 .       
 


              ,  :    ,       ,     .           ,         ,   .  :      ,        .





 

 .       



 2001, by Leonard Mlodinow

  , , 2013

 2013, Livebook



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           ,    . ,   ,           ,      .       ,    .  :    ?          ,    .    ,             :   .          .

     ,     . -   .        .  ,               --        .        ,          .     ,     ,     .  -        ,    , ,         .        .      ?  ,  ?     ?    ?        ?           .

     ,  :      ,      .    ,   ,    ,  ,   .      .  , ,                 .      ,    .      415           .     ,  ,    ,      ,           .

  ,      ,    , .            ,      :        .          .    ,        ,   ,     .            .       ,   ,   ,                   -,          .            :  .        180,          ?       .              ,    .        .         ,     -,         ,        . , ,   .   ,  ,      .

-   1984    ,  -    ,                  -    .   ,            ,      .         .

 ,     .        .           ,        ,      ,  .    ,    :      ,  ,     .

         -.                 ,  ,     .     ,    ,       .         ,     ,      ,      ,    .      ,       .     ,      ,                 .  ,            .




 I.  





    ?

         .





 1.  


, ,        .          ,    :         .            :  ,   .

  ,   ,       , .. .      ,      .       ,       .   ,    ,  ,      ,   .        ,    ,   .   ,     ,     .          .     ,  , ,       .




 2.  


         .  [1 -             (18651939)     ,  :   ,   ,   , ,       ,   ,              ,        . ,   .]     , -        .       ,    ,                 ,     .  - ?   ,       - , -      ,   .

   .    ,         .      30000   ..   ,      .      .     (   )     8000-     ,      .       ,     ,      .  ,   ,   [2 - Michael Williams, A History of Computing Technology (Englewood Cliffs, NJ: Prentice-Hall, 1985), . 3940.], ,        .

     [3 -        , . 1.]   ,       .  :      ,       ,    ,               [4 - Williams, . 3.].         . ,   ,              2,   .

            ..,               [5 - R.G. W. Anderson, The British Museum (London: British Museum Press, 1997), . 16.].             .    [6 - Pierre Montet, Eternal Egypt, trans. Doreen Weightman (New York: New American Library, 1964), . 18.],         ,  ,  ,     .         ,      ,       ,    .     ,     , III  ,   ,     , :        , ,       .           [7 - Alfred Hooper, Makers of Mathematics (New York: Random House, 1948), . 32.].


* * *

     .       ,         .       :  , ,   , .     ,   ,       ,  .       .         ,        .  3500   ..   -     .       [8 - Georges Jean, Writing: The Story of Alphabets and Scripts, trans. Jenny Oates (New York: Harry N. Abrams, 1992), . 27.].

     ,         . ,      [9 -  ,       . .: W. K. C. Guthrie, A History of Greek Phulosophy (Cambridge, UK: University Press, 1971), . 3435,  Herbert Turnbull, The Great Mathematicians (New York: New York University Press, 1961), . 1.]:    ,  ,    ,         ,     .               . ,   ,     ,    .  ,       ,  : 100% [10 - Rosalie David, Handbook of Life in Ancient Egypt (New York: Facts on File, 1998), . 96.].      ,   - ,       ,   .         ,    .     ,  


/


   3,16     , ..     ,   0,6%.    ,        .

       .        2580   ..         .  -  :  ,  ,     480   ,         .     . -,            -   .

  :                     .                 -             ,    ,    .  ,    ,  ,    [11 -                : James Putnam and Jeremy Pemberton, Amazing Facts about Ancient Egypt (London and New York: Thames & Hudson, 1995), . 46.]    ,     ,     .       .

    ,   ,  ,    .        .        ,     ,    -      , ,   . ,       30-, 40-  50- ,    30  40    . (  -    .) ,  ,     ,   .     ,      ,      .   ,                  ( ,  )               ,    .       .

    ,          [12 -       .: Edna E. Kramer, The Nature and Growth of Modern Mathematics (Princeton, NJ: Princeton University Press, 1981), . 212.].                 .. -    2000  1700   ..  ,      ,    .             .    [13 -       .: Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), . 1122. . : H. L. Resnikoff and R. O. Wells, Jr., Mathematics in Civilization (New York: Dover Publications, 1973), . 6989.]   ,    .

