H + : ω = ( a, b, c, d, ad bc > 0) 3.. ( c 0 )... ( 5z + 2 : ω = L (*) z + 4 5z + 2 z = z =, 2. (*) z + 4 5z+ 2 6( z+) ω + = + = z+ 4 z+ 4 5z+ 2 3( z 2) ω 2 = 2= z+ 4 z+ 4 ω + z + = 2 ω 2 z 2 x + T ( x) = x 2 T( ω ) = 2 T ( z) ' T O 2 C ' C ' 2x + ' C C ' C ' T ( x) = x C = T ( C )
C C ' ω + z + arg ( T( w) ) = arg ( T( z) ) ó arg = arg ( = θ ) ω 2 z 2 A( ),B(2) AB z = AwB= θ C A B ( AzB) z z 2 z 3 { z n } zn C T( ) = O, T(2) = z n C A B T( z ) n C A,B [ ] [T ] Cabri ( ) Drag z,c example.html
T(x) Cabri x + T ( x) = Cabri x 2 5z+ 2 3( z 2) ω = óω 2 = ó = 2 + ' z+ 4 z+ 4 ω 2 z 2 3 S( x)= x 2 S( ω) = 2 S( z) + S( ω) =2 S( z) 3 ó + + 3 3, S( z) S( ω) 3 2 S( x)= x 2, B(2) K (Cabri!) T( x) S( x) T( x) 2 x + S( x) + = + = = T( x) 3 x 2 3 3 x 2 3 T( ω) = 2 T( z) ó T( ω) = 2 T( z) 3 3 ( S x) hx ( ) = x+ ( T x) 3 ( S x) hx ( )
..2 2 z : ω = L (*) z + z z = z + z =± i. (*) z ( + i)( z+ i) ω + i = + i = z+ z+ z ( i)( z i) ω i = i = z+ z+ ω + i + i z + i i z + = = i ω i i z i z i x i T ( x) = + x i T( ω ) = it ( z) ' O 90 C ' C ' ' C T ( x) C = T ( C ) C C ' w+ i z+ i T( w) = T( z) ó = ( = r ) w i z i A( i), B( i), P( z),q( w) AP : BP=: r, AQ : BQ=: r C A,B ( z z 2 z 3 { z n } zn C A
[ ] [T ] Cabri ( ) Drag z,d example2.html T(x) Cabri ( i)( z i) i ω i = L = + z + ω i z i i S( x) = x i i i S( ω) = is ( z) + S( ω) = i S( z) i ó 2 2 i, S( z) S( ω) 2 90 S( x ) = x i B(i ) T( x) S( x) T( x) 2 i i i x+ i i S( x) = = = T( x) 2 x i 2 2 x i 2 i i T( ω) = i T( z) ó T( ω) = it ( z) 2 2 i S( x) hx ( ) = x T( x) 2 ( S x) hx ( )
..3 3 ) 3z 4 : ω = L (*) z 3z 4 z = z = 2 ( ). (*) z 3z 4 z 2 ω 2= 2 = z z z = = + ω 2 z 2 z 2 T( x) = x 2 T ( ω ) = T( z) + ' C ' C ' T ( x) = + 2 C = T ( C ) x S( x) = x S z = S C ' D T ( x) = S( x) + 2 C, A(2) [P,Q,R, S( x), S( x), T ( x) ]
z z 2 z 3 { z n } zn T(2) = z C A T( z ) ' C n n C A [ ] [T ] Cabri ( ) Drag z,c example3.html
..4. ( c 0 ) c 0 H + : ω = ( a, b, c, d, c 0, ad bc > 0) 2 z = ó cz + ( d a) z b = 0 L(**) 2, 2 (i) (*) 2, α β α, β aα + b aβ + b α =, β = cα cβ aα + b ( ad bc)( z α) ω α = = cα ( )( cα ) aβ + b ( ad bc)( z β ) ω β = = cβ ( )( cβ ) ω α cβ z α = L ω β cα z β x α cβ ( T x)=, k = x β cα T( ω ) = k T( z) ' 2 2 ( cα )( cβ ) = c αβ + cd( α + β) 2 b a d 2 = c cd + = ad bc> 0 L c c ( ) αβ,, k > 0 ( ) αβ,, k =, k ( k = cosθ+ isin θ, k ) () k ( k > 0) () θ ( θ 0) (), ()
(ii) (**) α (i) aα + b ( ad bc)( z α) ω α = = cα ( cz+ d)( cα ) α β 2 ( )( c α ) c d c d ( c d) c( c d ) = c α + α + = α + + α + = + ω α ( ad bc)( z α) z α ad bc z α ad bc ad bc α = β 2 ( cα ) = ad bc c = + ω α z α cα c T( x)=, k x α = cα T( ω ) = T( z) + k ' ad bc > 0, c 0 k 0 () (**)
.2. ( c = 0 ) : ω = ( a, b, c, d, ad bc > 0) c = 0 = ad bc ad > 0 : az + ω = b = a z + b d d d a b = p, = q ad > 0 p > 0 d d : ω = pz + q ( p > 0) L (*) (i) p ( a d) q b α = pα + q α = = (*) p d a ω α = pz ( α) T( x) = x α T ( ω ) = p T( z). : ω = 3z 2 ω = 3( z ) A() 3. (ii) p = ( a = d) ω = z+ q L (*) * (**) ω = z + 2 c = 0
.3. ( ) abcd,,,, ad bc 0 : ω = ( ad bc 0) L (*) ó + ( ) = 0 L(**) 2 z = cz d a z b #. c 0 A, x α cβ α β ( T x)=, k x β cα = T( ω ) = k T( z) L (#) c (B) α T( x)=, k x α = cα T ( ω ) = T( z) + k L (#) 0 c = b a (C) a d ( T x) = x α = x, k = d a d (D) a= d ( T x) = x, T( ω ) = k T ( z) L (#) b k = d T( ω ) = T( z) + k L (#) T ( ω ) = k T( z) k > 0, k k = T( ω ) = T( z) + k