Eykleidhs a 117_eykleidhs_2020
- 1. 了了侶僚旅虜流 留慮侶亮留旅虜流 留旅竜溜留
117虜了竜溜隆侶
亮僚略旅凌
E
留慮侶亮留旅虜 竜旅凌隆旅虜 粒旅留 凌
痢立
里裡
痢立
里裡
里留.留竜溜凌
..
里留.留竜溜凌
..
旅慮亮隆竜旅留
4156
旅慮亮隆竜旅留
4156
里HellenicPostHellenicPost
里立
里離裡里痢.裡1099/96..里離裡里痢.裡1099/96..
離裡 - 離離裡里裡 - 裡里痢裡 2019 竜 3,00
虜流竜旅 竜亮竜溜留 亮竜 ... 留溜竜侶虜流竜旅 竜亮竜溜留 亮竜 ... 留溜竜侶
Blaise Pascal (1623-1662)Blaise Pascal (1623-1662)
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- 2. 里 痢 痢陸痢裡裡
粒旅留 凌 粒亮僚略旅凌
虜了竜溜隆侶 留
痢律痢律
里竜凌 171
里旅亮流 里竜凌 3,00
e-mail: info@hms.gr, www.hms.gr
凌了旅凌 - 粒凌凌 - 裡竜劉亮硫旅凌 2020
留僚竜旅侶亮溜凌 34
里侶了 210
僚略粒凌 陸竜了了凌侶
留僚留粒旅ﾏ侶 凌留
.: 210 3617784 - 3616532
Fax: 210 3641025
虜隆侶
旅竜慮僚流
裡僚凌僚旅劉:
裡僚留虜旅虜流 旅凌流:
凌虜竜僚亮劉僚凌旅 僚竜粒略竜
竜凌粒了凌 裡劉留僚凌
里旅留僚留了了凌 僚隆劉留
陸竜竜僚溜僚凌 裡溜隆僚
隆留硫略僚侶
旅留亮留僚溜隆侶 侶亮流旅凌
凌粒旅略虜侶 略僚僚留
旅留虜凌凌了凌 慮留僚留溜留
留粒 竜ﾏ粒旅凌
亮竜凌了凌 竜ﾏ粒旅凌
略了了旅留侶 律流凌
旅虜凌了凌了凌 略僚僚侶
留了留旅凌粒旅留僚僚溜隆侶 侶亮流旅凌
留留隆略虜侶 僚僚留
留留略僚僚凌 侶亮流旅凌
裡溜虜凌 留溜留
里龍溜留 旅虜了留凌
里旅虜凌凌了凌 裡略亮侶
律旅凌了凌 留僚留粒旅ﾏ侶
竜粒旅略隆凌-留亮凌溜隆侶 留硫略留
旅ﾎ確穎 律流凌
凌凌了凌 留了了旅侶
留留隆略虜侶 留了硫溜僚留
痢溜龍凌 略僚僚侶
痢凌凌了侶 留溜留
留了了旅侶
旅亮劉了竜旅留 虜隆凌侶:
隆留硫略僚侶
凌粒旅略虜侶 略僚僚留
留粒 竜ﾏ粒旅凌
留了了旅侶
竜凌粒了凌 裡劉留僚凌
里旅留僚留了了凌 僚隆劉留
里裡 侶
裡 里裡 里痢裡
虜侶:
里 里痢
裡凌旅竜旅凌慮竜溜留 裡竜了旅隆凌凌溜侶侶:
ROTOPRINT ( ).
: 210 6623778 - 358里
A. 凌留了侶 & 裡
. 留留隆凌了凌
離竜慮僚凌 里凌粒留竜溜凌:
l
l
里留 隆旅留侶亮旅龍亮竜僚留 硫旅硫了溜留 隆竜 侶亮留溜僚竜旅 旅 凌竜溜僚凌僚留旅 侶僚 ...
