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Dynamic Construction and Rotation of a Quadrilateral Pyramid

Dynamic Construction and Rotation of a Quadrilateral Pyramid
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2020-12-18 12:00
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
① This example demonstrates a quadrilateral pyramid (a pyramid with a quadrilateral base) in 3D, with sliders controlling its shape and rotation to explore the solid from different viewpoints. ② Core mathematical concepts include solid geometry, the definition of a pyramid, the relationship between the quadrilateral base, apex, and lateral edges, as well as transformations and rotations in space. ③ Construction details: GeoGebra commands such as Line (for edges), Polygon (for the base), Rotate (for rotation), and Pyramid (to generate the solid) are used, along with multiple sliders (TextSlider1-6) to adjust parameters. Key objects include ShapePt1-4, ShapeBase, RotateAxis, and various text labels for dynamic interaction. ④ Suitable for high school or introductory college students learning solid geometry, this interactive model helps understand pyramid structure, rotational symmetry, and parametric modeling, and serves as an effective teaching tool for instructors.

GeoGebra Commands & Parameters

  1. Line((0, 1, 0), (0, 0, 0)) → RotateAxis
  2. If(ShowChi, "依據立體底的形狀命名", "Naming by the base of the shape") → TextShowName2
  3. If(ShowChi, "立體高度", "Height") → TextSlider1
  4. If(ShowChi, "立體大小", "Size") → TextSlider2
  5. If(ShowChi, "立體位置(高低)", "Vertical Position") → TextSlider3
  6. If(ShowChi, "立體位置(橫向)", "Horizontal Position") → TextSlider4
  7. If(ShowChi, "透明度", "Transparency") → TextSlider6
  8. If(ShowChi, "旋轉立體", "Rotate the shape") → TextSlider5
  9. Polygon(ShapePt1, ShapePt2, ShapePt3, ShapePt4) → ShapeBase, shapept1, shapept2, shapept3, shapept4
  10. Polygon(ShapePt1a, ShapePt2a, ShapePt3a, ShapePt4a) → ShapeBase2D, shapept1a, shapept2a, shapept3a, shapept4a
  11. If(ShowChi, "用這圖形調節立體底部的形狀", "Adjust the base of the 3D shape by this figure.") → TextName3
  12. If(ShowChi, "四角錐體", "Quadrilateral Pyramid") → TextName2
  13. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  14. Pyramid(ShapeBaseR, (S1 * S2)) → Shape, A, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  15. If(ShowChi, "角錐", "Pyramid") → TextName1

AI Drawing Prompt Reference

Draw a quadrilateral pyramid by adjusting the shape of the base with four points, and use sliders to change the height, size, position, and transparency of the pyramid. Rotate the pyramid around an axis to generate its sides and vertices.
The prompt above was compiled from the original drawing commands and is for reference only.