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: , 1. .
2. , , . , , , - , 3, , 4 , 5 . - 6, , , , . 7.
, , . 8 9 . 10. ; . , , , , , .
:
. ... .... ( ), ,....
, , 286 , 10-15 , , .
. ( )
, 986
1 , , . ( . , , ,26)2 - . , .3 . , , , 81, 15-254 >1.5 . , ( )6 . , , 58-59 , 142 ..7 . , , 142 . , , .8 , , . . .9 . www.live-pedia.gr 10 , . , , , , . , , . . http://oasigr.5.forumer.com/a/_post503.html ( )
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( ) . ;
. . . 189
11 , , , . - , 12
. , ( )
, 1002, 30-35
. , 13
, 1072, 25-30
: , , 14, , , . . , , , .15. , 16. , , - - 17.
, ,
11 . 152 e . (153 )12 . www.padamakos.gr http://users.otenet.gr/~adampan/ / , , , , 5 .. , , . : . ; ; ;13 : , ( ) ( ).14 , .. , , . 18, 19 .15 .16 , .17 : ,
, 1084, 40 , . 21 , .
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18, 19. , , 20 . ,
. . , . 118
; , , 21. , . ; ; ; 22; ; 3,4,5 ; 23 ; ;
:
. . , , , , ,
, 1079, 30-40 1080, 20
, . ; , , ; , . , , 24, , , , , .
18 / , , .19 ( - )20 .21 . , , 9922 , , ( 7 , . . 7 , 7 )23 , , , - : , . , , , . : , , .24 e . !
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, . ( , )
, , - , . . ;
, , .
. , . , .
: , , (3,4,5) . , , . , 25. , . , . , ( ) , . , . . !
= hc
e 2(
1371 )
e, h, c, G e=1.602*10 -19 C, h=6.626*10 -34 J.s, c=2.998*10 8 m/s, G=6.673*10 -11 m3.Kg -1.s-2
: , , , 26, - - , , , . , , , 35. T , , , , .
1 (1,3) (3,4,5)1 (1,3) - 27 (3,4,5) ( ),
: , : 1,3,5 28 1,3,3 1,3,4 ( 29) , (3,4,5).
25 . . . 6 1,2,3 1+2+3=626 - : , 27 , , 57-58-5928 , , . , 51, 20-25 .[ : 1 3 , 5( , 1,3,5), 4 ( 1,3,4), . 1,3,3 , 3 . .29 , , 16, 5. (= )
4
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30 . 1. .
, .. , , 29, 25. . , , . + , + ( - - ) . , 3.
( ) 31
, . 396 b. , , o T . . , , ( ), . 405-406 , 51 55. , . 30,31 - .
, , , , ( )
( - ) ( - ), ( ) , . .
.
30 , ,114. , , , .31 ( ) . , , . , .
. , 16-17 15
1
. , 1 . , 3, ( )
(1,3) ,
29, 30, 35, 37
1 1 1
. ( )
1, 3, 5 1,3, 31,3 ,4
5
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:
(,,) ,, , (,,)=1 2+2=2 ,
( , ) 1.
=3 : 3 2+2222
213
213
+=
(3,4,5)
=5 (5,12,13) . .
6
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2222
2 14
14
+=
+
( = .4)
/ ( , )
( , , ) ( + )/4 +(-1) ( * )
1 1,3 5,4,3 (5+3)/4=2= 2.1 2 2
2 3,5 17,8,15 (17+15)/4=8= 2.2 2 6
3 5,7 37,12,35 (37+35)/4=18= 2.3 2 6
4 7,9 65,16,63 (65+63)/4=32= 2.4 2 10
5 9,11 101,20,99 (101+99)/4=50= 2.5 2 10
6 11,13 145,24,143 (145+143)/4=72= 2.6 2 14
7 13,15 197,28,195 (197+195)/4=98= 2.7 2 14
! , , . . 7 , 32.
( ) 33, . , (1,3) . . . . (1) - (3). , (1,3) .
, , .
. , : , , (2)
32 . , 391 F33 , . Highs, . , - , , . . . , , , , .
8
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(2) =2
22 + , =2
22 = .
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34, -
. : ,
- , . 30, 20-25. ,
, .. , , . , , 35. , , , , , , . . 36 , 10, , 386. , 5. , () . 5, , 5 , : .
. . 37, , , . , . , , , , 38. . , , , . . , 39.. . , , , , . . 40;|=1 ||=2, |||=3 , ||||=4, =5 , |=6, ..., =10, |=11, ||=12,. |||=18,
5 . , , ,
34 . . . , . ( = ). , , , , ! ( . ( ), . , 11)35 ( ) , , 391 C36 37 , .38 . , , . , , . , , 385-38639 , , , , 391 D40 - 1 | .
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. , .
, , , , 1 3, , (1,3) . . | |||,
, , . . 1 3. . ;
41 . , , , , , , , ! , , .
. , 1, .( ) . , . . 189. , . ( . 44, F 309)
, , , " " , , 1, (1,3) , 6. : , , 391 c.
, , ,
. , , , 81, 15-25
41 ...
,
.
