Μαθηματικ και Τνη - math-art.eu£+æ+ÿ+ù+£+æ+ñ+Ö+Ü... · 9Ο ΓΥΜΝΑΣΙΟ...
Embed Size (px)
Transcript of Μαθηματικ και Τνη - math-art.eu£+æ+ÿ+ù+£+æ+ñ+Ö+Ü... · 9Ο ΓΥΜΝΑΣΙΟ...
-
9 2013-2014
.
- - .
NIKAIA 2014
-
- 1 / 52 -
9o / / 2013-2014
. ............................................................................................... 2
. ............................................................................... 3
. ...................... 5
IV. ....................................................................................................... 6
V. ............................................................................................ 16
VI. ............................................................................... 17
VII. ...................................................................................... 18
VII. .................................................................... 19
X. Da Vinci .................................................................. 22
X. .......................... 24
X. ............................................................. 45
XI. Wassily Kandinsky .................................................................................... 46
XI. .......................................... 49
XIV. ............................................................... 50
XV. - ................................................... 52
-
- 2 / 52 -
9o / / 2013-2014
.
,
, , ,
, .
,
.
, ,
.
.
Albert Einstein
, , .
.
, . .
Godfrey Harold Hardy
.
. ,
,
. .
, . ,
. ,
.
,
,
,
, ! !
! !
!
, ,
.
-
- 3 / 52 -
9o / / 2013-2014
.
* .
*
,
.
*
.
*
.
*
.
.
*
.
* .
* .
* .
* .
*
.
*
. .
*
.
-
- 4 / 52 -
9o / / 2013-2014
.
.
.
.
.
.
08 - 03 - 03
-
- 5 / 52 -
9o / / 2013-2014
.
, .
.
, .
, ( , ).
,
, ,
( ) ,
1 ,
.
.
2 3
-
- 6 / 52 -
9o / / 2013-2014
IV.
19/11/2013 1 .
.
.
25/11/2013
.
- -
.
3/12/2013 .
, .
Sol LeWitt, Victor Vasarely Wassily
Kandinsky
.
Sol LeWitt Victor Vasarely
Wassily Kandinsky
http://www.google.gr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=jDM5FxjQQVntrM&tbnid=LWU059tfnCxf8M:&ved=0CAUQjRw&url=http://www.husgallery.com/213-EN-VASARELY_Victor.html&ei=-79KU8KXCOKR0AWguoDgDw&bvm=bv.64542518,d.d2k&psig=AFQjCNFZX2zV0eu-7BAMTSHSndWV5Y76zA&ust=1397494111995227
-
- 7 / 52 -
9o / / 2013-2014
10/12/2013
.
17/12/2013
. - .
14/1/2014 - .
Wassily Kandinsky.
21/1/2014 Wassily Kandinsky Circles in a
circle ,
.
28/1/2014 .
.
.
4/2/2014 ,
.
.
-
- 8 / 52 -
9o / / 2013-2014
11/2 /2014 Wassily Kandinsky Circles in a
circle
.
.
18/2 /2014 .
.
25/2 /2014 ,
.
,
M. C. Escher.
-
- 9 / 52 -
9o / / 2013-2014
4/3 /2014 .
.
.
.
11/3 /2014
.
.
. . (
)
.
18/3 /2014 -
.
20/3/2014
... .
. ,
,
.
-
- 10 / 52 -
9o / / 2013-2014
25/3 /2014 , .
1/4 /2014 . .
,
.
-
- 11 / 52 -
9o / / 2013-2014
-
- 12 / 52 -
9o / / 2013-2014
8 /4 /2014 Sierpinski Pascal
. Pascal
. .
29 /4 /2014
.
. ,
, .
.
6/5 /2014 .
. .
. .
13/5 /2014
.
.
15/5/2014 .
.
-
- 13 / 52 -
9o / / 2013-2014
-
- 14 / 52 -
9o / / 2013-2014
-
- 15 / 52 -
9o / / 2013-2014
-
- 16 / 52 -
9o / / 2013-2014
V.
