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Dynamic Construction and Symmetry of a Triangular Prism

Dynamic Construction and Symmetry of a Triangular Prism
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2020-12-18 11:40
PolygonSolid GeometryMatrixTransformationSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
① This example demonstrates a triangular prism in 3D, with interactive sliders and text displays to explore its geometric properties. ② Core mathematical concepts include the definition of a prism, relationships between base and lateral faces, symmetry, perimeter, and the use of piecewise functions to control shape variations. ③ Construction highlights: GeoGebra commands such as Line, If, Polygon, Rotate, and Prism are used; objects include multiple points (ShapePt1, ShapePt2, etc.), a rotation axis (RotateAxis), base shapes (ShapeBase), and text objects (TextShowChi, TextShowName2) with sliders (TextSlider1-6) for dynamic adjustment. ④ Suitable for high school or early college students for intuitive teaching of solid geometry, and for exploring matrix transformations and symmetry in 3D shapes.

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. 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
  10. Polygon(ShapePt1a, ShapePt2a, ShapePt3a) → ShapeBase2D, shapept3a, shapept1a, shapept2a
  11. Polygon(ShapePt1, ShapePt2, ShapePt3) → ShapeBase, shapept3, shapept1, shapept2
  12. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  13. Prism(ShapeBaseR, (S1 * S2)) → Shape, A, edge3, edgeAB, edgeBC, edgeAC, B, C, face1, face3, face2, faceABC, edge1, edge2
  14. If(ShowChi, "角柱", "Prism") → TextName1
  15. If(ShowChi, "三角柱體", "Triangular Prism") → TextName2

AI Drawing Prompt Reference

Draw a triangular prism with its base and lateral faces. First, draw a triangular base, then rotate the base around the rotation axis to generate the lateral faces, and finally combine the base and lateral faces to form the triangular prism. Use sliders to adjust the prism's height, size, position, and transparency, and display the prism's name and the name of the base shape.
The prompt above was compiled from the original drawing commands and is for reference only.