旅 僚竜粒留溜竜, 留 略慮留, 凌旅 凌竜旅僚亮竜僚竜 留虜流竜旅, 凌旅 了竜旅 留虜流竜僚 虜了. 劉竜旅 僚留
劉了僚凌僚留旅 劉粒虜留旅留, 留 粒留竜溜留 侶 ... 亮竜 侶僚 竜僚隆竜旅両侶 束旅留 凌僚 虜了竜溜隆侶 . 里留 竜旅粒留留
隆竜僚 竜旅劉凌僚留旅. 了留 留 略慮留 虜竜旅留旅 竜 虜溜侶
(10,00+2,00 里留隆凌亮旅虜略=12,00 竜)
10,00 竜
里凌 留僚溜旅亮凌 粒旅留 留 竜侶 凌 留留粒粒劉了僚凌僚留旅 劉了僚竜留旅:
流旅留 僚隆凌亮流
流旅留 僚隆凌亮流 粒旅留 裡凌了竜溜留
里旅亮流 竜凌: 竜 3,00
1. 里略竜龍留
ALPHA
EUROBANK
留了流留隆凌亮旅虜流竜旅留粒流
粒留竜溜留
了凌粒留旅留亮 竜080/48002300 GR 87 0110 0800 0000 0804 8002 300
2. ,10100200201998GR8601401010101002002019988
3. ,0026.0201.94.0201575138GR9002602010000940201575138
4. M竜 竜隆旅留留粒流...里留留竜溜凌54里..30044
5. 了侶ﾎ塾杵留旅留 侶..
粒留侶凌溜 / 劉 留僚留粒僚ﾏ竜 留僚留粒僚ﾏ旅竜.
旅虜略 竜亮留竜 竜 了竜 虜留旅 了凌 僚留 竜溜僚留旅 留留粒粒旅虜流 虜留旅
隆侶亮旅凌粒旅虜流 侶 僚劉留 凌了旅虜流 虜溜 亮 亮竜 粒竜溜留. 裡凌 竜凌 留 凌僚
ﾏ凌 了粒凌 劉凌僚 留 留慮侶亮留旅虜略 凌 凌了竜溜凌.
慮留 隆旅留旅ﾏ竜竜 略竜旅 略慮凌僚凌 了旅虜 亮竜 凌硫了流亮留留 虜留旅
留虜流竜旅 粒旅留 了竜 旅 略両竜旅 虜留旅 了留 留 竜溜竜隆留 隆虜凌了溜留.
劉硫留旅留 隆竜僚 了竜溜凌僚 虜留旅 留 略慮留 粒竜僚旅虜凌 竜僚隆旅留劉凌僚凌 留 侶僚
旅凌溜留 僚 留慮侶亮留旅虜ﾎ, 留 留慮侶亮留旅虜略 侶僚 劉僚侶 留了了略 留虜亮侶 虜留旅
凌旅侶旅虜劉 隆侶亮旅凌粒溜竜 留僚留粒僚ﾎ 亮留.
亮留竜 僚留 竜略竜竜 劉僚留 留留了流 虜留旅 竜略旅凌 竜旅亮ﾎ塾.
虜 亮劉凌 侶 凌 竜旅凌隆旅虜凌
凌 竜旅凌隆旅虜凌.
裡僚留虜旅虜流 竜旅凌流
凌亮略隆留 僚凌僚旅亮凌
裡 里裡 裡 里裡 里痢裡
隆旅虜 .里. : 2054
ISSN: 1105 - 7998
裡僚留虜旅虜流 旅凌流
劉粒虜留旅侶 了侶亮流 侶 僚隆凌亮流 凌侶慮略竜旅
侶僚 劉虜隆凌侶 凌 竜旅凌隆旅虜凌
離凌侶旅虜流 里留隆凌亮旅虜ﾎ 離侶竜旅ﾎ
略亮亮留 侶 裡僚留両侶
里Hellenic PostHellenic Post
留慮侶亮留旅虜略 凌僚 亮凌
凌溜留 僚 留慮侶亮留旅虜ﾎ
里留 留慮侶亮留旅虜略 凌 裡凌了竜溜凌
里留 留慮侶亮留旅虜略 凌 裡凌了竜溜凌
留慮侶亮留旅虜凌溜 旅留粒僚旅亮凌溜
旅略凌留 律 隆旅略凌留
= 里略両侶
竜略 溜粒僚留 侶僚 留溜留 了了略隆留
虜留旅 侶 亮竜了劉侶 僚 旅粒ﾎ熟僚 流亮竜留.