1. 1
2. 4
3. 4
4. 1
5. 4
6. 4
7. 2
8. 4
9. 4
10. 3
11. 4
12. 4
13. 1
14. 4
15. 3
16. 4
17. 4
18. 4
19. 4
20. 08
21. 03
22. 03
-
- 17 / 52 -
9o / / 2013-2014
VI.
Howard Gardner :
(multiple intelligences).
. 8 (),
.
=
\
- .
) .
) .
) .
) .
()
) . ( ,-)
) . ( )
) - .
) .
-
- 18 / 52 -
9o / / 2013-2014
VII.
.
;
:
.
;
;
.
.
.
.
.
/
-
- 19 / 52 -
9o / / 2013-2014
VII. 40
47% 53% .
; 50%
45%
. 17,5%
.
.
. 14 40 , 35%
62,5%
.
5,00%
50,00%27,50%
17,50%
;
2,50%
35,00%
62,50%
2
20
11
7
1 0 14 25
-
- 20 / 52 -
9o / / 2013-2014
32 40 80%
. 17,5%
1
40 2,5%
.
; .
.
17,5%
. 67,5%
. 15%
.
1
7
32
0
5
10
15
20
25
30
35
KAMIA M
5 2 0 27 6
-
- 21 / 52 -
9o / / 2013-2014
.
.
12,50%5,00%
67,50%
15,00%
-
- 22 / 52 -
9o / / 2013-2014
X. Da Vinci
Da Vinci
Leonardo da Vinci
, . , ,
.
Leonardo da Vinci
.
,
.
1490
.
,
,
()
.
( 24 )
.
-
- 23 / 52 -
9o / / 2013-2014
-
.
- .
-
.
- .
- .
-
.
-
.
( )
16 , Leonardo Da Vinci
.
.
Da Vinci
( ).
=1,618 (
)
Da Vinci,
,
" ".
,
:
.
.
-
-
- 24 / 52 -
9o / / 2013-2014
X.
1.
(. 490 .. - 430 ..) ,
, 5 ..
.
, ,
.
. , ,
, ,
.
http://el.wikipedia.org/wiki/490_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/430_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B1%CE%AF%CE%B1_%CE%95%CE%BB%CE%BB%CE%AC%CE%B4%CE%B1http://el.wikipedia.org/wiki/%CE%93%CE%BB%CF%85%CF%80%CF%84%CE%B9%CE%BA%CE%AEhttp://el.wikipedia.org/wiki/%CE%9A%CE%BB%CE%B1%CF%83%CE%B9%CE%BA%CE%AE_%CE%B5%CF%80%CE%BF%CF%87%CE%AEhttp://el.wikipedia.org/wiki/%CE%86%CE%B3%CE%B1%CE%BB%CE%BC%CE%B1_%CF%84%CE%BF%CF%85_%CE%9F%CE%BB%CF%85%CE%BC%CF%80%CE%AF%CE%BF%CF%85_%CE%94%CE%B9%CF%8C%CF%82http://el.wikipedia.org/wiki/%CE%86%CE%B3%CE%B1%CE%BB%CE%BC%CE%B1_%CF%84%CE%BF%CF%85_%CE%9F%CE%BB%CF%85%CE%BC%CF%80%CE%AF%CE%BF%CF%85_%CE%94%CE%B9%CF%8C%CF%82http://el.wikipedia.org/wiki/%CE%9F%CE%BB%CF%85%CE%BC%CF%80%CE%AF%CE%B1http://el.wikipedia.org/wiki/%CE%95%CF%80%CF%84%CE%AC_%CE%B8%CE%B1%CF%8D%CE%BC%CE%B1%CF%84%CE%B1_%CF%84%CE%BF%CF%85_%CE%B1%CF%81%CF%87%CE%B1%CE%AF%CE%BF%CF%85_%CE%BA%