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Hexagonal Pyramid Dynamic Construction and Centroid

Hexagonal Pyramid Dynamic Construction and Centroid
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2020-12-18 12:07
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
This GeoGebra example demonstrates the dynamic construction of a regular hexagonal pyramid (six-sided pyramid) and visualizes the centroid (barycenter) as the apex moves. The core mathematical concepts include solid geometry, pyramid definition, regular hexagonal base, centroid calculation, and parametric control via sliders. The construction uses GeoGebra commands such as Line, Polygon, Rotate, and Pyramid to build the base hexagon and the pyramid, with multiple point objects (ShapePt1a to ShapePt6a) defining the base vertices. Sliders (TextSlider1 to TextSlider6) control rotation angles and apex position, while text objects (TextShowChi, ShowChi) display the centroid. This is suitable for high school or early college students learning solid geometry, spatial reasoning, and dynamic geometry software, and can be used in math lab activities to explore properties of pyramids.

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, ShapePt4a, ShapePt5a, ShapePt6a) → ShapeBase2D, shapept1a, shapept2a, shapept3a, shapept4a, shapept5a, shapept6a
  11. Polygon(ShapePt1, ShapePt2, ShapePt3, ShapePt4, ShapePt5, ShapePt6) → ShapeBase, shapept1, shapept2, shapept3, shapept4, shapept5, shapept6
  12. If(ShowChi, "六角錐體", "Hexagonal Pyramid") → TextName2
  13. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  14. Pyramid(ShapeBaseR, (S1 * S2)) → Shape, A, edge3, edge4, edge5, edge6, face1, face3, face4, face5, face6, face2, edge1, edge2
  15. If(ShowChi, "角錐", "Pyramid") → TextName1

AI Drawing Prompt Reference

Create a dynamic 3D construction of a regular hexagonal pyramid. Build the base as a regular hexagon defined by six base vertices, then place an apex above the base to form the pyramid with six lateral edges and corresponding faces. Make the shape respond to sliders controlling height, size, vertical position and horizontal position, as well as a rotation angle that rotates the solid while also rotating the base figure. Compute and display the centroid (barycenter) of the pyramid’s base and label it so its position can be seen as the apex moves. Include a transparency control to adjust visual appearance, and show a text title indicating “Hexagonal Pyramid / 六角錐体”.
The prompt above was compiled from the original drawing commands and is for reference only.