2
凌侶亮劉僚留 慮劉亮留留 粒旅留 了凌. 里略両侶
32
留溜留 裡溜虜凌
旅亮劉了竜旅留: 裡劉留僚凌 竜凌粒了凌
.............................................................. 8
.....................................
虜流竜旅 竜亮竜溜留 亮竜 ... 留溜竜侶
5留溜留 痢凌凌了侶, 旅ﾏ粒凌 留留劉侶...............................
粒留 虜留旅 侶亮劉竜 凌
1
Blaise Pascal (1623-1662)
旅ﾏ粒凌 留粒凌隆略虜凌 ....................................................
留慮侶亮留旅虜凌溜 旅留粒僚旅亮凌溜
................................... 33旅亮劉了竜旅留: 旅凌流 旅留粒僚旅亮ﾎ
亮旅了流凌亮竜 粒旅留 侶僚 竜僚旅虜流
37
留慮侶亮留旅虜流 凌溜侶侶
37
1凌 亮僚略旅凌 亮留凌溜凌
45
旅留虜竜隆留旅虜略 留慮侶亮留旅虜略,
48
Feynman
侶亮流侶 留留略僚僚凌 溜隆侶
略僚僚侶 痢溜龍凌, 慮侶僚留溜凌 略僚僚留
留慮侶亮留旅虜: 留竜溜僚留 痢凌亮流
留僚留粒旅ﾏ侶 律旅凌了凌
..................................
....................................
.....................................
...........................................
=
=
=
里略両侶
里略両侶
里略両侶
旅亮竜旅旅虜流 旅隆旅侶留 凌 凌了了留了留旅留亮凌
劉慮凌隆凌旅 凌了凌粒旅亮凌 竜留粒ﾎ熟僚 虜留旅
竜留粒僚旅虜ﾎ 旅龍ﾎ
14
凌侶亮劉僚留 慮劉亮留留 粒旅留 了凌. 里略両侶
19
里留侶竜 - 留留粒凌僚凌凌溜侶侶. 裡竜 旅 侶旅亮竜凌僚
2
留了了旅侶 隆留硫略僚侶, 律流凌 略了了旅留侶
裡了旅留僚 留留粒虜略虜侶, 僚隆劉留 里旅留僚留了了凌
旅亮劉了竜旅留: 裡劉留僚凌 竜凌粒了凌
裡劉留僚凌 竜凌粒了凌, 略僚 旅留虜凌凌了凌
.........................
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4
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100
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95
100
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100
- 3. 117 (2020) .1/1
Blaise Pascal
(1623-1662)
β E.T.Bell
=================================================================
4 Pascal : , ,
Antoinette Pascal
, Blaise
Etienne Pascal
Gilberte Jacqueline .
1631 .
. 12
.
,
.
.
14
Mersenne.
束 Mersenne損
.
16 (1639) 束
, ,
. ,
損
- 6. ----------------------------------------------------------------------------------------- Blaise Pascal -------------------------------------------------------------------------------------
117 (2020) .1/4
de M辿r辿 , ,
6 4
24 ;
Chevalier de M辿r辿
6 1/6,
1/36, , 4 , 4/6
6. 24 ,
24/36 . ,
. ,
, ;
,
Pierre de Fermat (1608-1665). Fermat
,
.
,
.
.
Chevalier de M辿r辿 Fermat
laise Pascal,
.
Pascal
.
.
!
Pascal 19 1662. 39 .
( Pascal Pa) ,
Pascal.
E.T.Bell 束 損 Pascal
束 Pascal
,
.損
- 7. 117 (2020) .1/5
===================================================== ,
束 Stijl損
.
. 1881-1973,
(1913-1919)
, , ,
[4].
Kazimir Malevich (1878-1935) [5]
束 損 , 1913
(Oil on linen).
:
,
, .