CF%8C%CF%83%CE%BC%CE%BF%CF%85http://el.wikipedia.org/wiki/%CE%95%CF%80%CF%84%CE%AC_%CE%B8%CE%B1%CF%8D%CE%BC%CE%B1%CF%84%CE%B1_%CF%84%CE%BF%CF%85_%CE%B1%CF%81%CF%87%CE%B1%CE%AF%CE%BF%CF%85_%CE%BA%CF%8C%CF%83%CE%BC%CE%BF%CF%85http://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%AChttp://el.wikipedia.org/wiki/%CE%91%CE%BA%CF%81%CF%8C%CF%80%CE%BF%CE%BB%CE%B7_%CE%91%CE%B8%CE%B7%CE%BD%CF%8E%CE%BDhttp://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%AC_%CE%A0%CE%B1%CF%81%CE%B8%CE%AD%CE%BD%CE%BF%CF%82http://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%81%CE%B8%CE%B5%CE%BD%CF%8E%CE%BD%CE%B1%CF%82http://el.wikipedia.org/wiki/%CE%86%CE%B3%CE%B1%CE%BB%CE%BC%CE%B1_%CF%84%CE%B7%CF%82_%CE%A0%CF%81%CE%BF%CE%BC%CE%AC%CF%87%CE%BF%CF%85_%CE%91%CE%B8%CE%B7%CE%BD%CE%AC%CF%82http://el.wikipedia.org/wiki/%CE%A0%CF%81%CE%BF%CF%80%CF%8D%CE%BB%CE%B1%CE%B9%CE%B1_(%CE%91%CE%BA%CF%81%CF%8C%CF%80%CE%BF%CE%BB%CE%B7_%CE%91%CE%B8%CE%B7%CE%BD%CF%8E%CE%BD)
-
- 25 / 52 -
9o / / 2013-2014
1.1
,
5 ..
.
,
.
,
. 465 ..
,
.
.
,
http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B1%CE%AF%CE%B1_%CE%91%CE%B8%CE%AE%CE%BD%CE%B1http://el.wikipedia.org/wiki/%CE%86%CF%81%CE%B3%CE%BF%CF%82http://el.wikipedia.org/wiki/465_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/%CE%9A%CE%AF%CE%BC%CF%89%CE%BD_%CE%BF_%CE%9C%CE%B9%CE%BB%CF%84%CE%B9%CE%AC%CE%B4%CE%BF%CF%85http://el.wikipedia.org/wiki/%CE%9C%CE%AC%CF%87%CE%B7_%CF%84%CE%BF%CF%85_%CE%9C%CE%B1%CF%81%CE%B1%CE%B8%CF%8E%CE%BD%CE%B1http://el.wikipedia.org/wiki/%CE%9C%CE%AC%CF%87%CE%B7_%CF%84%CE%BF%CF%85_%CE%9C%CE%B1%CF%81%CE%B1%CE%B8%CF%8E%CE%BD%CE%B1http://el.wikipedia.org/wiki/%CE%9C%CE%B9%CE%BB%CF%84%CE%B9%CE%AC%CE%B4%CE%B7%CF%82http://el.wikipedia.org/wiki/%CE%A0%CE%AD%CF%81%CF%83%CE%B5%CF%82http://el.wikipedia.org/wiki/%CE%94%CE%B5%CE%BB%CF%86%CE%BF%CE%AFhttp://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:NAMA_Ath%C3%A9na_Varvakeion.jpg
-
- 26 / 52 -
9o / / 2013-2014
,
.
.
8 - 9 2 .. ,
. ,
.
