STEM 遇上 GeoGebra 示例 (GeoGebra for STEM Exemplars)

Anthony OR 柯志明, Jun 9, 2016

Table of Contents

  1. 密鋪 Tessellation
    1. 密鋪正多邊形
    2. 密鋪四邊形
    3. Tessellation
    4. Daisy Tessellation
    5. Triangle Tessellation
    6. Hexagon Tessellation
    7. Kite Tessellation
    8. Cat Tiling
    9. Islamic Tessellation on Octagons and Squares
    10. Qarawiyyin Mosque
    11. Qarawiyyin Tiling (generalized)
  2. 繡曲線 Curve Stitching
    1. 繡曲線
    2. 製作及設計繡曲線
  3. 變換 Transformations
    1. Rotation of Regular Polygons
    2. Equiangular Spiral on Nautilus Shell
    3. Rotating and Dilating Squares
    4. combining spirals
    5. polygon ring
    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
    16. rings
  4. 幾何探索 Geometric Explorations
    1. 等邊三角形中的一點到三條邊的距離
    2. Quadrilateral Exploration 3
  5. 物理學的應用 Applications in Physics
    1. Projectile
    2. Parabolas
    3. Rebounds
  6. Other Exemplars
    1. making strange shapes from a circle and quadrilateral
    2. Halloween with sound
    3. Moon and Sea
    4. sun and sea
    5. Point of Division

1.

密鋪 Tessellation

  • 1. 密鋪正多邊形
  • 2. 密鋪四邊形
  • 3. Tessellation
  • 4. Daisy Tessellation
  • 5. Triangle Tessellation
  • 6. Hexagon Tessellation
  • 7. Kite Tessellation
  • 8. Cat Tiling
  • 9. Islamic Tessellation on Octagons and Squares
  • 10. Qarawiyyin Mosque
  • 11. Qarawiyyin Tiling (generalized)

1.1.

密鋪正多邊形

– Anthony OR 柯志明

1.2.

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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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1.8.

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1.9.

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1.10.

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1.11.

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2.

繡曲線 Curve Stitching

  • 1. 繡曲線
  • 2. 製作及設計繡曲線

2.1.

繡曲線

重覆點擊 ▶▶ 鈕，看看如何構作以下圖形。[br]根據老師指示，構作這個圖形。
使用 Sequence 指令構作以下圖形。
構作以下圖形。
– Anthony OR 柯志明, GeoGebra Institute of Hong Kong

2.2.

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3.

變換 Transformations

  • 1. Rotation of Regular Polygons
  • 2. Equiangular Spiral on Nautilus Shell
  • 3. Rotating and Dilating Squares
  • 4. combining spirals
  • 5. polygon ring
  • 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
  • 16. rings

3.1.

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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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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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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4.

幾何探索 Geometric Explorations

  • 1. 等邊三角形中的一點到三條邊的距離
  • 2. Quadrilateral Exploration 3

4.1.

等邊三角形中的一點到三條邊的距離

課業 2.5
下圖顯示等邊三角形中的一點 P 與邊 AB 的距離。[br]構作由 P 到 BC 及 AB 的距離。[br]這三個距離之和有甚麼特性？[br]你能夠解釋嗎？
– Anthony OR 柯志明, GeoGebra Institute of Hong Kong

4.2.

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5.

物理學的應用 Applications in Physics

  • 1. Projectile
  • 2. Parabolas
  • 3. Rebounds

5.1.

Projectile

– Anthony OR 柯志明

5.2.

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5.3.

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6.

Other Exemplars

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

6.1.

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

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6.5.

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Information