. ,
, , i,
, ,
, ,
[6]. 1919
.
Kazimir Malevich
Inspired Geometric Abstract Modern
Painting
1
(Black square Malevich 1913, ,
Tretyakov) 79,5 cm.
)
2
cm 2
m .
) 5,6cm
4 cm,
.
)
,
.
- 8. ----------------------------------------------------------------------------------- ------------------------------------
117 (2020) .1/6
2
(Black Circle,
Kazimir Malevich, 1915. Oil on canvas, State Russian
Museum, St. Petersburg, Russia) .
5,2cm ,
4cm.
)
) .
)
.
;
3
Malevich (1915, Oil on Canvas,
State Russian Museum, Saint Petersburg)
.
25
2
cm ,
2,2 cm 2,9 cm.
)
)
)
,
; ;
Malevich
Stijl ( 1917-1931) Theo van
Doesburg.
[1] , 51 c-d
[2] . , 1448 17
[3] , 1414a
[4] https://en.wikipedia.org/wiki/Suprematism
[5] https://www.youtube.com/watch?v=5xyVIzo-zIU www.artaspects.org
[6] 20 , 1, 1880-1920,
, University Studio Press
- 9. ----------------------------------------------------------------------------------- ------------------------------------
117 (2020) .1/7
1
) 79,5 =4 79,5=318 cm
= 2
79,5 6320,25 2
cm =
6320,25
0,632025
10000
2
m
)
. 2
5,6 31,36 2
4 16
31,36-16=15,36 2
cm
)
8, 64 2
cm
(2 5,6)族=11,2族=125,44 2
cm , 125,44-64=61,44 2
cm .
(;) .
4 15,36=61,44
2
) 4cm L= =3,14 4=12,56cm.
4
2
2 2
cm = 族=3,14 2族=3,14 4=12,56 2
cm
) 5,2族=27,04 12,56
27,04-12,56=14,48 2
cm
) .
=6cm = 族=3,14 6族=3,14 36=113,04 2
cm . 113,04-
12,56=100,48 100,48 2
cm .
(9=3族)
3
) =2 2,9+2 2,2=
5,8+4,4=10,2cm =2,2 2,9=6,38 2
cm
) 25 2
cm
5 cm.
= + + + + + =5+5+(5-2,2)+2,9+2,2+(5-2,9)=
=10+2,8+5,1+2,1=20cm.
= 2
25 6,38 18,62cm .
) . 4 25=100
10.
(4=2族)
- 10. 117 (2020) .1/8
================================================ -
1
6 -
, 1.
.
,
.
, , 6
- :
1,2,3,4,5,30,31,.40, 41,42,240.
2
1,2,3,4,..19,20,114
1,2,3,421,22,126 .
, ,
,
. 6 240
.
- 11. 117 (2020) .1/9
:
: 19
: 21
: 19+21=40
6 : 6 40 =240
, ,
6,
6
240 .
: 19
6 6 19 =114
: 21
6 : 6 21=126
6 : 114+126 = 240
: 240.
****
6 (19+21) =6 19 +6 21 = 114 + 126 = 240
:
,
.
:
:
( )
( )
1:
- 13. 117 (2020) .1/11
/ ,
. .
+ =
: 3 + 2 = 5
3 + 2 = (3+2) = 5
3 + 2 = ( 3 + 2 ) = 5 . ;
. 14 53.
14+53=67
. :
14=1 +4 53=5 +3 ,
14+53=(1 +5 )+(4 +3 )=(1+5) +(4+3) =6 + 7 =67.
;
3.6 m, 2.5m
4m . :
=3.6m+2.5m+4m=10,1m 3.6m+2.5m+4m =(3.6 +2.5+4)m=10.1m.
;
. . 3.6m 4m )
3.6m 4m =14.4m2
) .
: 3.6 =3 + 0.6
3 4 =12 0.6 4 =2.4. ,
12+2.4 =14.4m2
.
=3,6m 4m=(3+0,6) 4m2
=(3 4+0.6 4)m2
=(12+2,4)m2
=14,4m2
.