,
,
. ,
,
. ,
' ,
. ,
, .
http://el.wikipedia.org/wiki/%CE%91%CF%80%CF%8C%CE%BB%CE%BB%CF%89%CE%BDhttp://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%AChttp://el.wikipedia.org/wiki/%CE%9C%CE%B9%CE%BB%CF%84%CE%B9%CE%AC%CE%B4%CE%B7%CF%82http://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%85%CF%83%CE%B1%CE%BD%CE%AF%CE%B1%CF%82http://el.wikipedia.org/wiki/%CE%A3%CE%BF%CF%8D%CE%BD%CE%B9%CE%BFhttp://el.wikipedia.org/wiki/%CE%A0%CE%B5%CF%81%CE%B9%CE%BA%CE%BB%CE%AE%CF%82http://el.wikipedia.org/wiki/%CE%94%CE%B7%CE%BB%CE%B9%CE%B1%CE%BA%CE%AE_%CE%A3%CF%85%CE%BC%CE%BC%CE%B1%CF%87%CE%AF%CE%B1http://el.wikipedia.org/wiki/%CE%A0%CE%BB%CE%BF%CF%8D%CF%84%CE%B1%CF%81%CF%87%CE%BF%CF%82http://el.wikipedia.org/wiki/%CE%A0%CE%B5%CE%BD%CF%84%CE%B5%CE%BB%CE%B9%CE%BA%CF%8C_%CF%8C%CF%81%CE%BF%CF%82#.CE.A4.CE.BF_.CE.BC.CE.AC.CF.81.CE.BC.CE.B1.CF.81.CE.BF_.CE.A0.CE.B5.CE.BD.CF.84.CE.AD.CE.BB.CE.B7.CF.82
-
- 27 / 52 -
9o / / 2013-2014
,
,
.
, ,
, ,
. 447-432 ..
(442-438 ..)
, ,
. ,
,
.
, .
()
, , 438-
432 .. .
(446-438 ..),
http://el.wikipedia.org/wiki/%CE%91%CE%AD%CF%84%CF%89%CE%BC%CE%B1http://el.wikipedia.org/wiki/%CE%91%CE%BB%CE%BA%CE%B1%CE%BC%CE%AD%CE%BD%CE%B7%CF%82http://el.wikipedia.org/wiki/%CE%9C%CF%8D%CF%81%CF%89%CE%BDhttp://el.wikipedia.org/wiki/447_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/432_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/442_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/438_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/%CE%94%CE%AF%CE%B1%CF%82_(%CE%BC%CF%85%CE%B8%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1)http://el.wikipedia.org/wiki/%CE%89%CF%81%CE%B1_(%CE%BC%CF%85%CE%B8%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1)http://el.wikipedia.org/wiki/438_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/432_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/446_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/438_%CF%80.%CE%A7.
-
- 28 / 52 -
9o / / 2013-2014
.
3 . ..
.
5 .. . (11,544
.) .
, Lenormant
( ).
1,20 ., .
, ,
, .
,
.
44 (1.140 ).
.
,
.
.
.
, ,
.
.
,
4 .. ,
http://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%B1%CF%8A%CE%BA%CE%AE_%CE%B4%CE%B7%CE%BC%CE%BF%CE%BA%CF%81%CE%B1%CF%84%CE%AF%CE%B1http://el.wikipedia.org/wiki/%CE%A0%CE%BB%CE%AF%CE%BD%CE%B9%CE%BF%CF%82_%CE%BF_%CE%A0%CF%81%CE%B5%CF%83%CE%B2%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CF%82http://el.wikipedia.org/wiki/%CE%A1%CF%89%CE%BC%CE%B1%CF%8A%CE%BA%CE%AE_%CE%91%CF%85%CF%84%CE%BF%CE%BA%CF%81%CE%B1%CF%84%CE%BF%CF%81%CE%AF%CE%B1http://el.wikipedia.org/wiki/%CE%95%CE%B8%CE%BD%CE%B9%CE%BA%CF%8C_%CE%91%CF%81%CF%87%CE%B1%CE%B9%CE%BF%CE%BB%CE%BF%CE%B3%CE%B9%CE%BA%CF%8C_%CE%9C%CE%BF%CF%85%CF%83%CE%B5%CE%AF%CE%BFhttp://el.wikipedia.org/wiki/%CE%95%CF%81%CE%B9%CF%87%CE%B8%CF%8C%CE%BD%CE%B9%CE%BF%CF%82http://el.wikipedia.org/wiki/%CE%A7%CF%81%CF%85%CF%83%CF%8C%CF%82http://el.wikipedia.org/wiki/%CE%91%CE%BC%CE%B1%CE%B6%CF%8C%CE%BD%CE%B5%CF%82
-
- 29 / 52 -
9o / / 2013-2014
. . ,
,
, 11 .,
, .