,     -     23400000000000000 ,          .   ,    ,       .              ,     . [14 -     ;    (, 18331863)    . . .],      ,    ,       .          ,    1500 .  ,       .                 [15 - Resnikoff and Wells, . 69.].         ,        .    ,    ,      .

 ,  ,             .  , , ,      ,   ,   , ,      ,    ,    .        [16 - Kline, . 11.].

    .      . ,      :       .  ?   .      .       .     ,  .    ,   ?      .   [17 - . : The First Mathematicians (, 2000); ,        , . 9.].     : 


 = 5


  4


.          ,   ,        ,   ,       - .       :           1481 [18 - Kline, . 259.].

  ,      :      .       ,   , ,   ,          ,   .        3, 4, 5  5, 12, 13,      , 3456, 3367, 4825.             .     1, 2, 12       ,   3, 4, 5   .       ,     ,  ,         ,    .

      ,               .     ,     ,    ,  ,      . ,       ,  ,       ,      a


 + b


 = c


(      ,   b     ). , ,    ,         ,    .      ?  ,    .         ?     ,      .

 ,        ,      ,  ,   .              ?      1,4142129 (  ).          (    ). - ,            ,  ,  ,            : 1,414213562     ,   , -         ,         .    ?      .




 3.   


 ,     [19 -      .: Sir Thomas Heath, A History of Greek Mathematics (New York: Dover Publications, 1981), . 118149; Jonathan Barnes, The Presocratic Philosophers (London: Routledge & Kegan Paul, 1982), . 116; George Johnston Allman, Greek Geometry from Thales to Euclid (Dublin, 1889), . 717; G. S. Kirk and J. E. Raven, The Presocratic Philosophers (Cambridge, UK: University Press, 1957), . 7498; Hooper, . 2738; Guthrie, . 3971.],        ,    ,  ;   ,     2500  .         ,  ,    .    ,          ,    .      560   ..      .   -      ,     551   ..,        .      .

      ,      meander[20 - Meander (.) , , , . . .],     ,     .     2500           .          ,   .         ,       ,       ,            . ,     ,       ,   ,         .

    VII   ..    ,      ;         .

    -           ,      .       ,     .  , ,       ,     .

    ,    ,      640   ..         .    ,          .   ,   ,         ,       ,     [21 - Reay Tannahill, Sex in History (Scarborough House, 1992), . 9899.].  ,     ,  ,     ,     ,      ,   ,     .

        ,  -,  ,     .           ,                         . ,   ,       , ,  .    .        ,        .    V   ..        [22 - Richard Hibler, Life and Learning in Ancient Athens (Lanham, MD: University Press of America, 1988), . 21.].

     .         . ,   ,  ,  ,      .               , .     ,  ,         .   .

,   ,      ,    .  ,          ,      .          585   ..  ,      [23 - 28  585   ..   ;     . . .],         .

     .     ,     ,     .     ,   .   ,        ,     ,   ,         .        [24 - Hooper, . 37.],        .          .      .

               .     ,           . ,        - [25 - Erwin Schroedinger, Nature and the Greeks (Cambridge: Cambridge University Press, 1996), . 81.],         ,    ,    .

      .     ,  ,       .    ,       ,      .        :       ,       ,       .             .    ,    ,      .                , ..           ,       ,   .          [26 - Hooper, . 33.],      ,   .

 ,          .         ,     .       .     ,     .           ,     .

      .  ,    ,    ,         .         .    :     ?    [27 -    .: Adelaide Dunham, The History of Miletus (London: University of London Press, 1915).], ,  ,   . :    ,           ,   ,    , [28 - .: Guthrie, . 5580,  Peter Gorman, Pythagoras, A Life (London: Routledge & Kegan Paul, 1979), . 32.].

     ,    ,         .          ,   .              ,    .     .    18,   .    -               ,      .

 ,              ,         .       ,      .         ,     .

   [29 - Gorman, . 40.]:     ,      ,       ,   .      ,       .   ,  ,   ,      .

 ,     ,        .      ,  ,         .        :          ,        [30 -   (18111872)    , -,      ,  13  1865.:   ,  ,   䅻 . .],   .




 4.  


   [31 -    ,   , .  .: Leslie Ralph, Pythagoras (London: Krikos, 1961).]    ,       .     .   ,  ,   .         .   ,   .  ,     ,   :      ,    ,         .      .           ,   ,     .      .

 ,   -    ,       .  .   ,    ,            .   , ,     .    ,                .