;
:
103 8=(100+3) 8=100 8+3 8=800 +24=824.
;
3 x + 5 x = (3 + 5) x = 8 x, ;
+ + + + = 5 , ;
- 14. 117 (2020) .1/12
- 2:
, + , + .
= ( + ) ( + )
,
:
= + + +
( + ) ( + ) = + + +
( + ) ( + ) = ( + ) + ( + ) = + + +
3:
=3( +2)+5( -1) =2
1 =2
= 3(2+2)+5(2-1) = 3 4 +5 1= 12+5=17
2
=3( +2)+5( -1)=3 +3 2+5 -5 1=3 +6+5 -5 = 3 +5 +1 = (3+5) +1=8 +1
=2 = 8 2+1 = 16+1=17
=1, =2 , =3, =5, =10
; 2 ;
4:
- 15. 117 (2020) .1/13
=2 +2 -5 + =4
1
, .
2
=2 +2 -5 = 2( + )-5= 2 4 -5 = 8 - 5=3
;
:
:
5 37=5 (30+7) =5 30+5 7=150+35=185
52 11=52 (10+1) = 52 10+52 1=520+52=572
42 3=(40+2) 3 =40 3+2 3=120+6 =126
42 13= 42 (10 +3)= 42 10 +42 3= 420+ 126 =546
57 99 =57 (100-1) =57 100 -57 1= 5700-57 = 5643
5.37 98 = 5.37 (100-2) = 5.37 100- 5.37 2 =537-10.74=526.26
6 10.7 = 6 (10+0.7) = 6 10 +6 0.7 =60+4.2 =64.2
5
:
=
=
=
=
=
6
:
7
( , , )
:
=( +3) ( +2) = 1, 2, 3, 4, 5, 6
= ( +1) ( +3) =2, =5
- 16. 117 (2020) .1/14
========================================= -
.
,
, .
,
.
1 10.
12
=1, 22
=4, 32
=9, 42
=16, 52
=25, 62
=36, 72
=49, 82
=64, 92
=81, 102
=100.
1 10 :
0, 1, 4, 5, 6, 9.
1 30
0, 1, 4, 5, 6, 9.
2, 3, 7 8.
, . . 34567238 .
, 0, 1, 4, 5, 6, 9
;
, 19 .
, 0, 1, 4, 5, 6, 9 .
0, 1,
4, 5, 6, 9.
, , 1 10,
12
=1, 22
=4, 32
=9, 42
=16, 52
=25, 62
=36, 72
=49, 82
=64, 92
=81, 102
=100.
:
1 9,
2 8,
3 7,
- 17. 117 (2020) .1/15
4 6, .
0 5 0 5, .
:
2344, 59236;
2346, 59238;
1
,
, :
(34)2
= ; (34)2
1. ,
0 9 1 6
+2 4
1 1 5 6
(34)2
=1.156
2.
, 2 (3 x 4 x 2 = 24),
.
, .
:
(14)2
(67)2
(78)2
(91)2
116 3649 4964 8101
(1 4 2) 8 (6 7 2) 84 (7 8 2) 112 (9 1 2) 18
196 4489 6084 8281
(14)2
=196 (67)2
=4.489 (78)2
=6.084 (91)2
=8.281
2
2
- 2
=( + )( - ) 2
=( + )( - )+ 2
(1)
(86)2
.
, 86, 86,
10. , 4.
(109)2
, (987)2
(496)2
:
118
(1)
(109)2
=(118)(100)+92
=11800+81
+9
109
-9
90
(1)
(86)2
=(86+4)(86-4)+42
=90 82+16
9 82 = 738,
(86)2
=7380+16=7.396.
+4
86
-4
82
,
, ,
10, 100, .