,
.
. :
' .
, .
, ,
. ,
. 1958,
, ,
, ,
http://el.wikipedia.org/wiki/%CE%9D%CE%BF%CE%BC%CF%8C%CF%82_%CE%97%CE%BB%CE%B5%CE%AF%CE%B1%CF%82http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Workshop_of_Phidias.jpg
-
- 30 / 52 -
9o / / 2013-2014
1.2
.
. .
' , ..
.
,
http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Lemnia_torso04_pushkin.jpg
-
- 31 / 52 -
9o / / 2013-2014
, , :
1. "" , , ,
.
2. , .
3.
.
4. ,
(451-445 ..).
5. (. ) .
6. .
7. .
8. .
9. .
1.3
.
.
.
.
.
.
, , ,
,
.
.
http://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%AChttp://el.wikipedia.org/wiki/%CE%91%CF%80%CF%8C%CE%BB%CE%BB%CF%89%CE%BDhttp://el.wikipedia.org/wiki/%CE%9C%CE%B9%CE%BB%CF%84%CE%B9%CE%AC%CE%B4%CE%B7%CF%82http://el.wikipedia.org/wiki/%CE%9C%CE%AC%CF%87%CE%B7_%CF%84%CE%BF%CF%85_%CE%9C%CE%B1%CF%81%CE%B1%CE%B8%CF%8E%CE%BD%CE%B1http://el.wikipedia.org/wiki/%CE%94%CE%B5%CE%BB%CF%86%CE%BF%CE%AFhttp://el.wikipedia.org/wiki/%CE%A0%CE%B5%CE%BB%CE%BB%CE%AE%CE%BD%CE%B7http://el.wikipedia.org/wiki/%CE%9D%CE%BF%CE%BC%CF%8C%CF%82_%CE%91%CF%87%CE%B1%CE%90%CE%B1%CF%82http://el.wikipedia.org/wiki/%CE%A0%CE%BB%CE%B1%CF%84%CE%B1%CE%B9%CE%AD%CF%82http://el.wikipedia.org/wiki/%CE%91%CE%B8%CE%B7%CE%BD%CE%AC_%CF%84%CE%B7%CF%82_%CE%9B%CE%AE%CE%BC%CE%BD%CE%BF%CF%85http://el.wikipedia.org/wiki/%CE%9B%CE%AE%CE%BC%CE%BD%CE%BF%CF%82http://el.wikipedia.org/wiki/451_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/445_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/%CE%91%CF%86%CF%81%CE%BF%CE%B4%CE%AF%CF%84%CE%B7_(%CE%BC%CF%85%CE%B8%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1)http://el.wikipedia.org/wiki/%CE%9C%CE%AC%CF%81%CE%BC%CE%B1%CF%81%CE%BF_%CE%A0%CE%AC%CF%81%CE%BF%CF%85http://el.wikipedia.org/wiki/%CE%89%CE%BB%CE%B9%CE%B4%CE%B1http://el.wikipedia.org/wiki/%CE%9D%CE%B1%CF%8C%CF%82_%CF%84%CE%B7%CF%82_%CE%91%CF%81%CF%84%CE%AD%CE%BC%CE%B9%CE%B4%CE%BF%CF%82_%CF%83%CF%84%CE%B7%CE%BD_%CE%88%CF%86%CE%B5%CF%83%CE%BF
-
- 32 / 52 -
9o / / 2013-2014
,
,
( )
.
