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  1. #1
      Eiman
    Jul 2011
    -
    14,750

    ɡ . ǡ ǡ .







    :

    ɡ .



    ABC C [AB] ѡ AB=c AC=b BC=a. :







    . : b=3 a=4





    ɡ (5 4 3) .




    ( 47 ):

    ˡ . ڡ .

    . :

    ABC AC+BC=AB C.



    ɡ . . ʡ ( ) (5 4 3) . .

    ( ) (2500 ). ( Plimpton 1800 ) 1000 ɡ .

    ɻ ɻ () ɻ .


    ڡ . :

    ɡ .

    : .

    ߡ Proclus ( 400 ) Proclus .

    . . 1 2. 2 . .

    ʡ . ʡ Zhoubi suanjing. ݡ Han Dynasty ( ) (206 ϡ 220 ) Zhou Dynasty. ( ϡ 256 ). ɡ Gougu ( ) Jiuzhang suanshu ( ʡ 100 ϡ 50 ) .

    ( ɡ ).

    ɡ : . : an + bn = cn 1994 (: Andrew Wiles).

    ɡ ӡ ϡ (: James Abram Garfield). : .



    ߡ ( Quadratic reciprocity). :



    ӡ . ( 35 ) :

    ɡ .




    ABCD BCFE [BC] (BC) (AF) AD=BC ( ABCD) BC=EF ( BCFE) AD=EF.

    ( ) E D : E D D D. :

    1. E D [ED] [AD] [EF] AD EF . [AB] [DC] ( ABCD) D E A F ɡ . BAE CDF . ABCD CBEF BEDC BAE ( CDF).

    2. E D BAE CDF ABCD BCFE BAE ( CDF) BCD.

    3. E D AD=EF DE AE=DF. 1 2 BAE CDF BADG CGEF . ABCD CBEF BCG BADG ( CGEF).

    . :

    ɡ .

    ABCD E (AD] [AD]. ABCD BEC. [AC] ABCD ABC. ABC BEC ( ). BEC ABC ABCD. ABCD BEC



    :




    ABC A. ABFG ACIH BCED AB AC BC . J (BC) (AK). BCED ABFG ACIH. ABFG BJKD ACIH CEKJ.

    FB BC AB BD . ( \ ( . ɡ FBC ABD . XLI ABFG FBC BJKD ABD. ABD FBC ABFG BJKD.

    : IC CB AC CE [\widehat{ICB}] [\widehat{ACE}] ICB ACE . ACIH ICB CEKJ ACE ICB ACE ACIH CEKJ.

    BCED BJKD CEKJ ABFG ACIH. .
    .......

  2. #2

    Jul 2011
    -
    936



  3. #3

    Mar 2012
    127





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