- 18. 117 (2020) .1/16
100 (109)2
=11.881
, 109 9 = 100
987+ 13 =1.000
496+ 4 =500
3
5,
:
452
, 852
, 1252
1652
:
452
= 2025 852
= 7225
5x5 452
=2.025 5x5 852
=7.225
4 x 5 8 x 9
1252
= 15625 1652
= 27225
5x5 1252
=15.625 5x5 1652
=27.225
12 x 13 16 x 17
:
(16)2
(57)2
(88)2
(41)2
(75)2
(106)2
(37)2
(98)2
(111)2
(55)2
(996)2
(1006)2
(103)2
(98)2
(116)2
1000
(1)
(987)2
=(1000)(974)+132
=974000 +169,
(987)2
=974.169
+13
987
-13
974
500
(1)
(496)2
=(500)揃(492)+42
=500 492+16
500 492 = 1000 492/2 = 1000 246 = 246000,
4962
= 246000+16 = 246016.
+4
496
-4
492
(55)2
.
, , ( 5x6 =30).
52
, (25)
(3025).
- 19. 117 (2020) .1/17
.
,
1 2 3 4 5 6 7 8 9 10
1 1,414 1,732 2 2,236 2,449 2,646 2,828 3 3,162
, . .
, .
64, 81, 121, 225.
, 8, 9, 11 15
.
64=8, 81=9, 121=11 225=15. 40;
40, .
1
6,3 6,4 6,35
6,3 6,4.
,
, . . .
40
6,3245553203367586639977870888654.
,
.
, 40 .
1) : 6 6 = 36 7 7 = 49,
6 7.
2) 6
7, 6,5. 6,5 6,5 = 42,25
6,4.
3) 6,4 6,4 = 40,96 6,3.
4) 6,3 6,3 = 39,69.
- 20. 117 (2020) .1/18
2
6,32
6,324
:
3
,
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4) 2, 12,6:2=6,3.
5) , 6,3 2)
40:6,3 ...
1) 2 40, 5 8 = 40
2)
3)
4)
, .
- 22. -------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------
117 (2020) .1/20
: 2) 3)
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2019:
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: 1
5, 13, 25, 41, 61, 85, 113.
152
+1122
=1132
.
2) .
, 2009= 揃 +7 :
- 23. -------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------
117 (2020) .1/21
揃 =2002. 2002
. 2002=2揃7揃143
2002 揃 200< <300 7揃286 =7
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.
5) x
y .
15x
9y.
x+y 13
13(x+y), : 15x+9y=13(x+y) 2x=4y
x=2y. 3 2 , 66,6%.
- 24. -------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------
117 (2020) .1/22
束 損 115.
Pierce
, 1) 4).
,
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1)
;
2)
, = (1) = (2).
: 3 , :
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4) 116.
40.
.
:
, 2
.
2
.
- 25. -------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------
117 (2020) .1/23
2 .
,
3 40,
2.
2 402 =38.
38 2 : 3,5,7,11, 13, 17, 19,
23, 29, 31, 37. 38 31 7.
31 7 =24
4) 5
5,
.
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1.
1, 2, 3, 4, 5, 6. 1,
=90 = / =5/1=5, =90 .
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=90 .
4, = / =1/3, = / =1/2, =180
.
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.
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=1/ , =180 ( + ).
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, 1 3 束 損
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, , , ,
.
,
.
- 26. 117 (2020) .1/24
.
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. ;
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1) :
2
2
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-22 +121
, ,
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:
111 .
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22 +121=( 11)2
2
( -11) ( +11) +11
( -11) -11
=111
122
1,22
100
.
:
i) 2 2 2 - +
( - - +2 ):
+ -
:
=1+ 2, = 5 1 = 2 : 5
ii)
3 -2 -6
-2
=0,0982 =3.
: 0
iii). 4 2
+4 +2 + 2
+4 +1 =4,36 =2,32.
: 100
- 27. . ;
117 (2020) .1/25
2) ,
.
:
2x3
+x2
8x4=0 (x )
,
.
2x3
+x2
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4)=0
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4)揃(2x+1)=0
(x+2)揃(x2)揃(2x+1)=0 x=2 x=2
1
x
2
:
:
i) 6x3
+8x2
2x=0
: x=0 x=1 x=1/3
ii) 16x3
32x2
x+2=0
: x=賊1/4 x=2
iii) 18x3
24x2
+27x=36
: x=4/3
3) . .
.
x.
x=4
H .
x .
