868-1 -8 L*7*,09 ,6 n \ 8- */8?\
n ∼ 0 \ n + 1 ∼ 1 0 861 L67** = „61 161 ;,-:-2:-7?,01 P · b.217M\
                                         ––

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