Home >Documents >Grupuri de Simetrii

Grupuri de Simetrii

Date post:14-Oct-2015
Category:
View:45 times
Download:1 times
Share this document with a friend
Transcript:
  • 5/23/2018 Grupuri de Simetrii

    1/43

    http://find/http://goback/
  • 5/23/2018 Grupuri de Simetrii

    2/43

    S

    S

    ( , )

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    3/43

    S

    S

    ( , )

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    4/43

    P

    : P P R

    ( , ) , , P ( , ) = =

    (

    ,

    ) =

    (

    ,

    )

    ( , ) ( , ) + ( , ), , , P ( , ) = ( , ) + ( , )

    P

    : P P

    ( ( ), ( )) = ( , ), , P.

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    5/43

    P

    : P P R

    ( , ) , , P ( , ) = =

    (

    ,

    ) =

    (

    ,

    )

    ( , ) ( , ) + ( , ), , , P ( , ) = ( , ) + ( , )

    P

    : P P

    ( ( ), ( )) = ( , ), , P.

    http://find/http://goback/
  • 5/23/2018 Grupuri de Simetrii

    6/43

    O( )

    O( ) =

    M

    (R) | = =

    =

    ( ,R) | =

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    7/43

    O( )

    O( ) =

    M

    (R) | = =

    =

    ( ,R) | =

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    8/43

    O( )

    O( ) =

    M

    (R) | = =

    =

    ( ,R) | =

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    9/43

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    10/43

    F

    F P P F : P P F

    (F) = F

    F P P

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    11/43

    F

    F P P F : P P F

    (F) = F

    F P P

    http://find/http://goback/
  • 5/23/2018 Grupuri de Simetrii

    12/43

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    13/43

    = { ,

    ,

    ,

    }

    = <

    ,

    = , >

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    14/43

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    15/43

    D

    , , , , , , , ,

    =

    , ,

    D

    =

    , , , = , , , ,

    = =

    = = = =

    = =

    =

    =

    =

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    16/43

    D

    , , , , , , , ,

    =

    , ,

    D

    =

    , , , = , , , ,

    = =

    = = = =

    = =

    =

    =

    =

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    17/43

    D

    , , , , , , , ,

    =

    , ,

    D

    =

    , , , = , , , ,

    = =

    = = = =

    = =

    =

    =

    =

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    18/43

    D

    , ,

    = () = = ,

    = ( ) = = ,

    = (

    )

    =

    =.

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    19/43

    D

    C =

    , ,

    ,

    =< >

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    20/43

    D

    C =

    , ,

    ,

    =< >

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    21/43

    C

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    22/43

    D

    =

    = ,

    = =

    D

    =

    , , , , ,

    = () = =

    = ( ) = =

    D

    http://find/http://goback/
  • 5/23/2018 Grupuri de Simetrii

    23/43

    D

    C

    =

    , ,

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    24/43

    C

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    25/43

    D

    =

    , , , , , , , , , ,

    , = ,

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    26/43

    C

    = { , , , , }

    D C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    27/43

    , , , , , , , ,

    D

    =< , >

    C

    =< >

    D

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    28/43

    , , , , , , , ,

    D

    =< , >

    C

    =< >

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    29/43

    = =

    (

    )

    =

    ,

    ,

    = , , .

    D

    =< > C

    = { }

    D

    =< , , = >= C = { , ,}

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    30/43

    = =

    (

    )

    =

    ,

    ,

    = , , .

    D

    =< > C

    = { }

    D

    =< , , = >= C = { , ,}

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    31/43

    = =

    (

    )

    =

    ,

    ,

    = , , .

    D

    =< > C

    = { }

    D

    =< , , = >= C = { , ,}

    D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    32/43

    = =

    (

    )

    =

    ,

    ,

    = , , .

    D

    =< > C

    = { }

    D

    =< , , = >= C = { , ,}

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    33/43

    N D

    C

    D

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    34/43

    N D

    C

    D

    C

    http://goforward/http://find/http://goback/
  • 5/23/2018 Grupuri de Simetrii

    35/43

    N D

    C

    D

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    36/43

    C

    D

    D

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    37/43

    C

    D

    D

    C

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    38/43

    C

    D

    G P

    G

    G

    G= C

    = { }

    , G, , =

    , G =

    ,

    , , , G

    G

    N : = G = G

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    39/43

    N : , = , G

    , = , G

    ,

    G

    , G, N

    =

    ,

    = ,

    ,

    G=< ,

    >= C

    , ,

    =

    G

    G

    C

    = { , , , } G

    N : = G = G

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    40/43

    N : , = , G

    , = , G

    ,

    G

    , G, N

    =

    ,

    = ,

    ,

    G=< ,

    >= C

    , ,

    =

    G

    G

    C

    = { , , , } G

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    41/43

    G ,, , ,

    =

    G=

    G=

    , , , ,,, , ,

    =

    G=< >= D

    >

    , , G= D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    42/43

    G ,, , ,

    =

    G=

    G=

    , , , ,,, , ,

    =

    G=< >= D

    >

    , , G= D

    http://find/
  • 5/23/2018 Grupuri de Simetrii

    43/43

    http://find/

Click here to load reader

Reader Image
Embed Size (px)
Recommended