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Creating a Cube by Stacking Three Pyramids

Creating a Cube by Stacking Three Pyramids
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2017-02-12 21:29
TrigonometrySolid GeometryGeometric Construction
In collections Volume of a pyramid
This example demonstrates how to construct a cube by stacking three pyramids. It involves core mathematical concepts such as solid geometry, volume calculation, and geometric transformations. The construction uses GeoGebra commands like Min, Max, Pyramid, Line, Rotate, Segment, and Plane. Suitable for high school geometry education, helping students understand the construction and volume relationships of polyhedra.

GeoGebra Commands & Parameters

  1. Min((Max[t - 4, 0] * 2), 2) → b_3
  2. Min((Max[t - 3, 0] * 2), 2) → b_2
  3. Max(0, Min[t - 1, 1]) → b_1
  4. Pyramid(A_1, A_2, A_3, A_4, A_5) → a, Fläche5, Kante3, Kante5, Kante7, Kante8, Fläche1, Fläche3, Fläche4, Fläche2, Kante1, Kante4, Kante6, Kante2
  5. Pyramid(B_1, B_2, B_3, B_4, B_5) → c_1, Fläche6, Kante13, Kante14, Kante15, Kante16, Fläche7, Fläche8, Fläche9, Fläche10, Kante9, Kante10, Kante11, Kante12
  6. Pyramid(C_1, C_4, C_5, C_6, C_3) → e, Fläche11, Kante21, Kante22, Kante23, Kante24, Fläche12, Fläche13, Fläche14, Fläche15, Kante17, Kante18, Kante19, Kante20
  7. Min((Max[t - 2, 0] * π / 2), 1.5707963267948966) → dw_3
  8. Line(D, D_1) → s_x
  9. Rotate(e, (-dw_3), s_x) → e'
  10. Segment(A_5, Fp_1) → lot_1
  11. Segment(B_5, Fp_2) → lot_2
  12. Segment(Fp_3, Fp_3 + (0, 0, 4)) → lot_3
  13. Line((2, 0, 0), (2, 1, 0)) → s_{xy1}
  14. Line((-2, 0, 0), (-2, 1, 0)) → s_{xy2}
  15. Plane((0, 0, 4), (1, 0, 4), (1, 1, 4)) → c

AI Drawing Prompt Reference

Draw a cube constructed by stacking three pyramids, illustrating core geometric concepts. First, create three pyramids with square bases of decreasing sizes, then stack them sequentially using rotation and translation to form a cube. The pyramids' apexes meet at the center of the cube's top face, while their bases form the bottom face of the cube. The structure should clearly display the geometric relationships and volume relationships between the pyramids and the cube.
The prompt above was compiled from the original drawing commands and is for reference only.