ΕΥΚΛΕΙΔΗΣ a t91
DESCRIPTION
ΕΥΚΛΕΙΔΗΣ ΕΜΕTRANSCRIPT
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.: 2054ISSN: 1105 - 7998
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91 .3/1
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, . . , : ,
. , Fred T. Hodgson [1] A practical treatise on the steel square and its application to everyday use. .
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91 .3/2
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91 .3/3
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: 13 x 11 x 1 = 13
12 x 11 x 1 = 143
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111112
, 11 11 . . ; , . . - 1. Hodgson Fred, A Practical Treatise on the Steel Square and Its Application to Everyday Use,
Chicago, Frederick J. Drake & Co., Publishers, 1913 2. Cobleigh Rolfe, Handy Farm Devices and How to Make Them - The Steel Square
http://journeytoforever.org/farm_library/device/devices2.html
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91 . 3/4
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91 . 3/5
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91 . 3/6
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. : 1) 2000. 2) Barbin, E. (1996):The role of problems in the history and teaching of mathematics, in Ronald Calinger (Ed) Vita Mathematica 3) Heath T.: (1981) A History of Greek Mathematics Dover Publications Inc. 4) Katz, V. (1993): A History of Mathematics, Harper Collins College Publishers, New York. : http://www.anselm.edu/homepage/dbanach/thales.htm http://jnocook.net/pyramids/ http://en.wikipedia.org/wiki/Triangulation http://www.mhs.ox.ac.uk/measurer/text/fig19.htm
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91 .3/7
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91 .3/8
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91 .3/9
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91 .3/10
{48, 108, 12, 216}; . 4. , 4. 4: 48, 108, 12 216; 5: ; , ! , . 1, 2 3 1: . 2: . 3: 48, 108, 12 216. : 1: : 1. . 2. . , . 2: ( , , ). 48, , , 48. 3: 4
. . . 2 4 . 108 2 54 . . 48, 108, 12 216. 1 . 2 : (40, 72, 104, 8, 72), (80, 55, 5, 65, 35, 95, 35, 90), (42, 66, 54, 90, 120) . : {(15), (48, 108, 12, 216), (40, 72, 104, 8, 72), (80, 55, 5, 65, 35, 95, 35, 90), (76, 60, 80), (42, 66, 54, 90, 120), (36, 3, 54)}. 2 . . . . Geogebra. Geogebra . . http://www.geogebra.org/cms/el/ ) , tablet ) GeoGebra Chrome App . ( , : )
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91 . 3/11
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91 . 3/12
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91 . 3/13
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91 .3/14
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91 .3/15
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91 .3/16
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91 .3/17
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91 .3/18
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91 .3/19
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91 .3/20
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1.60 1.55 1.50 1.57 1.62 1.61 1.51 1.57 1.59 1.63 1.54 1.50 1.59 154 1.52 1,68 1.67 1.61 1.56 1.55 1.66 1.67 1.68 1.69 1.70
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91 .3/21
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1.50-155 6 0.24 24% 1.55-1.60 7 0.28 28% 1.60- 1.65 5 0.20 20% 1.65-170 7 0.28 28 % -
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91 .3/23
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91 .3/24
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12
23,1445=62,8 cm2
, =. +2E. =276,32 cm2. 1. 37,68cm2 =4cm. , . (=3cm, = 7 2,646cm, V=3 7 cm3 24,92cm3) 2. 4cm =10cm. , - . (=125,6cm2, =150,72cm2, V=125,6cm3) 3. 90. . (=78) 4. - 12cm =10cm. . (=384cm2, V=384cm3) 5. - 1m =2m. - . (=( 17+1)m2) 6. - . () - () . (= 2
) 7. 3m2 30m3. ;(: , - - . V= 32 m89,7
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91 .3/25
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91 .3/26
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P=600 atm V=18 m3, V P 900atm .
P=600 V=18 P=1 V=60018=10800
P=900 V=10800900=12 P=900atm V 12 m3.
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91 .3/27
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91 .3/28
20.000 3 , 6+8+11=25 ,
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11 8.800 . : 4800+6400+8800=20000 .
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91 .3/29
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91 .3/30
- - . . 2013 . , - . - . 1 x, y, z x -1, y +1, z + 5 2, 3 4 -: -2x + 3y + 5z = -5 x1, y+1, z + 5 - 2,3 4 -: x 1 y 1 z 5
2 3 4 . x = 3, y=2, z=1
2 (x) = (17x2 1)2 64x4. ) - . ) (x) = 0 ) - (x) = (5x+1)(5x 1)(3x+1)(3x 1) - . 3 ) >0 , 1+ 2 ) 2f(x) = -2x + 4x ) 21x + + 2x - 4x = 0
x
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2
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1x 2x
, 22x 4x 2 f (1) -
2 x = 1 . 4 , :
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2 2 2( 3 5) 1 ( 3) 4 ( 6) 9 6 6 = 3 5 , = 3, = 6. - ) ,) 3 5 - , . , - ( ) . . . : : -. : 1 . . , . . . () = 5/8, () = 7/8, () = 3/8.
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91 .3/31
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91 .3/32
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=3cm.
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91 .3/33
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91 .3/34
1
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91 .3/35
1 1 x =1212=144
.= 7 3 3 152 P( )=
. 15 0,104 144 . 2 .=32 +32 =18
P( )= .+. 15 18 144 .
.=.+.+.+.=15+18+15,5+24=72,5 P( )= -. 144 72,5 144
BHMA 3o
H P( )= .-. 144-24. 144 4 : P( )= .-. 144 15. 144
P( )= P( )= P( )= . 2 1 1=10cm, 2=20cm, 3=30cm, 4=40cm .=42
P( )= =2 22
1 12
44
10 1 6 40 16 96
96 P( )=
=2 2 2 2
2 1 2 1 2 1 2 12 2 2 2
4 4 4
( )( + ) (20 10)(20 10) 3 1816 96 40
2 P( bonus)=0
240
24
302 1 163606 96
BHMA 3 P( 90 )=0
2 2 2101
244
302 1 1 10 13606 6 40 96
4 P( 30 )=
=
02 2
2 23 203 2 3 2 3 2
2 2 2 24 4 4
302 ( ) ( )( )1 1 1 (30 20)(30 20) 53606 6 6 96 40
: Discovering Geometry Michael Serra
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91 .3/36
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91 .3/37
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2 800 800 400 800 800 3200002
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91 .3/38
800 320000 796000 800 476000 595x x x 595 605x x 10, 600x . 600 , =1400 800 600 320000 480000 320000 800000 , 800 . 3 30 . 90 . , . N . : () . () . () 180 180 30 75
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91 .3/39
, 55% . - - 7 55 35
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91 .3/40
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