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Hexagon Spiral Tessellation

Hexagon Spiral Tessellation
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2015-12-12 22:11
PolygonSequenceCoordinate Geometry
This example demonstrates the construction and dynamic transformation of hexagon spiral tessellations. Core math concepts include polygons, rotation, coordinate geometry, and transformation. It uses commands like Polygon, Circle, Point, Rotate, Angle, Intersect, Sequence, and Translate in GeoGebra. Suitable for middle school students and above learning geometric construction, spatial reasoning, and mathematical modeling.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, a, b, c, d, e, C_1, D, E
  2. Circle(B, A) → f
  3. Point(f) → C
  4. Rotate(C, -72°, G) → F'
  5. Angle(F', A, B) → α
  6. Circle(C, B) → g
  7. Circle(H, F') → h
  8. Intersect(g, h, 1) → I
  9. Polygon(C, B, A, F', H, I) → poly2, f_1, b_1, a_1, f', h_1, i
  10. Sequence(Polygon[Rotate[C, ((i * 72))°, G], Rotate[B, ((i * 72))°, G], Rotate[A, ((i * 72))°, G], Rotate[F', ((i * 72))°, G], Rotate[H, ((i * 72))°, G], Rotate[I, ((i * 72))°, G]], i, 1, 4) → list1
  11. Rotate(A, 108°, B) → C_s
  12. Sequence(Sequence[Translate[Polygon[Translate[C, Vector[(i * Vector[A, C])]], Translate[B, Vector[(i * Vector[A, C])]], Translate[A, Vector[(i * Vector[A, C])]], Translate[F', Vector[(i * Vector[A, C])]], Translate[H, Vector[(i * Vector[A, C])]], Translate[I, Vector[(i * Vector[A, C])]]], Vector[(j * Vector[B, F'])]], j, 0, i], i, 1, N) → list4
  13. Sequence(Rotate[list4, ((i * 72))°, G], i, 1, 4) → list5
  14. Translate(Mirror[list4, Line[A, H]], Vector[A, F']) → list2
  15. Angle(A, B, C) → β
  16. Sequence(Rotate[list2, ((i * 72))°, G], i, 0, 4) → list3