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Mario Geometry Challenge

Mario Geometry Challenge
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2018-07-22 06:15
Solid GeometryTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This GeoGebra example demonstrates the image of Mario through geometric shapes. It involves rational numbers, solid geometry, and random experiments. Using commands like Polygon, Segment, Midpoint, Point, Dilate, Mirror, users can perform geometric constructions. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Segment(D, B) → j
  3. Midpoint(j) → E
  4. Polygon(C, A, B) → t1, b, c, a
  5. Point(j) → F
  6. Dilate(C, 5 / 6, F) → C'
  7. Dilate(A, 5 / 6, F) → A'
  8. Dilate(B, 5 / 6, F) → B'
  9. Polygon(C', A', B') → t1', b', c', a'
  10. Dilate(C', 5 / 6, F) → C''
  11. Dilate(A', 5 / 6, F) → A''
  12. Dilate(B', 5 / 6, F) → B''
  13. Polygon(C'', A'', B'') → t1'', b'', c'', a''
  14. Dilate(C'', 5 / 6, F) → C'''
  15. Dilate(A'', 5 / 6, F) → A'''
  16. Dilate(B'', 5 / 6, F) → B'''
  17. Polygon(C''', A''', B''') → t1''', b''', c''', a'''
  18. Dilate(C''', 5 / 6, F) → G
  19. Dilate(A''', 5 / 6, F) → H
  20. Dilate(B''', 5 / 6, F) → I
  21. Polygon(G, H, I) → t2, i_1, g_1, h_1
  22. Dilate(G, 5 / 6, F) → G'
  23. Dilate(H, 5 / 6, F) → H'
  24. Dilate(I, 5 / 6, F) → I'
  25. Polygon(G', H', I') → t2', i', g', h'
  26. Mirror(C, E) → C'_1
  27. Mirror(A, E) → A'_1
  28. Mirror(B, E) → B'_1
  29. Polygon(C'_1, A'_1, B'_1) → t1'_1, b'_1, c'_1, a'_1
  30. Mirror(C', E) → C''_1
  31. Mirror(A', E) → A''_1
  32. Mirror(B', E) → B''_1
  33. Polygon(C''_1, A''_1, B''_1) → t1''_1, b''_1, c''_1, a''_1
  34. Mirror(C'', E) → C'''_1
  35. Mirror(A'', E) → A'''_1
  36. Mirror(B'', E) → B'''_1
  37. Polygon(C'''_1, A'''_1, B'''_1) → t1'''_1, b'''_1, c'''_1, a'''_1
  38. Mirror(C''', E) → J
  39. Mirror(A''', E) → K
  40. Mirror(B''', E) → L
  41. Polygon(J, K, L) → t3, l, j_1, k
  42. Mirror(G, E) → G'_1
  43. Mirror(H, E) → H'_1
  44. Mirror(I, E) → I'_1
  45. Polygon(G'_1, H'_1, I'_1) → t2'_1, i'_1, g'_1, h'_1
  46. Mirror(G', E) → G''
  47. Mirror(H', E) → H''
  48. Mirror(I', E) → I''
  49. Polygon(G'', H'', I'') → t2'', i'', g'', h''
  50. Dilate(G', 5 / 6, F) → G''_1
  51. Dilate(H', 5 / 6, F) → H''_1
  52. Dilate(I', 5 / 6, F) → I''_1
  53. Polygon(G''_1, H''_1, I''_1) → t2''_1, i''_1, g''_1, h''_1
  54. Mirror(G''_1, E) → M
  55. Mirror(H''_1, E) → N
  56. Mirror(I''_1, E) → O
  57. Polygon(M, N, O) → t4, o, m, n

AI Drawing Prompt Reference

This is a geometric pattern composed of multiple triangles. The pattern includes an original triangle and multiple triangles obtained through scaling and mirroring transformations. The construction order is: first draw the original triangle, then scale it, and then mirror it, ultimately forming a series of similar and symmetric triangles. The sizes and positions of the triangles are determined by the scaling ratio of 5/6 and the mirroring center, resulting in a geometrically symmetric overall appearance.
The prompt above was compiled from the original drawing commands and is for reference only.