STEM workshop 2018

Arthur Lee, Nov 9, 2018

Table of Contents

  1. Start Here
    1. workshop guide
    2. Workshop Videos
    3. Sine Effect
    4. Moss Egg or Euclidean Egg
    5. polygon patterns from rotation
    6. dilate and rotate
    7. Curve Stitching
  2. Transformation tutorial
    1. Rotation and Dilation
    2. Using sequence command
    3. More about sequence
    4. Modify triangle spiral
    5. Other spirals
    6. Different sequences
  3. Tessellation tutorial
    1. Translation in 2 directions
    2. Simple tessellation
    3. Setup for tessellation
    4. Common tessellations
    5. making pentagonal tiles
  4. Animation
    1. sun and sea
    2. Moon and Sea
    3. Halloween with sound
    4. making strange shapes from a circle and quadrilateral
    5. Stormy Night
  5. Cone Modeling
    1. Making a cone
    2. maximum cone
    3. relating variables
    4. spreadsheets
    5. wet surface (angle)
    6. wet surface (ratio)
    7. cone analysis
  6. Voronoi
    1. River excursion
    2. nearest sites
    3. Voronoi 3
    4. nearest among 4 sites
    5. Voronoi Diagram
    6. Voronoi Diagram of 4 points
    7. Voronoi Diagram of 5 points
    8. where perpendicular bisectors intersect
    9. perpendicular bisectors and angles

1.

Start Here

  • 1. workshop guide
  • 2. Workshop Videos
  • 3. Sine Effect
  • 4. Moss Egg or Euclidean Egg
  • 5. polygon patterns from rotation
  • 6. dilate and rotate
  • 7. Curve Stitching

1.1.

workshop guide

Please follow this link for more info about this workshop:[br][url=https://www.evernote.com/l/AAOqYsqdOypPxbpyToq6YpASSxb6SW2l5qg]https://www.evernote.com/l/AAOqYsqdOypPxbpyToq6YpASSxb6SW2l5qg[/url]
[color=#9900ff]Activities in this workshop mainly come from the following books:[/color][br][br][color=#a61c00]When STEM meets GeoGebra[/color] [url=https://www.geogebra.org/m/DmXMD4wP]https://www.geogebra.org/m/DmXMD4wP[/url] [br][br][color=#a61c00]GeoGebra Courses for STEM: Examples[/color] [url=https://ggbm.at/KDx5BTeZ]https://ggbm.at/KDx5BTeZ[/url] [br][br][color=#a61c00]Symmetry, Transformation and Tessellation[/color] [url=https://ggbm.at/keCJGAcP]https://ggbm.at/keCJGAcP[/url] [br][br][color=#a61c00]Art and Design[/color] [url=https://ggbm.at/FecdkeK4]https://ggbm.at/FecdkeK4[/url] [br][br][color=#a61c00]Voronoi Partitioning [/color][url=https://ggbm.at/Ff6ZJdux]https://ggbm.at/Ff6ZJdux[/url] [br][br][color=#a61c00]Demo Collection[/color] [url=https://ggbm.at/KWSttU5t]https://ggbm.at/KWSttU5t[/url] 
– Arthur Lee

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1.3.

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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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2.

Transformation tutorial

  • 1. Rotation and Dilation
  • 2. Using sequence command
  • 3. More about sequence
  • 4. Modify triangle spiral
  • 5. Other spirals
  • 6. Different sequences

2.1.

