Mobilis in mobili symmetry (generalised)

Mobilis in mobili symmetry (generalised)
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2019-06-05 12:54
This example demonstrates the 'Mobilis in mobili' symmetry. It involves key concepts such as symmetry and geometric transformations. Using GeoGebra commands like Circle, Point, Segment, Rotate, etc., a dynamic geometric figure is constructed. Suitable for high school and above students or teachers for teaching or self-study.

GeoGebra Commands & Parameters

  1. Circle(D, d) → h
  2. Point(h) → E
  3. Circle(A, a) → e
  4. Point(e) → B
  5. Circle(B, b) → f
  6. Point(f) → C
  7. Segment(C, E) → s
  8. Circle(C, c) → g
  9. Point(g) → G
  10. Segment(G, E) → p
  11. Rotate(G, 90°, C) → G'
  12. Midpoint(G', G) → P
  13. Line(C, P) → j_1
  14. Intersect(g, j_1, 2) → Q
  15. Segment(Q, E) → p_1
  16. Segment(G', E) → q
  17. Line(G', C) → k
  18. Intersect(g, k, 2) → I
  19. Midpoint(G, I) → N
  20. Line(C, N) → i_1
  21. Intersect(g, i_1, 2) → O
  22. Segment(O, E) → t_1
  23. Segment(I, E) → n
  24. Line(G, C) → i
  25. Intersect(g, i, 2) → H
  26. Midpoint(H, I) → L
  27. Line(C, L) → f_1
  28. Intersect(g, f_1, 2) → M
  29. Segment(M, E) → s_1
  30. Midpoint(G', H) → J
  31. Line(C, J) → t
  32. Intersect(g, t, 2) → K
  33. Segment(K, E) → r_1
  34. Segment(H, E) → r
  35. Angle(G, C, G') → α
  36. Segment(C, G') → j
  37. Segment(G, H) → l
  38. Segment(G', I) → m
  39. Segment(C, K) → k_1
  40. Segment(C, O) → l_1
  41. Segment(C, Q) → m_1
  42. Segment(C, M) → n_1
  43. Polygon(G, Q, G', K, H, M, I, O) → poly1, g_1, q_1, g', k_2, h_1, m_2, ı, o

AI Drawing Prompt Reference

Draw a dynamic geometric figure demonstrating 'Mobilis in mobili' symmetry. Start by creating a circle and points on it, then draw new circles centered at these points. Connect specific points to form segments, and use rotations and symmetry operations to build a complex geometric structure. Finally, connect multiple points and segments to form a polygon, highlighting the core concepts of symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.