.
.
.
:
(x+1)2
+(x+2)2
=x2
+(x+3)2
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2x2
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+6x+9
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- 28. . ;
117 (2020) .1/26
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8 2 15 8 2 12 , 3 5
2 6 .
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+3y2
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:
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- 29. . ;
117 (2020) .1/27
4. x+y=2 5 x揃y=6, : x2
+y2
, x3
+y3
,
x y
y x
, xy.
: , , x+y=2 5
x揃y=6.
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2852
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+w2
5zw, z= 5 7 w= 7 5 .
: .
8. 11-4 7 11+4 7 .
:
22
11-4 7 4 7 2 2 7 2 7 2 2 7
9. 2551 254925522
+25482
.
: 2551揃2549
25482
25522
.
10. 4x2
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=0, x, y , x y.
: .
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630
.
3 1
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;
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630
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630
-3
630 630
1
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.
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- 33. ---------------------------- -------------------------
117 (2020) .1/31
. ;
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ii. ( 1 )
iii. ( )
. .
- 34. 117 (2020) .1/32
=============================================================
1) 2 2
x+xy+y = 2+3 2
x + y = 6
2) x>9 x2
+80 x =36
4 x x .
3) , -
. 10
( ) .
;
: , -
, , . . .
4) (x8)揃(x+10)揃(x+8)揃(x10) x
. ;
5) x x2
13x+1=0. -
4
4
1
x +
x
116
1) : =(22
12
)+(42
32
)+(62
52
)+(82
72
)+ +(1002
992
)
,
=3+7+11+15++187+191+195+199.
3+199=222, 7+195=222. 25 ( ;) 25222=5.550
2) 2 15
x - =4
x
x 0 3 x3
4x15=0.
x3
4x15 x=3 x3 x2
+3x+5 -
x3
4x15=(x3)( x2
+3x+5)=0 x 3 x2
+3x+5=0 x2
+3x=5 (1).
x揃(x+3)揃(x+1)揃(x+2) = (x2
+3x)揃(x2
+3x+2)=(5)揃(5+2)=15
3) , x2
3x+1=0 x揃(x3)=1
(1), x6
18x3
x3
揃(x3
18). -
.
(1) x3
揃(x3)3
=1 x3
揃(x3
9x2
+27x27)=1 :
x3
揃[(x3
18)9x2
+27x9)=1 x3
揃[(x3
18)9(x2
3x+1)=1 x2
3x+1=0 x3
揃(x3
18)=1.
4) -
.
2
+
2
2
= 2
+
2
2
=2
5) =3, =5 =4 ( ).
=3 =2 ( ).
=
10
3
. ( ;)
3
2
=6.
= 28
3
( ).
- 35. 117 (2020) .1/33
====================================================== :
22002200
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x xy y 3
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- 36. ---------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------
117 (2020) .1/34
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- 37. ---------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------
117 (2020) .1/35
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- 38. ---------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------
117 (2020) .1/36
1
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12n 119 75n 539 . , 2013
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12n 119 2
75n 539 b , ,b .
n
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119 b 539
25 119 4 b 539
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2b 5 1 2b 5 3 2b 5 7
2b 5 819 2b 5 273 2b 5 117
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,
2b 5 91 2b 5 63 2b 5 39
,b 11,31 , ,b 5,19 , , n 20 n 12.
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41. , , 2 3 5 6
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- 44. 117 (2020) .1/42
================================================================================
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16 400 .
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2019-2020 .
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- 47. 117 (2020) .1/45
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.
, 747b.
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.
;
束 9損 束 10損
束 100損 束 1000
4 .
. . . 4657+6574=11231.
8612, 12859, 4322, 11452, 9812, 9807
12859 9812.
;
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, .
.
束 損. ;
1 .
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- 51. ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------
117 (2020) .1/49
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.
,
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5 . 6 .
13/17
13/30 17/30
13.7/30.7 17.7/30.7 91/210 119/210. 91 119.
, :
100 = + + 100 = 3 + 2 +
, , :
2 5 8 1 1 14 17
30 25 20 15 10 5
68 70 72 74 76 78
1/5 (8, 20, 72)
4 6 5
, 36 .