       -   [32 - .: Donald Johanson and Blake Edgar, From Lucy to Language (New York: Simon & Schuster, 1996), . 106107.],         ,    -   ,   .   .           ,        .      ,          . ,  ,  ,           ,   .

           .        ,     .  ,     ,          ,      .. ,   .     ,     ,  ,         : 4, 9, 16  ..  ,   ,   ,   : 3, 6, 10  ..

      . ,   , 4,      , 1 + 3.   , 9,      , 1 + 3 + 5,  .. (      : 1 = 1.)    , ,         ,       ,   .        :         ,   .

     .   ,    ,     ,     ,       .      ,      .

       ,      -  .  .        :           . ,      , , , ,         ,  -   ,      .        - :      ,  , :       .






   



         ?      ,     . ,        ,         . -           ,   ,       .     :         .

          :       .  -      .           :   ,  ,     ,     .            .   ,   ,   ,    ,     ,      .

  ,    .     ,   ,    ,         ,   :      ,   .       .  :       .       ,    ;         (         ).    ,          .       ,        ,     .     ,   ,   ,   , . 43.     ,    ,    -.     ,      ,      -,         ,    ,         .

   .      ,      -   ,      .        ,   ,           ,    .  !

          [33 - Jane Muir, Of Men and Numbers (New York: Dodd, Mead & Co., 1961), . 6.],       ,       .        ໠   , .. , .      ,         ,  ,    ,       XIX.

        ,      .             .

       ,     :   ,    ()   ().       : 1, ,   , 2   , 4   .  4     ,      ,  ,    square deal[34 - Square deal (. .)   ,    ,  . . .].   ,  ,          -   .

     ,       .        ,    ,   ,                   .               .        .               .    ,            .         .          ,   .       .






 



       ,     .   ,     .     , ,   -         .   ,  -        ,     ,  ,    , [35 - Gorman, . 108.].           ,        .         ,          ,  ,  . -      .

   ,   ,            .  ,  ,   ,      -   .  ,  [36 - Gorman, . 19.],     ,     .    ,   .                .       , ,      .     ,     , ,   ,    ,    .          : ,        ,        ,       .  , ,      [37 - Gorman, . 110.].

      -   .  ,  ,     .          ,    (. 560480.  ..).    [38 - Gorman, . 111.],     ,  ,     ,   .                 ,     . ,   -    ,    ,  -           [39 - Gorman, . 111.].

 ,       .      ,        .        ,   ,  ,            .               ,    .          , ,    ,      ,    .      ,            . ,        ,             [40 - Gorman, . 123.].

        ,        .  ,    ,   ,      .       , ,  ,       .

          .          ,     .     .    ,    -    ,     ? , ,   ,         ,         .      .     :     ?  ,  ,      .

-  ,            .  ,                        ,       .          ,        .

    . ,    [41 -     .         ,         , m/n,    m  n   ,         .     . : ,  


 = 2, , m


 = 2n


. : m


   .      , ,  m      . :  m n     , , n   . :    m


 = 2n


   .  m  ,     2q,   q.   m  m


 = 2n


  2q,  4q


 = 2n


,    ,   2q


 = n


.  ,  n


,  ,  n  .   ,        = m/n,  m  ,  n  .  ,  ,  ,       = m/n, .   ,     ,   ,   ,     ,  reductio ad absurdum.     ,     .]        , , ,    ,     .   :  ? ,   ,    ,      ?

   :    - ,  d,      ?2       ,            .    ,      ,       -          .                  ,         .     , ,     .     :        .         ,      ,  ,      ,    [42 - Muir, . 1213.]   .          - , , , ,   ,  -  -     .      ,       ,  .

     .   XIX,         ,    -   ,   ,     ,    ,              . ,     ,   [43 - Kramer, . 577.]         .

     .  510   .. -         ,    .       ;  ,   .         ,        .    .         :    .      .  ,  ,      :    .  500   ..   .  .     ,  :   ,     ;     ,           .

    -       ,    460   ..,      ,    .     300-   ..         . .,        .          , ,    ,    , .  II  ..           .     IV      -  .      [44 - Gorman,  192193.]      ,        ,       .       .     ,         VI ..




  .


   .

   ,     (https://www.litres.ru/leonard-mlodinov/evklidovo-okno-istoriya-geometrii-ot-parallelnyh-pryamyh/)  .