. ,
,
, " " .
,
.
, ,
.
.
http://el.wikipedia.org/wiki/%CE%A0%CE%B1%CE%BD%CE%B1%CE%B8%CE%AE%CE%BD%CE%B1%CE%B9%CE%B1
-
- 33 / 52 -
9o / / 2013-2014
1.4
200 .. 125
..
. ,
(), ,
.
4753 Phidias.
2. - !
Henri Poincar :
, .
. ,
. ,
. :
;
. ,
,
,
.
1,618...
. , ,
. :
http://el.wikipedia.org/wiki/200_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/125_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/125_%CF%80.%CE%A7.http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B1%CE%AF%CE%B1_%CE%9C%CE%B5%CF%83%CF%83%CE%AE%CE%BD%CE%B7http://el.wikipedia.org/wiki/%CE%A7%CF%81%CF%85%CF%83%CE%AE_%CF%84%CE%BF%CE%BC%CE%AEhttp://el.wikipedia.org/wiki/%CE%9A%CF%8D%CF%81%CE%B9%CE%B1_%CE%96%CF%8E%CE%BD%CE%B7_%CE%91%CF%83%CF%84%CE%B5%CF%81%CE%BF%CE%B5%CE%B9%CE%B4%CF%8E%CE%BDhttp://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AChttp://el.wikipedia.org/wiki/%CE%A4%CE%AD%CF%87%CE%BD%CE%B7http://el.wikipedia.org/wiki/%CE%9B%CF%8C%CE%B3%CE%BF%CF%82
-
- 34 / 52 -
9o / / 2013-2014
. :
-
, :
. b / a = 1 / ,
:
:
,
:
http://content-mcdn.ethnos.gr/filesystem/images/20100130/low/assets_LARGE_t_420_8271363.JPG
-
- 35 / 52 -
9o / / 2013-2014
,
:
,
:
-
1) : ,
:
2) .
, ! , , ,
, ,
.
; :
, , !
,
. 5
,
=1,618 , !
http://el.wikipedia.org/wiki/%CE%94%CE%B5%CF%85%CF%84%CE%B5%CF%81%CE%BF%CE%B2%CE%AC%CE%B8%CE%BC%CE%B9%CE%B1_%CE%B5%CE%BE%CE%AF%CF%83%CF%89%CF%83%CE%B7http://el.wikipedia.org/w/index.php?title=%CE%A3%CF%85%CE%BD%CE%B5%CF%87%CE%AD%CF%82_%CE%BA%CE%BB%CE%AC%CF%83%CE%BC%CE%B1&action=edit&redlink=1http://el.wikipedia.org/wiki/%CE%91%CE%BA%CE%BF%CE%BB%CE%BF%CF%85%CE%B8%CE%AF%CE%B1_%CE%A6%CE%B9%CE%BC%CF%80%CE%BF%CE%BD%CE%AC%CF%84%CF%83%CE%B9
-
- 36 / 52 -
9o / / 2013-2014
,
: 1, 1, 2, 3, 5,
8, 13, 21, 34, ,
Fibonacci,
Leonardo Fibonacci .
, ;
!
Fibonacci,
.
, ,
.
.
2 , 3,
5, 8 ... ,
Fibonacci!
,
, (),
,
.
-
- 37 / 52 -
9o / / 2013-2014
,
. ,
, , .
, ...
,
...
, !
; ,
.
(
1,618..),
. ,
, ,
. , ,
-
- 38 / 52 -
9o / / 2013-2014
, X T,
1,618033... !
, ,
.
, , ..
.
, ,
(
). (
)
,
.
. ,
,
,
.
-
- 39 / 52 -
9o / / 2013-2014
, :
. ,
.
2.1
,
.
.
,
.
-
- 40 / 52 -
9o / / 2013-2014
.
.
: ,
, (5 +
1)/2 ,
, .
.
.