11
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12
(1,3)
72 o
216 =
216 3
0 72
3 , ( 63)
72=
; !
!
,
!
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( ) .
, , (),
, . . , . : 1 (1,3) (3,4,5) , (1,3) (3,4,5) (2) . (3,4,5) , (3 , 4 , 5 ) , : (3,4,5), (6,8,10),(9,12,15), (12,16,20), (15,20,25), (18,24,30), (3,4,5). : 1 (1,5) (5,12,13) : (5,12,13), (10,24,26), (15, 36, 39), (20, 48, 52), (25, 60, 65), .,
(5,12,13).
, , : .
( ) ( ) .
- , , , (5,12,13) :(10,24,26), (15, 36, 39), (20, 48, 52), (25, 60, 65), .. .
, , , , - .42 , , - . ;
, . , ! , , , - , . () , .
E ( .)
3 : 42 . . , 60 87. () .
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31. (,,) :
=+ ()
43
( )
33. () [] ( ). (,,) ( , ) :
+ ,
21,
21 22 (1, ).
():22
2..
2..
...
+=
+ . . 254 , . .
, .
53 - .
() []:( )
( 5,4,3 ) (5,4,3) 44 - ( ) - ( ) - (17,8,15) :
=+
:
53
81715 =+ 5
32515 = [] : [ ]
22
25.325.15
25.325.15
5.3.25.15
+=
+ 752+180 2=195 2 - (13,
12, 5), (75,180,195)=15
- (37,12,35) :
=+ :
75
123735 =+ 7
54935 = [] :
22
25.735.49
25.735.49
5.7.49.35
+=
+
245 2 + 840 2 = 875 2 - (25,24,7) 3 (875,840,245)=35, (65,16,63) (41,40,9) (101,20,99) (61,60,11) (145,24,143) (85,84,13) (197,28,195) (113,112,15)
, , - , , ! www.padamakos.gr http://users.otenet.gr/~adampan , - , , , , , , .
43 . !44 () ()
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, . (), . , ( ) . ( ,,) ,, 2+2=2 6, , (3,4,5)
(2) .
=2
22 + , =2
22 = . 2=2+2 , . .( + )( - ) 24 . , 3, : . .( + ).( - )= .( .3).( .4).( .2)= .24 . .( + ).( - )= .( .3).( .2).( .4)= .24, 1, + - 2 .4 ( . 1)
. , 3, =3+1 =3+2 =3 +1 =3 +2, :. =3+2, =3 +2. =3+2, =3 +1. =3+1 , =3 +2. =3+1, =3 +1 , + =3+2+3 +1= .3, - =3+1-3 -1=3 -3 = .3 - =3+2-3 -2=3 -3 = .3 + , - .3, . ( + ).( - )= .24 2
{ . . + = .3, : . ( + )( - )= . [( .3).( .2)]( .4)= .24 . ( + )( - = . [( .3).( .4)]( .2)= .24,
15
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( + ),( - ) 2 4 ( 1), - = .3},
E=( + )( - ) /4 = .24/4= .6
. . , . 46 .-
.- . 2002 .
12 = = = 12 , 12 , 12 .
: , 6, , .
: 3, 24
: , , , , ., , , , , , , , ,, (3,4,5) , 6, - , , .
.
5. (2). :..= . .
2.
2
2222 +. 5 .
=5 +1, =5 +2, =5 +3, =5 +4 =5+1, =5+2, =5+3, =5+4
=5 +1 =5+1, 2- 2= ( + )( - )= .5 =5 +1 =5+2, 2+ 2= .5 =5 +1 =5+3, 2+ 2= .5 =5 +1 =5+4, 2- 2= .5
5 .
, 5.12=60 45
45 ., , , 6, 12
16
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: . ! ! - !
1 2 3 4
, , , . . . , , . , , .
A
A
5
3
46, . , . .
: =3,2 =1,8 =1,08 =1,44 =1,92 =2,56 =1,44 =2,4567 =0,77776 =1,3824 =1,3824
: 16049382,37776,04567,22
1==
=
1=1,777777777
777777,13824,14567,122
2==
=
46 ,
17
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2=1,333333333
13824,13824,12
3==
=
3=1 1, 2, 3 . : 100( 1. 2- 3)=137,0368741 !
, , .
. , , .
, ,
.
. - . . , . ;
. . ; . , , .
, . . . ,
Highs , , , , , .
, , , , . , , . .
. - - , , , . .
, , , , , . . 47 , , , , .
- - , , , .
; - . , , .
47 , , 39, 5
18
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. . , , , , , . , () ( ), Highs. 48
. , . . . 49, , , , , . , . , , , , . 156 . 50.
. . 51 . .
, . , , , . ,
. , ( * ) . , , . . , , , , , , . . . , , . , . , , . , . ,
, . , , . .
(**) , , , ,
37, 10-11 . , .
48 49 13, 222b 15-16. . . 41, . 50 51 . 84-85
19
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( * ) ( ), (1,3 ). ,
(**) .
, , 52. . ( ).
, . (2) , . . , , . . . () () . ,
. , , .
52 . , , . . +2 -2. (+2-2=0). ( ). , : , , , .
. , . , , . . , , , . . . , . . .