โครงงานคณิตศาสตร์...

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  โครงงานคณ ตศาสตร  เร  อง การประย กต ของอ ตราส วนทองค ดท าโดย 1.เด กชาย ทร ฒนก ลจร   นม ธยมศ กษาป   3/11 2.เดกชาย รภพ กด นอก   นม ธยมศ กษาป   3/11 3.เด กชาย อภ นท  อศรางก อย ธยา   นม ธยมศ กษาป   3/11 4.เดกชาย อภ ชญ  จร ยาน เคราะห     นม ธยมศ กษาป   3/11  โรงเร ยนว ดสทธ วราราม เขตสาทร กรงเทพมหานคร รายงานฉบ บน   เป นส วนหน  งของโครงงานคณ ตศาสตร  รายว ชา 20205 เพ มพ นประสบการณ  5 ระด บช   นม ธยมศ กษาปท   3

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หวังเป็นอย่างยิ่งว่าโครงงานนี้จะเป็นประโยชน์ต่อผู้อ่านไม่มากก็น้อย

TRANSCRIPT

  • 1. 3/11

    2. 3/11

    3. 3/11

    4. 3/11

    20205 5

    3

  • 1. 3/11

    2. 3/11

    3. 3/11

    4. 3/11

  • 1. 3/11

    2. 3/11

    3. 3/11

    4. 3/11

    The Geometers Sketchpad

    Adobe illustrator

  • ..

    1 ..1

    1.1 ..1

    1.2 ...1

    1.3 ..1

    1.4 .2

    2 ..3

    2.1 ..3

    2.2 The Geometers sketchpad.12

    2.3 Adobe illustrator..15

    3 .19

    3.1 .19

    3.2 ..19

    4 ...22

    4.1 : ..22

    4.2 : .23

  • ()

    4.3 : .25

    4.4 : ..26

    4.5 : ..29

    4.6 : .31

    4.7 .34

    4.8 THE BEST.35

    4.9 .37

    4.10 .38

    4.11 A1 200 43

    5 ...44

    5.1 .44

    5.2 ..44

    5.3 .44

    5.4 45

    5.5 .45

    .46

    ..47

  • 2.1 (Golden rectangle)................................................................................4

    2.2 ...........................................................................5

    2.3 (the Vitruvian Man)..........................................................................5

    2.4 Jan Tschichold.6

    2.5 .6

    2.6 (Mona Lisa).7

    2.7 .8

    2.8 ..9

    2.9 ..10

    2.10 10

    2.11 .11

    2.12 .12

    2.13 .13

    2.14 13

    2.15 .14

    2.16 18

    4.1 1 122

    4.2 1 2.22

    4.3 2 1.23

  • ()

    4.4 2 2....23

    4.5 2 3.24

    4.6 2 4.24

    4.7 3 .25

    4.8 3 1.25

    4.9 3 2...26

    4.10 4 1..26

    4.11 4 2..27

    4.12 4 3..27

    4.13 4 4..28

    4.14 4 5..28

    4.15 5 1..29

    4.16 5 2..29

    4.17 5 3..30

    4.18 5 4.30

    4.19 6 1.31

    4.20 6 2.31

    4.21 6 3.32

    4.22 6 4.33

  • ()

    4.23 6 5..33

    4.24 THE BEST (FIRST)..35

    4.25 THE BEST (SECOND)..36

    4.26 137

    4.27 237

    4.28 138

    4.29 1..38

    4.30 239

    4.31 239

    4.32 340

    4.33 3..40

    4.34 441

    4.35 441

    4.36 5.. 42

    4.37 .42

    4.38 THE BEST (FIRST) A1.43

    .1 ...51

    .2 .51

  • ()

    .3 ..52

    .4 .52

  • 1

    1.

    2. The

    Geometers Sketchpad illustrator

    The Geometer's

    Sketchpad illustrator

    8 ( 8 31 2557)

    4

  • 2

    The Geometers Sketchpad Adobe illustrator

    1.

    (Golden Ratio) (, Phi) 2

    a>b>0

    +

    =

    =

    ()

    =

    = 1.6180339887..

    20

    Phi

  • 2.1 (Golden rectangle)

    2

    +

    =

    =

    +

    =

    +

    = 1 +

    + 1 =

    1 = 0

    =

    = 1.6180339887..

    =

    = 0.6180339887..