      Visa, MasterCard, Maestro,    ,   ,     ,  PayPal, WebMoney, ., QIWI ,       .



notes








1


            (18651939)     ,  :

		   ,   ,
		   , ,
		    
		   ,
		   ,  
		  
		     
		     ,
		     

   . ,   .




2


Michael Williams, A History of Computing Technology (Englewood Cliffs, NJ: Prentice-Hall, 1985), . 3940.




3


       , . 1.




4


Williams, . 3.




5


R.G. W. Anderson, The British Museum (London: British Museum Press, 1997), . 16.




6


Pierre Montet, Eternal Egypt, trans. Doreen Weightman (New York: New American Library, 1964), . 18.




7


Alfred Hooper, Makers of Mathematics (New York: Random House, 1948), . 32.




8


Georges Jean, Writing: The Story of Alphabets and Scripts, trans. Jenny Oates (New York: Harry N. Abrams, 1992), . 27.




9


 ,       . .: W. K. C. Guthrie, A History of Greek Phulosophy (Cambridge, UK: University Press, 1971), . 3435,  Herbert Turnbull, The Great Mathematicians (New York: New York University Press, 1961), . 1.




10


Rosalie David, Handbook of Life in Ancient Egypt (New York: Facts on File, 1998), . 96.




11


               : James Putnam and Jeremy Pemberton, Amazing Facts about Ancient Egypt (London and New York: Thames & Hudson, 1995), . 46.




12


      .: Edna E. Kramer, The Nature and Growth of Modern Mathematics (Princeton, NJ: Princeton University Press, 1981), . 212.




13


      .: Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), . 1122. . : H. L. Resnikoff and R. O. Wells, Jr., Mathematics in Civilization (New York: Dover Publications, 1973), . 6989.




14


    ;    (, 18331863)    . . .




15


Resnikoff and Wells, . 69.




16


Kline, . 11.




17


. : The First Mathematicians (, 2000); ,        , . 9.




18


Kline, . 259.




19


     .: Sir Thomas Heath, A History of Greek Mathematics (New York: Dover Publications, 1981), . 118149; Jonathan Barnes, The Presocratic Philosophers (London: Routledge & Kegan Paul, 1982), . 116; George Johnston Allman, Greek Geometry from Thales to Euclid (Dublin, 1889), . 717; G. S. Kirk and J. E. Raven, The Presocratic Philosophers (Cambridge, UK: University Press, 1957), . 7498; Hooper, . 2738; Guthrie, . 3971.




20


Meander (.) , , , . . .




21


Reay Tannahill, Sex in History (Scarborough House, 1992), . 9899.




22


Richard Hibler, Life and Learning in Ancient Athens (Lanham, MD: University Press of America, 1988), . 21.




23


28  585   ..   ;     . . .




24


Hooper, . 37.




25


Erwin Schroedinger, Nature and the Greeks (Cambridge: Cambridge University Press, 1996), . 81.




26


Hooper, . 33.




27


   .: Adelaide Dunham, The History of Miletus (London: University of London Press, 1915).




28


.: Guthrie, . 5580,  Peter Gorman, Pythagoras, A Life (London: Routledge & Kegan Paul, 1979), . 32.




29


Gorman, . 40.




30


  (18111872)    , -,      ,  13  1865.:   ,  ,   䅻 . .




31


   ,   , .  .: Leslie Ralph, Pythagoras (London: Krikos, 1961).




32


.: Donald Johanson and Blake Edgar, From Lucy to Language (New York: Simon & Schuster, 1996), . 106107.




33


Jane Muir, Of Men and Numbers (New York: Dodd, Mead & Co., 1961), . 6.




34


Square deal (. .)   ,    ,  . . .




35


Gorman, . 108.




36


Gorman, . 19.




37


Gorman, . 110.




38


Gorman, . 111.




39


Gorman, . 111.




40


Gorman, . 123.




41


    .         ,         , m/n,    m  n   ,         .     . : ,  


 = 2, , m


 = 2n


. : m


   .      , ,  m      . :  m n     , , n   . :    m


 = 2n


   .  m  ,     2q,   q.   m  m


 = 2n


  2q,  4q


 = 2n


,    ,   2q


 = n


.  ,  n


,  ,  n  .

   ,        = m/n,  m  ,  n  .  ,  ,  ,       = m/n, .   ,     ,   ,   ,     ,  reductio ad absurdum.     ,     .




42


Muir, . 1213.




43


Kramer, . 577.




44


Gorman,  192193.


