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Sphere Structure Pattern

Sphere Structure Pattern
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2017-11-12 05:04
FunctionSolid GeometryProbability & StatisticsTransformationGeometric Construction
This example demonstrates the generation and transformation process of a sphere structure pattern. Core mathematical concepts include sphere, similarity transformation, Poisson distribution, scalene triangles, differential equations, and function graphs. Construction highlights from the summary involve commands like Polygon, Vector, Sphere, Translate, and Sequence in GeoGebra. Suitable for high school and above learners to understand the integration of spatial geometry, transformations, and probability & statistics.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3, xOyPlane) → poly1, f, g, h, C
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. Sphere(A, B) → a
  5. Translate(a, Vector[(2 * u)]) → a'
  6. Translate(a, Vector[(2 * v)]) → a'_1
  7. Sequence(Sequence[Translate[a, Vector[((2 * c) * u) + ((2 * r) * v)]], c, 1, s], r, 1, s) → L_1
  8. Sequence(Sequence[Translate[a, Vector[((2 * c) * u) + ((2 * r) * v)]], c, 1, s - r], r, 1, s) → L_2
  9. Vector((0, 0, 0), (0.5, 0.2888, 0.6666)) → w
  10. Sequence(Sequence[Sequence[Translate[a, Vector[((2 * c) * u) + ((2 * r) * v) + ((2 * l) * w)]], c, 1, s - r], r, 1, s], l, 1, s) → L_3
  11. Sequence(Sequence[Sequence[Translate[a, Vector[((2 * c) * u) + ((2 * r) * v) + ((2 * l) * w)]], c, 1, s - r], r, 1, s - l], l, 1, s) → L_4
  12. Sequence(Sequence[Sequence[Translate[a, Vector[((2 * c) * u) + ((2 * r) * v) + ((2 * l) * w)]], c, 0, s - r - l - 1], r, 0, s - l - 1], l, 0, s - 1) → L_5