Symmetry Number of a Complex System by Timur Kapitsa

Symmetry Number of a Complex System by Timur Kapitsa
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2019-05-27 14:17
This example demonstrates the geometric representation and calculation of symmetry in complex systems. It involves core mathematical concepts such as symmetry, geometric transformations, vectors, and polygons. Key GeoGebra commands/objects used include Circle, Point, Segment, Rotate, and Angle. Suitable for high school mathematics students and geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(C, c) → f
  2. Point(f) → N
  3. Segment(N, O) → r_1
  4. Rotate(N, 120°, C) → Q
  5. Segment(Q, O) → q_1
  6. Rotate(Q, 120°, C) → R
  7. Segment(R, O) → s_1
  8. Circle(B, b) → e
  9. Point(e) → H
  10. Segment(H, O) → k_1
  11. Rotate(H, 60°, B) → I
  12. Segment(I, O) → j_1
  13. Rotate(I, 60°, B) → J
  14. Segment(J, O) → m_1
  15. Rotate(J, 60°, B) → K
  16. Segment(K, O) → n_1
  17. Rotate(K, 60°, B) → L
  18. Segment(L, O) → p_1
  19. Rotate(L, 60°, B) → M
  20. Segment(M, O) → l_1
  21. Circle(A, a) → d
  22. Point(d) → D
  23. Segment(D, O) → f_1
  24. Rotate(D, (-(90°)), A) → G
  25. Segment(G, O) → h_1
  26. Rotate(D, 90°, A) → E
  27. Segment(E, O) → g_1
  28. Rotate(E, 90°, A) → F
  29. Segment(F, O) → i_1
  30. Segment(A, D) → g
  31. Angle(D, A, E) → α
  32. Segment(A, E) → h
  33. Angle(E, A, F) → β
  34. Segment(A, F) → i
  35. Angle(G, A, D) → δ
  36. Segment(A, G) → j
  37. Segment(B, H) → k
  38. Angle(H, B, I) → γ
  39. Segment(B, I) → l
  40. Angle(I, B, J) → ε
  41. Segment(B, J) → m
  42. Angle(J, B, K) → ζ
  43. Segment(B, K) → n
  44. Angle(K, B, L) → η
  45. Segment(B, L) → p
  46. Angle(L, B, M) → θ
  47. Segment(B, M) → q
  48. Segment(C, N) → r
  49. Angle(N, C, Q) → ι
  50. Segment(C, Q) → s
  51. Angle(Q, C, R) → κ
  52. Segment(C, R) → t

AI Drawing Prompt Reference

Draw a complex symmetric system with a circle and three 60-degree rotated points to form a hexagon. Then, rotate points around the circle center by 90 degrees to form a square. Finally, connect the circle center with the points on the circle to form multiple angle markings.
The prompt above was compiled from the original drawing commands and is for reference only.