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Pentagonal Pyramid Dynamic Construction and Geometric Transformations

Pentagonal Pyramid Dynamic Construction and Geometric Transformations
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2020-12-18 12:05
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
This GeoGebra example demonstrates the construction of a pentagonal pyramid (a solid with a regular pentagonal base and an apex), with interactive sliders and draggable points for dynamic exploration. Core mathematical concepts include solid geometry properties of pyramids, polygons, rotation, centroid/barycenter, linear equations, and angle relationships. The construction uses GeoGebra commands such as Line, Polygon, Rotate, and Pyramid, along with auxiliary points (ShapePt1 to ShapePt5) and a rotation axis (RotateAxis) to build the base and lateral faces. Conditional statements (If) control visibility, and multiple sliders (TextSlider1-6) allow parameter adjustments. This resource is suitable for high school or early college students to understand pyramid geometry, spatial transformations, and parametric modeling.

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(ShapePt1a, ShapePt2a, ShapePt3a, ShapePt4a, ShapePt5a) → ShapeBase2D, f, g, h, i, j
  10. 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
  11. Polygon(ShapePt1, ShapePt2, ShapePt3, ShapePt4, ShapePt5) → ShapeBase, k, l, m, n, p
  12. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  13. Pyramid(ShapeBaseR, (S1 * S2)) → Shape, A, edge4, edge5, face1, face3, face4, face5, face2, edge1, edge2, edge3
  14. If(ShowChi, "五角錐體", "Pentagonal Pyramid") → TextName2
  15. If(ShowChi, "角錐", "Pyramid") → TextName1

AI Drawing Prompt Reference

Draw a pentagonal pyramid with a regular pentagonal base and an apex directly above the center. Include sliders to adjust the height, size, vertical and horizontal position, and transparency of the pyramid, as well as a slider to rotate the shape. The base is defined by five draggable points, and the lateral faces are created by rotating the base around an axis. Display the name and relevant information of the pyramid.
The prompt above was compiled from the original drawing commands and is for reference only.