-
- 41 / 52 -
9o / / 2013-2014
2.2
, ,
: 1,
( G), (5 1)/2,
. (5 1)/2
:
1:
. .
2: 5/2. .
3: ( AV)
AG (5 1 )/2.
2.3
: , ,
. ,
,
:
http://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Golden_Rectangle_Construction2.png
-
- 42 / 52 -
9o / / 2013-2014
.
.
36,36 108 72, 72
36.
2.4
36,
.
. ,
.
.
.
.
-
- 43 / 52 -
9o / / 2013-2014
2.5
,
, .
4
.
. ,
, .
.
-
, ,
.
( )
( ) 1,61804
. 2
,
,
.
.
, .
.
,
,
,
.
-
- 44 / 52 -
9o / / 2013-2014
,
.
2.6
.
. ,
.
, Hurwitz,
.
:
. ,
,
!
1. http://el.wikipedia.org
2. http:// www.math.uoa.gr/me/dipl/dipl_vazoura.pdf
3. http:// www.tovima.gr/science/article/?aid=481370
4. http:// www.livepedia.gr/index.php/__
5. http:// olympia.gr/2011/11/26/h------/
http://el.wikipedia.org/
-
- 45 / 52 -
9o / / 2013-2014
X.
19 .
.
.
,
.
, , .
20 .
, .
.
.
-
- 46 / 52 -
9o / / 2013-2014
XI. Wassily Kandinsky
Kandinsky
16 1866
, .
,
.
. 30
. 1901
.
.
1911
.
.
.
.
-
- 47 / 52 -
9o / / 2013-2014
Kandinsky
1912 Concerning the Spiritual in Art
.
Kandinsky
. 1917
.
.
.
Kandinsky
,
.
.
13 1944 ,
-
- 48 / 52 -
9o / / 2013-2014
KANDINSK:
1901-1905-1909
1913- 1918-1923-1924
-
- 49 / 52 -
9o / / 2013-2014
XI.
.
.
:
1) 0 1
. O
CD.
2) 21 30
.
-
- 50 / 52 -
9o / / 2013-2014
XIV.
-
2013 , .
. .
,
.
,
.
.
( ,
)
. ,
,
.
, , .
,
.
... . ,
,
, ,
.
. , , .
,
-
- 51 / 52 -
9o / / 2013-2014
.
.
.
.
.
,
.
.
. .
.
.
.
08 - 03 - 03
-
- 52 / 52 -
9o / / 2013-2014
XV. -
1. E , 29/10/2011
2. , , , 2011
3.
, ., , . & , . (2011).
, : (,
).
4. .
5. Annie Siety
6. http://www.tovima.gr/science/article/?aid=457203
7. http://el.wikipedia.org
8. http://www.mathher.gr/s/attachments/660_i-aksiopoiisi-twn-texnwn-sti-didaskalia-
twn-mathimatikwn-sto-sxoleio.pdf
9. http://maths-art.blogspot.gr/
10. http://www.blod.gr/lectures/Pages/viewlecture.aspx?LectureID=632
11. http://el.wikipedia.org
12. http:// www.math.uoa.gr/me/dipl/dipl_vazoura.pdf
13. http:// www.tovima.gr/science/article/?aid=481370
14. http:// www.livepedia.gr/index.php/__
15. http:// olympia.gr/2011/11/26/h------/
http://www.tovima.gr/science/article/?aid=457203http://el.wikipedia.org/http://www.mathher.gr/s/attachments/660_i-aksiopoiisi-twn-texnwn-sti-didaskalia-twn-mathimatikwn-sto-sxoleio.pdfhttp://www.mathher.gr/s/attachments/660_i-aksiopoiisi-twn-texnwn-sti-didaskalia-twn-mathimatikwn-sto-sxoleio.pdfhttp://maths-art.blogspot.gr/http://www.blod.gr/lectures/Pages/viewlecture.aspx?LectureID=632http://el.wikipedia.org/