7632 : 24
.32
.53.
: 12x636 16x477 18x424 24x318 72x106 36x212 48x159
144x53. 48x159=7632
. =159 =48.
100 = 102
,
10 = 101
. 102
101
= 10 (101) = 90.
, ,
> 10 1
10 1
=10 1
(10
1).
999999 = 10000001 =106
1,
999 = 10001 =103
1.
: (106
1) (103
1) = 106
103
= 103
(103
1)= 1000x999 = 999000.
, ,
(10 1)(10 1) = 10 10 = 10 (10
1).
6
3 . . . 452
452452 7, 11, 13, 1001.
+( +1)+( +2)+( +7)+( +9)+( +14)+( +15)+( +16) = 8 +64 = 8( +8).
8. 8
(168:8=21).
- 52. 留僚竜旅侶亮溜凌 34 - 慮流僚留
fax: 210 3641025
www.hms.gr e-mail: info@hms.gr
侶了.: 210 3616532, 210 3617784
竜僚旅虜流 旅略慮竜侶: 留僚竜旅侶亮溜凌 34 - 慮流僚留
fax: 210 3641025
www.hms.gr e-mail: info@hms.gr
侶了.: 210 3616532, 210 3617784
竜僚旅虜流 旅略慮竜侶:
侶 了了侶僚旅虜流 留慮侶亮留旅虜流 留旅竜溜留侶 了了侶僚旅虜流 留慮侶亮留旅虜流 留旅竜溜留虜隆竜旅
里旅亮流 竜凌: 3
里旅亮流 12硫旅硫了溜凌: 里旅亮流 12硫旅硫了溜凌: 里旅亮流 12硫旅硫了溜凌:
里旅亮流 竜凌: 3,5里旅亮流 竜凌: 3
里旅亮流 18硫旅硫了溜凌: 里旅亮流 15硫旅硫了溜凌: 里旅亮流 20硫旅硫了溜凌:
里旅亮流 硫旅硫了溜凌: 30 里旅亮流 硫旅硫了溜凌: 20 里旅亮流 硫旅硫了溜凌: 25
竜旅凌隆旅虜略旅留粒僚旅亮凌溜了亮旅略隆竜旅硫了溜留
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![117 (2020) .1/5
===================================================== ,
束 Stijl損
.
. 1881-1973,
(1913-1919)
, , ,
[4].
Kazimir Malevich (1878-1935) [5]
束 損 , 1913
(Oil on linen).
:
,
, .
. ,
, , i,
, ,
, ,
[6]. 1919
.
Kazimir Malevich
Inspired Geometric Abstract Modern
Painting
1
(Black square Malevich 1913, ,
Tretyakov) 79,5 cm.
)
2
cm 2
m .
) 5,6cm
4 cm,
.
)
,
.](https://image.slidesharecdn.com/eykleidhsa117eykleidhs2020-201129055152/85/Eykleidhs-a-117_eykleidhs_2020-7-320.jpg)
![----------------------------------------------------------------------------------- ------------------------------------
117 (2020) .1/6
2
(Black Circle,
Kazimir Malevich, 1915. Oil on canvas, State Russian
Museum, St. Petersburg, Russia) .
5,2cm ,
4cm.
)
) .
)
.
;
3
Malevich (1915, Oil on Canvas,
State Russian Museum, Saint Petersburg)
.
25
2
cm ,
2,2 cm 2,9 cm.
)
)
)
,
; ;
Malevich
Stijl ( 1917-1931) Theo van
Doesburg.
[1] , 51 c-d
[2] . , 1448 17
[3] , 1414a
[4] https://en.wikipedia.org/wiki/Suprematism
[5] https://www.youtube.com/watch?v=5xyVIzo-zIU www.artaspects.org
[6] 20 , 1, 1880-1920,
, University Studio Press](https://image.slidesharecdn.com/eykleidhsa117eykleidhs2020-201129055152/85/Eykleidhs-a-117_eykleidhs_2020-8-320.jpg)
