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Alternate Sub-Division for Geodesic Dome

Alternate Sub-Division for Geodesic Dome
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2016-05-13 22:21
TrigonometrySolid GeometryParametric EquationGeometric ConstructionSlider Animation
This example demonstrates alternate sub-divisions for a geodesic dome. The parameter V can be varied from 1-30 to show different division patterns. Key math concepts include trigonometry, similarity transformation, and ratios. GeoGebra commands used in construction are Intersect, Point, Polygon, Sequence, and Mirror. Suitable for high school and above students to understand spherical geometry, trigonometry, and transformations.

GeoGebra Commands & Parameters

  1. Intersect(C_2, B_2, 1) → A
  2. Point(A_2) → B
  3. Intersect(C_2, A_2, 1) → C
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Sequence(A + (i * (C - A)), i, 0, 1, 1 / V) → L1
  6. Sequence(B + (i * (C - B)), i, 0, 1, 1 / V) → L2
  7. Sequence(A + (i * (B - A)), i, 0, 1, 1 / V) → L3
  8. Mirror(L3, x = 4) → L4
  9. Sequence(Segment[Element[L1, k], Element[L2, k]], k, 2, V) → L5
  10. Sequence(Segment[Element[L2, k], Element[L4, k]], k, 2, V) → L6
  11. Sequence(Segment[Element[L3, k], Element[L1, k]], k, 2, V) → L7
  12. Sequence(Segment[Element[L1, k], Element[L2, k + 1]], k, 1, V) → L8

AI Drawing Prompt Reference

Draw a spherical structure with adjustable subdivisions to show different patterns. Start from the center and draw lines connecting points on the sphere's surface, forming a triangular mesh. The lines decrease in proportion and generate new subdivision levels through symmetry transformations, resulting in a complex spherical geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.