Art and Design

Arthur Lee, Sep 24, 2017

visual art and design with mathematics

Table of Contents

  1. draw
    1. Moss Egg or Euclidean Egg
    2. Ratio
    3. Parthenon
    4. Ratio
    5. Napoleon Tiling
    6. Curve Stitching in a Cube
    7. stitching in a cube
    8. Cairo Tiling 1
    9. Cairo Tiling 2
    10. symmetries of Napoleon's tessellation
  2. Islamic design
    1. Islamic design 1
    2. Islamic design 2
    3. 6 fold star pattern
    4. 6-fold star pattern analysis
    5. 5 fold star pattern experiment
  3. spiral
    1. Draw and Trace
    2. dilate and rotate
    3. Spiral from polygons
    4. Equiangular Spiral on Nautilus Shell
    5. Equiangular Spiral
    6. right triangle spiral
    7. combining spirals
    8. Spiraling cube faces
  4. polygon
    1. star polygon (double)
    2. polygon ring
    3. polygon ring double
    4. ring4
    5. polygon patterns making
  5. animation
    1. making strange shapes from a circle and quadrilateral
    2. sun and sea
    3. Moon and Sea
    4. Halloween with sound
    5. Complex Addition and Multiplication
  6. circular
    1. unit circle pattern 1
    2. Dot Pattern 2
    3. Dot Pattern 3
    4. creating symmetry

1.

draw

Check this book about transformation and tessellation: [url=https://ggbm.at/keCJGAcP]https://ggbm.at/keCJGAcP[/url]

  • 1. Moss Egg or Euclidean Egg
  • 2. Ratio
  • 3. Parthenon
  • 4. Ratio
  • 5. Napoleon Tiling
  • 6. Curve Stitching in a Cube
  • 7. stitching in a cube
  • 8. Cairo Tiling 1
  • 9. Cairo Tiling 2
  • 10. symmetries of Napoleon's tessellation

1.1.

Moss Egg or Euclidean Egg

Drag the green dot to change the egg to fish.
See the construction:[br][url=https://youtu.be/JE-L0VarQzo]https://youtu.be/JE-L0VarQzo[/url] [br][br]Based on Robert Dixon's Mathographics[br][url=https://books.google.com.hk/books?id=1fDgb17bgBkC&lpg=PP1&pg=PA3#v=onepage&q&f=false]https://books.google.com.hk/books?id=1fDgb17bgBkC&lpg=PP1&pg=PA3#v=onepage&q&f=false[/url]
– Arthur Lee

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

Islamic design

  • 1. Islamic design 1
  • 2. Islamic design 2
  • 3. 6 fold star pattern
  • 4. 6-fold star pattern analysis
  • 5. 5 fold star pattern experiment

2.1.

Islamic design 1

see my note[br]https://www.evernote.com/shard/s3/sh/0a24b81c-7071-4cc0-b145-ea52f72729a2/89dc07a9a7ce5162540165bf7dbeaf65
– Arthur Lee

2.2.

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2.3.

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2.4.

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2.5.

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3.

spiral

  • 1. Draw and Trace
  • 2. dilate and rotate
  • 3. Spiral from polygons
  • 4. Equiangular Spiral on Nautilus Shell
  • 5. Equiangular Spiral
  • 6. right triangle spiral
  • 7. combining spirals
  • 8. Spiraling cube faces

3.1.

Draw and Trace

Draw It
Draw and Trace
– Arthur Lee

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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4.

polygon

  • 1. star polygon (double)
  • 2. polygon ring
  • 3. polygon ring double
  • 4. ring4
  • 5. polygon patterns making

4.1.

star polygon (double)

– Arthur Lee

4.2.

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4.3.

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4.4.

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4.5.

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5.

animation

  • 1. making strange shapes from a circle and quadrilateral
  • 2. sun and sea
  • 3. Moon and Sea
  • 4. Halloween with sound
  • 5. Complex Addition and Multiplication

5.1.

making strange shapes from a circle and quadrilateral

Have some fun with the section formula (point of division). Use the slider to switch between a square and circle.
Click 'control' to display the original shapes. Drag the vertices to experiment with different starting quadrilateral.
[b]'[color=#ff0000]Pixar in a Box[/color]'[/b] has similar materials about modelling and 'weighted averages' -> [url=https://www.khanacademy.org/partner-content/pixar/environment-modeling-2]see the page on Environment Modeling[/url][br]https://www.khanacademy.org/partner-content/pixar/environment-modeling-2
These slides show more examples based on this applet.
How to make this file:
– Arthur Lee

5.2.

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5.3.

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5.4.

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5.5.

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6.

circular

  • 1. unit circle pattern 1
  • 2. Dot Pattern 2
  • 3. Dot Pattern 3
  • 4. creating symmetry

6.1.

unit circle pattern 1

The coordinates of A and B are expressed in terms of sin and cos of [math]\theta[/math]. [br]By varying the angle with the slider, points on the unit circle (or related to it) will be generated. [br]You may click the coordinates in the algebra window to reveal or edit the expressions. [br][br]Experiment with the tracing of segment to make different patterns.
quick silent demo
You can find a special example of pattern made in this way:[br][url=https://www.geogebra.org/m/aCjWafaN]https://www.geogebra.org/m/aCjWafaN[/url] [br][br]What other interesting patterns can you create?
Check how I make this applet.
– Arthur Lee

6.2.

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6.3.

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6.4.

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