Rotation and Dilation

combine rotation and dilation
In this example, a triangle (named 'poly1') is rotated and dilated with a specified angle t and factor r, about the center A. The two transformations can be combined as one in the command.[br][br][color=#ff0000]Dilate[Rotate[poly1, t, A], r, A][/color]
repeat the action
We can continue with this action on each object formed, resulting in a series of triangles, which can be named as poly2, poly3, poly4, etc by repeating the command in the following way:[br][br][color=#ff0000]poly2=Dilate[Rotate[poly1, t, A], r, A][br]poly3=Dilate[Rotate[poly2, t, A], r, A][br]poly4=Dilate[Rotate[poly3, t, A], r, A][br]poly5=Dilate[Rotate[poly4, t, A], r, A][br]…...[/color]
figure 2
varying the parameters
Here is another way for creating each of these triangles by varying the angle and factor each time, but applying the transformation to the first figure only.[br][br][color=#ff0000]Dilate[Rotate[poly1, n*t, A], r^n, A][/color][br][br]We use the letter n to indicate suitable angle and factor if the action is repeated on the first triangle. Drag the slider for n to see the effect.
figure 3
– Arthur Lee, GeoGebra Institute of Hong Kong

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3.

Tessellation tutorial

  • 1. Translation in 2 directions
  • 2. Simple tessellation
  • 3. Setup for tessellation
  • 4. Common tessellations
  • 5. making pentagonal tiles

3.1.

Translation in 2 directions

translation by combination of vectors
An object can be translated with various combinations of given vectors. For example, the following shape (poly1) is translated by the vector u+2v. The command is:[br][br][color=#ff0000]Translate[poly1, u+2v][/color][br][br]This means that poly1 is moved by the vector u, and then further moved by the vector 2v. Change vector u or v to see how the movement is affected.
figure 13
translate repeatedly in the same direction
We create a list of objects by translating ploy1 using different multiples of vector u (from -3u to 3u). [br][br]The command is:[br][color=#ff0000][br]list1=Sequence[Translate[poly1, m*u], m, -3, 3][/color][br][br]The result is a set of 7 copies called list1. This list1 can then be transformed in another way as a single object.
figure 14
moving in another direction
The list1 created in previous example can be moved in another direction by the vector v. The slider k is used to illustrate how this result may change by using different multiples of vector v.[br][br]The new list is created by the command:[br][br][color=#ff0000]Translate[list1, k*v][/color]
figure 15
array of objects
An array of objects can be made by generating another list, which contains multiple translations of previous object 'list1'. The command is:[br][color=#ff0000][br]Sequence[Translate[list1, n*v], n, -3, 3][/color]
figure 16
– Arthur Lee, GeoGebra Institute of Hong Kong

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3.3.

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3.4.

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3.5.

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4.

Animation

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

4.1.

sun and sea

Create simple animation with basic graphical objects.
Do you see a circle, sine graph and a parabola?[br]Try a more wavy version here: [br]https://www.geogebra.org/m/VBdJAxb6
– Arthur Lee

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4.5.

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5.

Cone Modeling

  • 1. Making a cone
  • 2. maximum cone
  • 3. relating variables
  • 4. spreadsheets
  • 5. wet surface (angle)
  • 6. wet surface (ratio)
  • 7. cone analysis

5.1.

Making a cone

This applet shows folding of a paper cone. Various geometric features in this process can be discussed. [br]In particular, the relation among the angle of the sector ([math]\theta[/math]), slant height ([i]l[/i]) and base radius of the cone ([i]r[/i]) can be carefully examined: [br][br][math]\frac{r}{l}=\frac{\theta}{360^\circ}[/math][br][br]Drag [color=#ff0000]V[/color] to fold/unfold the cone. Drag [color=#1e84cc]B[/color] to change the size of the paper sector.
Check this tutorial for this construction:[br]https://ggbm.at/mrXDrjMQ
– Arthur Lee

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5.4.

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5.5.

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5.6.

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5.7.

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6.

Voronoi

  • 1. River excursion
  • 2. nearest sites
  • 3. Voronoi 3
  • 4. nearest among 4 sites
  • 5. Voronoi Diagram
  • 6. Voronoi Diagram of 4 points
  • 7. Voronoi Diagram of 5 points
  • 8. where perpendicular bisectors intersect
  • 9. perpendicular bisectors and angles

6.1.

River excursion

Drag points A-E to positions along the river, which are equally far away from rescue stations U and V.
– Arthur Lee

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6.9.

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Information