Three Holes in a Cube: Nested Sequence Commands in 3D Geometry

Three Holes in a Cube: Nested Sequence Commands in 3D Geometry
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2016-10-22 02:27
① This example demonstrates how to create three through-holes inside a cube, producing a hollowed 3D solid that visually illustrates spatial boolean operations. ② Core mathematical concepts include solid geometry (polyhedra, cylinders/spheres intersecting a cube), vectors in 3D, and unit circle parameterization for positioning holes. ③ Construction highlights: The GeoGebra commands Sequence, objects like sphere (pallo) and list (lista3) are used with nested loops to generate multiple holes at controlled positions and orientations, showcasing advanced scripting for parametric modeling. ④ Suitable for high school or university courses in solid geometry, and for learners exploring GeoGebra's nested sequence commands to build complex 3D structures, enhancing skills in spatial reasoning and computational geometry.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[If[j^(2) + k^(2) + m^(2) ≤ 9, (j, k, m)], j, -3, 3], k, -3, 3], m, -3, 3) → pallo
  2. Sequence(Sequence[Sequence[If[¬(-1 ≤ j ≤ 1 ∧ -1 ≤ k ≤ 1 ∨ -1 ≤ j ≤ 1 ∧ -1 ≤ m ≤ 1 ∨ -1 ≤ k ≤ 1 ∧ -1 ≤ m ≤ 1), (j, k, m)], j, -3, 3], k, -3, 3], m, -3, 3) → lista3