  • (Fibonacci)

    2

    1597:2584 1:1.618

    2.2

    (the Vitruvian Man)

    Phi

    2.3 (the Vitruvian Man)

  • 2.4 Jan Tschichold

    2:3 1:1:2:3

    2.5

    (Mona Lisa)

    (La Joconde)

    (La Gioconda)

    (sfumato)

  • 2.6 (Mona Lisa)

    16 Agrippa

    The Last Supper

    .. 1496

    The Last Supper

    Perspective

  • Perspective

    The Divine Propotion

    The most excellent painter in perspective , architect , musician , the man endowed

    with all virtues , Leonado Da Vinci , who deduced and elaborated a series of diagrams

    of regular solids.

    565 ..

    1999

    1.34 1.04 (Goya) 1.46

    (Bellini) Pablo Tosto 350 100

    -5, -2, 3, 4,

    6

    2.7

  • :

    1. AB, BC BC B BC

    AB AC

    2. C BC AC D

    3. AD AB S AB

    AS SB

    2.8

    ABC

    C CXB

    BCX = XCA = CAB =

    ; ABC = 2 BXC = 2

    180 5 = 180 = 36

    36-72-72 AXC (

    Golden gnomon) 36-36-108

    XB 1 BC

    XC = XA BC = XC AC = AB

    + 1 ABC CXB AC / BC = BC / BX

    AC ^2 2 = + 1,

  • AXC

    CXB - 1

    2.9

    ( 1 / )

    Phi

    2.10

  • The

    Divine Propotion 60

    The

    Divine Propotion

    2.11

    b, a = +

    (Geometry

    progression) 1 : r : r2, r -1

  • 2, r -1

    1 : : ( 1 + = 2)

    2.12

    2. The Geometers sketchpad

    AB

    1. 1 C

    2. C AB -->

    C AB

    3. C -->

    D

    D CD

    AB

  • 4. >

    2.13

    1. 1 ABCD

    2. A, B, C D ()

    2.14

  • 1. AB

    2. A AB

    3. C

    4. AC BC

    2.15

    1.

    2 . ----> ---->

    3. 2

    2

    4.

    ---> --->

    ---> --->

  • 2

    B A

    30 B

    3

    E D A

    E

    3. Adobe illustrator

    Selection tool

    Selection tool ()

    Direct-selection tool () points path ( Alt)

    Magic wand tool ()

    Lasso tool Drag Photoshop ( Alt

    Shift)

    Create tool

  • Pen tool path -

    curved

    ( Alt)

    Type tool

    paths

    Line segment tool

    Basic shape tool flare

    tool Affect lens-flare

    Paintbrush tool path drag

    brush

    Pencil tool paintbrush tool

    Transform tool

    Rotate tool

    Reflect tool

    Twist tool

    Scale tool

    Shear tool

    Reshape tool

    The warp tool

    Twirl tool

    Pucker tool

    Bloat tool

    Scallop tool

    Crystallize tool

    Wrinkle tool

    Free transform tool

  • Special tool Symbol graph

    Symbol tool symbol

    Graph tool graph

    Paint color tool

    Mesh tool point (

    Gradient tool 2 Linear

    Radial

    Eyedropper tool copy copy

    Paint bucket tool eyedropper tool

    Measure tool

    Blend tool 3

    Auto trace tool trace bitmap Vector

    View tool

    Slice tool

    Scissors tool Outline 2

    Knife tool drag 2 close

    paths

    Hand tool

    Page tool print size

    Zoom tool

  • illustrator

    .

    2.16

    4

    .. 2555

    10

  • 3

    1.

    Windows XP Service Pack 3 Windows 7 Service Pack 1

    Mac OS X 10.6.8 ( OS X 10.8)

    1 GB

    1024 x 768 ( 1280 x 800)

    The Geometers Sketchpad

    Adobe illustrator CS6

    Adobe Photoshop CS6

    Inkscape 0.48.5

    2.

    1

    A4

    2

    1) 2) 3) 4) 5)

    6) 7) 8) - 9) 10)

  • 11) 12) 13) 14) 15) 16)

    17) 18) 19) 20)

    3 2

    Adobe Photoshop

    1.

    2.

    4 2

    -

    5 2

    2

    2

    1.

    2.

