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GeoGebra Geometry Construction Example by GeoGebra Institute of Hong Kong

GeoGebra Geometry Construction Example by GeoGebra Institute of Hong Kong
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2014-08-07 17:12
VectorSequenceTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the construction of complex geometric figures using GeoGebra commands. The math concepts involved include vectors, sequences, and geometric transformations. Key construction steps involve commands like Segment, Rotate, Midpoint, Mirror, Vector, Sequence, and Line. Suitable for high school and above students to understand the application of geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. Segment(C, B) → h
  2. Segment(L, M) → c
  3. Segment(M, N) → d
  4. Segment(M, P) → e
  5. Segment(M, Q) → f
  6. Rotate(cell1a, 240*°, E) → cell1c
  7. Rotate(cell1a, 120*°, E) → cell1b
  8. Midpoint(A, B) → H
  9. Segment(E, H) → b
  10. Mirror(cell1, h) → cell2
  11. Midpoint(C, A) → G
  12. Midpoint(B, D) → I
  13. Midpoint(D, C) → J
  14. Midpoint(C, B) → K
  15. Vector(A, B) → u
  16. Vector(A, C) → v
  17. Segment(E, G) → a
  18. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  19. Vector(B, D) → w
  20. Vector(C, D) → g
  21. Segment(F, J) → j
  22. Segment(F, I) → k
  23. Segment(E, F) → i
  24. Segment(A, E) → p
  25. Segment(E, C) → q
  26. Segment(E, B) → r
  27. Segment(F, C) → s
  28. Segment(F, B) → t
  29. Segment(F, D) → a_1
  30. Line(C, B) → b_1
  31. Line(C, A) → c_1
  32. Line(A, B) → d_1
  33. Line(G, K) → e_1
  34. Line(K, H) → f_1
  35. Line(H, G) → g_1

AI Drawing Prompt Reference

Draw a complex geometric figure involving multiple line segments, midpoints, and vectors. Start with a basic shape, then create intricate geometric structures through rotations, reflections, and vector transformations. Use vectors to define a sequence, generating a series of translated shapes to demonstrate the application of geometric transformations. Finally, add auxiliary line segments and midpoints to complete the figure.
The prompt above was compiled from the original drawing commands and is for reference only.