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Dynamic Construction and Rotation of a Quadrilateral Prism

Dynamic Construction and Rotation of a Quadrilateral Prism
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2020-12-18 11:44
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
① This GeoGebra example dynamically demonstrates the construction of a quadrilateral prism (a four-sided prism), allowing users to adjust the prism's shape, rotation axis, and display options via sliders to observe changes in the 3D solid. ② Core mathematical concepts include solid geometry definitions of prisms, quadrilateral bases, lateral faces and edges, as well as spatial rotation transformations; it also involves basic geometric elements like polygons, lines, and points. ③ Construction highlights: from the construction summary, commands such as Line, If, Polygon, Rotate, and Prism are used, along with multiple control points (e.g., ShapePt1~4, ShapePtAxis) and sliders (TextSlider1~6). The rotation axis (RotateAxis) enables dynamic rotation, and text objects (TextShowChi, etc.) provide interactive toggles. ④ Suitable for middle/high school solid geometry lessons or math lab activities, helping students understand prism structure, rotational symmetry, and parametric construction methods, as well as exploring how different base shapes affect the prism's appearance.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a quadrilateral prism with dynamic construction and rotation. The base is a quadrilateral, and its shape, as well as the prism's height, size, position, and transparency, can be adjusted using sliders. Set a rotation axis to allow the prism to rotate around it. Include text labels for naming the prism and its adjustable properties.
The prompt above was compiled from the original drawing commands and is for reference only.