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Dynamic Illustration of a Regular Hexagon

Dynamic Illustration of a Regular Hexagon
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2018-02-06 00:20
PolygonTransformation
This is a dynamic and modifiable illustration of a regular hexagon problem, demonstrating the properties and related geometric transformations of a regular hexagon. Key mathematical concepts include polygons, rotation, and translation. It is constructed using GeoGebra commands such as Polygon, Circle, Rotate, etc. Suitable for middle school and above students to learn about geometric transformations and properties of polygons.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  2. Circle(F, A) → c
  3. Line(F, D) → l
  4. Intersect(c, l) → G, H
  5. Line(D, B) → m
  6. Circle(D, Distance[A, F]) → d
  7. Intersect(d, m) → I, J
  8. Segment(A, F) → n
  9. Segment(F, E) → p
  10. Segment(E, D) → q
  11. Segment(D, C) → r
  12. Segment(C, B) → s
  13. Segment(B, A) → t
  14. Distance(E, H) → a
  15. Distance(H, J) → b
  16. Dilate(F, If[0 < u ≤ 1, 1 - u, 0], H) → F'
  17. Segment(F, F') → f_1
  18. Dilate(H, If[1 < u ≤ 2, 2 - u, 0], D) → H'
  19. Segment(H, H') → g_1
  20. Dilate(D, If[2 < u ≤ 3, 3 - u, 0], J) → D'
  21. Segment(D, D') → h_1
  22. Dilate(J, If[3 < u ≤ 4, 4 - u, 0], B) → J'
  23. Segment(J, J') → i_1
  24. Rotate(A, If[4 < u ≤ 5, ((u - 4) * π / 2), π / 2], F) → A'
  25. Rotate(F, If[4 < u ≤ 5, ((u - 4) * π / 2), π / 2], F) → F'_1
  26. Segment(A', F'_1) → n'
  27. Rotate(D, If[5 < u ≤ 6, ((-(u - 5)) * π / 2), ((-π)) / 2], D) → D'_1
  28. Rotate(C, If[5 < u ≤ 6, ((-(u - 5)) * π / 6), ((-π)) / 6], D) → C'
  29. Segment(D'_1, C') → r'
  30. Dilate(E, If[7 < u ≤ 8, 8 - u, 0], H) → E'
  31. Segment(E, E') → j_1
  32. Dilate(H, If[8 < u ≤ 9, 9 - u, 0], J) → H'_1
  33. Segment(HH, H'_1) → k_1