STEM 遇上 GeoGebra：陳瑞祺永援中學

Anthony OR 柯志明, Feb 22, 2017

Table of Contents

  1. Construction Tasks
    1. Equilateral Triangles and Regular Hexagons Inscribed in Circles
    2. Tessellation
    3. polygon ring
    4. Rotating and Dilating Squares
    5. Constructing Loci
  2. 3D Constructions and Explorations
    1. Cross-Sections of the Cube
    2. Rotational Symmetry of Cubes
    3. Other Net of Tetrahedron
    4. Unwrapping a Cylinder Cut by An Oblique Plane (Answer)
    5. Movable Dandelin spheres
  3. Inquiry and Problem Solving
    1. Inquiry Task (Elementary)
    2. Inquiry Task (Intermediate)
    3. Triangle on Parallel Lines
  4. Algebraic Thinking and Coding
    1. Curve Stitching
  5. Tessellation 密鋪平面
    1. Tessellation
    2. Tessellation
    3. Daisy Tessellation
    4. Triangle Tessellation
    5. Hexagon Tessellation
    6. Kite Tessellation
    7. Cat Tiling
    8. Islamic Tessellation on Octagons and Squares
    9. Qarawiyyin Mosque
    10. Qarawiyyin Tiling (generalized)
  6. Transformations 變換
    1. Rotation of Regular Polygons
    2. polygon ring
    3. Equiangular Spiral on Nautilus Shell
    4. Spirals in a Square
    5. combining spirals
    6. Dilations of a star
    7. Spiral from polygons
    8. math and art 1
    9. maths and art2
    10. Maths and art 3
    11. Maths and art4
    12. Maths and art5
    13. Sine Wave Rotating Triangle
    14. converging color spirals
    15. Spiral Square
  7. Applications in Physics 物理學的應用
    1. Projectile
    2. Parabolas
    3. Relative Velocity: Boat Crossing a River
    4. Lens Simulation for iPad
    5. 2D Image Formation by Lenses
    6. iPad Spherical Mirror Simulation
    7. Dispersion of Light
    8. The Doppler Effect with Sound
    9. Double Slit Interference
    10. Wave interference
    11. Combination Electric Circuit with Four Identical Bulbs
  8. Applications in Chemistry 化學科的應用
    1. Models of the water molecule
    2. Models of the methane molecule
    3. Models of the ethyl spirit molecule
    4. Models of the benzene molecule

1.

Construction Tasks

  • 1. Equilateral Triangles and Regular Hexagons Inscribed in Circles
  • 2. Tessellation
  • 3. polygon ring
  • 4. Rotating and Dilating Squares
  • 5. Constructing Loci

1.1.

Equilateral Triangles and Regular Hexagons Inscribed in Circles

Drag the points in the two figures below to see the effects.[br]Can you construct these two figures?
[b]Task 2.1[/b][br]Construct the following regular hexagon and start the animation.[br]Save your answer in the name "2.1[color=#0000ff][i]x[/i][color=#000000]_[i][color=#ff0000]yourname[/color][/i].ggb", where[color=#0000ff][i] x[/i][/color] denotes the letter of the part (a to e) and [color=#ff0000][i]yourname[/i] [color=#000000]is your name in English. Send an email titled [color=#0000ff][color=#000000][color=#ff0000][color=#000000]"[b]MATP1331 Lesson 2 Answers[/b]" [/color][/color][/color][/color]with your answers of this session attached to [b]geogebra.hk@gmail.com [/b][/color][/color][/color][/color]
– GeoGebra Institute of Hong Kong

1.2.

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1.3.

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1.4.

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1.5.

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2.

3D Constructions and Explorations

  • 1. Cross-Sections of the Cube
  • 2. Rotational Symmetry of Cubes
  • 3. Other Net of Tetrahedron
  • 4. Unwrapping a Cylinder Cut by An Oblique Plane (Answer)
  • 5. Movable Dandelin spheres

2.1.

Cross-Sections of the Cube

What are the possible shapes of a cross-section of the cube?
Cross-Sections of the Cube
– GeoGebra Institute of Hong Kong

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.

