047 Η ΛΕΞΑΡΙΘΜΙΚΗ ΘΕΩΡΙΑ 1
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Λεξαριθμικη θεωρια
Transcript of 047 Η ΛΕΞΑΡΙΘΜΙΚΗ ΘΕΩΡΙΑ 1
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( . ) ( , 1976): [email protected] .: www.hellenes-markatos.gr
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, , , , , , .
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27 , 24 . (), () () .
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, . , : ... ===> +++...+ .., = +++++ = 20 +70 + 200 +40+70+200 = 600..: .
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, ( -) ( ), . , : .., + > + > + > :.., + > > .
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, (, , ) , ( ) ( ). , ( ) ( ). , ( ).
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(.) ( ) (,, ), : (.) 66 ( ): , , , , , , , -, , , , , , , , , , , . , , .
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4 :
1: (, , ): = = 430 = = 1160 = = 324 = =284 = = 725 = = 600 > 430, 1160, 324, 284, 725 600 ..: ()
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2: (, , ), ( - ): .., (=1) =501 =500 = 891 = 890 (), : (+) ( =1, + (, , ) (, , ). : ( ) (+) ().
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Fibonacci ( ): 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 610,... (1+1=2, 1+2=3, 2+3=5, ..., 144+233=610 ...)> : 1/1, 2/1, 3/2, 5/3, 8/5, ... : =(1+5)/2 =1, 6180339... . () :[ (47), = (76), = (123), = = (199), = (322), (521), - (843), (1364)]. Fibonacci:47+76=123, 76+123=199, 123+199=322, ...
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3: (, , ), - : (-2) / (-1) = (-1) / () =3, 4, 5...
1 +2 = 3 2 +3 = 4 3 +4 = 5 ............................................(-2)- +(-1)- = -
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( ) = (1+5)/2 1,6180339...
2 /1 3 /2 4 /3 5 /4 ...................................................................- / (-1)- .
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4: (, , ), : (8 / 1 = 2): : - . .. : [ (185), (370), = (740), (1480), (2960)]> 1852=370, 3702=740, 7402=1480, 14802=2960 > , (, . .) , (, ( ) .
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(. 72, 72, 360), 1 - 1 ( 1) - ( - ), . 2, 3, 4, 5... : 1 > 2 . 2 > 3 . 3 > 4 . 4 > 5 . , . 46 , (. 72, 72, 36).
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():
, , . , , , , . (, , ). , , .
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1: , , , ..., : () .., ()
: : ( ), ( ) ( ).
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2: . ( ), , , , , ,,,,, .
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===> ( )
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3: - . = = 1264 () , , , ( ) . ( )
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3.1: :* (, , ) ( ).* (, , ) ( ).* (, , ) ( - ). (, , ) () ().
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: , : : : :
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3.2: , , : .., [ (105), (169), (274), (443), (717), (1160), (1877), ...]105+169 = 274, 169+274 = 443, 274+443 = 717,443+717 = 1160, 717+1160 = 1817, ... > .
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1: - (), (): 1, 2, 3, 4 5 ().
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: 1 ==> . 2 ==> . 3 ==> . 4 ==> . 5 ==> . : ==>
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2: , () , : () - ().
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() 66 1--> (66): , . 2--> (66): . 3--> (66): , . 4--> (66): . 5--> (66): . 6--> (66): , . ==> : ( ) , , .
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: . (). ()
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- , - , ( , ) , . . , , .
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: (+) , : = + () = > () ., .: : () : ()
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: ( ), , , ().531 = 1+530 = + () = (+)
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891 = 1+890) = + ()= (+) > () : - , , (), - ( ).
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2091=1+2090 + ( ) = (+ ) . : , . >
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:( : ;) , . , . ). ; , .
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- () ( - Fibonacci) , ( ) :
[(291), (470), (761), (1231)].
> 470/291=1,615, 761/470=1,619, 231/761 = 1,618 .
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( ) = 328, = 531 : 203, 328, 531, 859, 1390, 2249, 3639, > 531/328 = 1,619 . , () , (), (, ).
> , , .
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, (DNA), () (), : (DNA). () ()
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= ( -) = ( , -)= ( )= - = 795) ( ]. , , - . , , .
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= = 725 (. ) . :1. : . 2. ( ): - . - , ( ( ). > - .
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() (725) [ (106) (), ( )= (171) (), (277) (-), = (448) ( -), (725), ( ) = ( ) = - (1173) ( ), - (1898) ( ) = (1898) ( )] > , , FIBONACCI:106+171=277, 171+277=448, 277+448=725, ...
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= = 471 - , - . .
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[ (621), (1004), (1625)]. [ (683), = (1105), (1788)]. [ (616), (996), (1612)]. [( (776), (1255), (2031)]> , , - FIBONACCI:621+1004=1625 // 683+1105=1788 616+996=1612 // 776+1255=1255
() DNA
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: 25 41 66 107 173 280 ... , ( , - ), ( , .. ), - , ...
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() (289): [ (179), (289), (468)] : > (, - ) , , .
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() (179): [(111), (179), (290), ( (469)]. : > , () ()..: ( ), ( ). ( ), , ().
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[(116), (187), = - (303), = (490), = (793)] : () , () .
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() - (). - ( ; ), - - . - .