    6 3 2

  • 7

    A4

    8

    A3

  • 4

    1.:

    4.1 1 1

    4.2 1 2

    4

  • 2.:

    4.3 2 1

    30*0,618

    4.4 2 2

    code Brainfuck

    "Hello World"

  • 4.5 2 3

    1.618

    1.618 4

    4.6 2 4

    1.618 .. 1.618 4

    90

    4

  • 3.:

    4.7 3

    2

    4.8 3 1

    Plastic

    filter 61.8% 30*1.618

  • 4.9 3 2

    neon filter 61.8% 30

    * 1.618

    4.:

    4.10 4 1

    1 .

    1.618 2

  • 4.11 4 2

    1 .

    1.618 3

    4.12 4 3

  • 4.13 4 4

    4.14 4 5

  • 5.:

    4.15 5 1

    61.8% 61.8 pixels

    161.8%

    4.16 5 2

    1/3

    2/3 2/3

  • 4.17 5 3

    4.18 5 4

    0.618 1 .

    1.618 4 5

    4

  • 6.:

    4.19 6 1

    26.18 2

    45

    4.20 6 2

  • Isometric

    0.618 .

    1 . 1 . 45 1.618 .

    1 . 0.618 . 1.618 2

    3 1.618 1

    L 1.618 . 0.618 . 0.309 45

    4.21 6 3

    Perspective

  • 4.22 6 4

    Perspective

    GEEK

    4.23 6 5

    Extrude 168.1

  • 7.

  • 8. THE BEST

    4.24 THE BEST (FIRST)

  • 4.25 THE BEST (SECOND)

  • 9.:

    4.26 1

    4.27 2

  • 10.

    4.28 1

    4.29 1

    Golden Ratio

  • 4.30 2

    4.31 2

  • 4.32 3

    4.33 3

  • 4.34 4

    4.35 4

  • 4.36 5

    4.37 5

  • 11. A1 200

    THE BEST (FIRST)

    4.38 THE BEST (FIRST) A1

  • 5

    1.

    -

    The Geometers Sketchpad

    Adobe illustrator

    2.

    Golden rectangle

    3.

    A3 A1 200

  • 4.

    3

    5.

  • Golden ratio Wikipedia [Online]. 30 2557 :

    http://en.wikipedia.org/wiki/Golden_ratio,

    The Golden Ratio [Online] '.

    30 2557 : http://travel.truelife.com/detail/818648

    Golden Ratio [Online]. 5 2557 :

    http://mathworld.wolfram.com/GoldenRatio.html

  • Inkscape

  • Inkscape

    1. Ctrl+

    2. , Shift+ ,

    3.

    4.

    Zoom ,

    Inkscape Zoom ()

    Zoom ()

    Zoom

    1. + Zoom , Zoom

    2. Ctrl+ Zoom , Shift+ Zoom

    3. Ctrl+

    4 . Zoom ()

    F3 Zoom

    5. %

    Inkscape Inkscape

  • Inkscape (Undo)

    Ctrl+Z (Redo) Shift+Ctrl+Z

    , ,

    Inkscape ,

    /

    F1 Inkscape

    1.

    2. Ctrl+

    3. /

    4. Ctrl+ /

    5.

    6. Ctrl+ 15

    7.

    8. Alt+ 1

    9. /

    10. Ctrl + / 1

    11. Alt + / 1

    12. [,] 15

    13. Ctrl + [,] 90

    14. Alt + [,] 1

    Inkscape

    1.

  • 2. Shift+ (2)

    3. (1)

    4. Shift+

    Group

    ( 2 ) group

    group group

    / group

    group Ctrl + G group

    group group Shift + Ctrl + G

    group

    Fill Stroke

    Inkscape Fill Stroke Fill

    Stroke Fill Stroke

    Shift + Ctrl + F

    Fill Stroke Fill Stroke

    Inkscape

    1. Home

    2. End

    3. PageUp 1

    4. PageDown 1

  • Tab

    Shift + Tab

    Selecting under

    Alt+

    1

    (Text to Pattern)

    .1

    .2

    1.

    2. Edit > Object(s) to Pattern

  • 3.

    Edit path nodes or control handles F2

    4.

    5. Object > Fill and Stroke

    6. Fill Pattern Pull down

    .3

    .4

    1.

    2. 2

    3. Text > Put on Path

    1 Geek 2 3 4 11111 5 inkscape