Inquiry and Problem Solving

  • 1. Inquiry Task (Elementary)
  • 2. Inquiry Task (Intermediate)
  • 3. Triangle on Parallel Lines

3.1.

Inquiry Task (Elementary)

Task 2.4
Construct the following figure.[br]At what positions of P would the two rectangles have equal areas?[br]Can you justify your observation?
– Anthony OR 柯志明, GeoGebra Institute of Hong Kong

3.2.

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3.3.

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4.

Algebraic Thinking and Coding

  • 1. Curve Stitching

4.1.

Curve Stitching

– Anthony OR 柯志明

5.

Tessellation 密鋪平面

  • 1. Tessellation
  • 2. Tessellation
  • 3. Daisy Tessellation
  • 4. Triangle Tessellation
  • 5. Hexagon Tessellation
  • 6. Kite Tessellation
  • 7. Cat Tiling
  • 8. Islamic Tessellation on Octagons and Squares
  • 9. Qarawiyyin Mosque
  • 10. Qarawiyyin Tiling (generalized)

5.1.

Tessellation

1.1 Tessellation of Regular Polygons
Follow the teacher's instructions, construct the following figure using the [b]"Slider" tool[/b], "[b]Regular Polygon" tool[/b], the [b]"Vector" tool[/b] and the [b]"Translate by Vector" tool[/b].[br][br]Explore what regular polygons could tessellate the plane.
1.2 Tessellating a Quadrilateral
Investigate whether a quadrilateral could tessellate the plane.
1.3 Tessellating Regular Polygons using Commands
Use the [b]Sequence[/b] command to construct the following figure.
– Anthony OR 柯志明, GeoGebra Institute of Hong Kong

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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6.

Transformations 變換

  • 1. Rotation of Regular Polygons
  • 2. polygon ring
  • 3. Equiangular Spiral on Nautilus Shell
  • 4. Spirals in a Square
  • 5. combining spirals
  • 6. Dilations of a star
  • 7. Spiral from polygons
  • 8. math and art 1
  • 9. maths and art2
  • 10. Maths and art 3
  • 11. Maths and art4
  • 12. Maths and art5
  • 13. Sine Wave Rotating Triangle
  • 14. converging color spirals
  • 15. Spiral Square

6.1.

Rotation of Regular Polygons

2.1 Rotating the Regular Pentagon
Follow the teacher's instructions, construct the following figure using the "[b]Regular Polygon" tool[/b], the [b]"Point" tool [/b]and the [b]"Rotate around Point" tool[/b].
2.2 Rotating the Regular Pentagon with Sequence Command
Use the [b]Sequence[/b] command to construct the following figure.
Task 2.2 Rotating the Regular Octagon
Draw the following figure. Do you know how to locate the red point precisely?[br]Save your answer in the name "2.[color=#000000]2[/color][color=#0000ff][color=#000000]_[i][color=#ff0000]yourname[/color][/i].ggb", where [color=#ff0000][i]yourname[/i] [color=#000000]is your name in English. Send an email titled [color=#0000ff][color=#000000][color=#ff0000][color=#000000]"[b]MATS2320 Lesson 2 Answers[/b]" [/color][/color][/color][/color]with all your answers of this session attached to [b]geogebra.hk@gmail.com.[/b][/color][/color][/color][/color]
– GeoGebra Institute of Hong Kong

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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7.

Applications in Physics 物理學的應用

  • 1. Projectile
  • 2. Parabolas
  • 3. Relative Velocity: Boat Crossing a River
  • 4. Lens Simulation for iPad
  • 5. 2D Image Formation by Lenses
  • 6. iPad Spherical Mirror Simulation
  • 7. Dispersion of Light
  • 8. The Doppler Effect with Sound
  • 9. Double Slit Interference
  • 10. Wave interference
  • 11. Combination Electric Circuit with Four Identical Bulbs

7.1.

Projectile

– Anthony OR 柯志明

7.2.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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8.

Applications in Chemistry 化學科的應用

  • 1. Models of the water molecule
  • 2. Models of the methane molecule
  • 3. Models of the ethyl spirit molecule
  • 4. Models of the benzene molecule

8.1.

Models of the water molecule

Models of the water molecule
Models of the water molecule
– uStas

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8.4.

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