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Octagon Folding Demonstration

Octagon Folding Demonstration
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2018-02-26 19:46
PolygonVectorGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the dynamic process of folding an octagon through geometric transformations. Key math concepts include polygon construction, vector operations, and transformations such as rotation, reflection, and translation. GeoGebra commands like Polygon, Segment, Vector, If, Translate, CircleArc, Mirror, Rotate, and Midpoint are utilized in the construction. Suitable for high school geometry transformation lessons and exploratory learning.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment(DD, E) → f
  3. Vector((0, -0.15)) → u
  4. Polygon(B, DD, E, D) → vierhoek2, b_1, dd, e, d_1
  5. Polygon(A, C, E, DD) → vierhoek3, a_1, c_1, e_1, dd_1
  6. If(s < 1, vierhoek3, If[1 < s ≤ 2, Polygon[Translate[A, Vector[((s - 1) * u)]], Translate[C, Vector[((s - 1) * u)]], Translate[E, Vector[((s - 1) * u)]], Translate[DD, Vector[((s - 1) * u)]]], Polygon[Translate[A, u], Translate[C, u], Translate[E, u], Translate[DD, u]]]) → vierhoek4
  7. Vector(D, B) → v
  8. Translate(afbeelding1, Vector[(1.25 * ((s - 1) * v))]) → afbeelding1'
  9. Segment(B, E) → g
  10. CircleArc(B, DD, D) → h
  11. Segment(DD, D) → i
  12. Polygon(A2, A1, D1, D2) → vierhoek5, a2, a1, d1, d2
  13. Mirror(D, d1) → DB
  14. Mirror(DD, a2) → DDB
  15. CircleArc(D2, DB, D) → k
  16. CircleArc(A2, DD, DDB) → p
  17. Polygon(B, A2, A1, E, D1, D2) → veelhoek1, b_2, a2_1, a1_1, e_2, d1_1, d2_1
  18. Polygon(D1, D, D2) → driehoek1, d2_2, d1_2, d_2
  19. Rotate(D1, (((-(s - 3)) * 180))°, d1) → D1'
  20. Rotate(D, (((-(s - 3)) * 180))°, d1) → D'
  21. Rotate(D2, (((-(s - 3)) * 180))°, d1) → D2'
  22. Polygon(D1', D', D2') → driehoek1', d2', d1', d'
  23. Polygon(D2, DB, D1) → driehoek2, d1_3, d2_3, db
  24. Midpoint(B, E) → M
  25. Rotate(D2, 180°, M) → D2'_1
  26. Rotate(DB, 180°, M) → DB'
  27. Rotate(D1, 180°, M) → D1'_1
  28. Polygon(D2'_1, DB', D1'_1) → driehoek2', d1'_1, d2'_1, db'
  29. Polygon(B, B1, B2) → driehoek4, b2, b_3, b1
  30. Polygon(A2, DD, A1) → driehoek3, a1_2, a2_2, dd_2
  31. Rotate(A2, (((-(s - 3)) * 180))°, a2) → A2'
  32. Rotate(DD, (((-(s - 3)) * 180))°, a2) → DD'
  33. Rotate(A1, (((-(s - 3)) * 180))°, a2) → A1'
  34. Polygon(A2', DD', A1') → driehoek3', a1', a2', dd'
  35. Polygon(B2, B1, A2, A1, C1, C2, D1, D2) → veelhoek2, b2_1, b1_1, a2_3, a1_3, c1, c2, d1_4, d2_4
  36. Polygon(B1, C1, C2, B2) → vierhoek6, b1_2, c1_1, c2_1, b2_2
  37. Segment(DDB, DB) → j
  38. Rotate(B, (((s - 5) * 180))°, b_3) → B'
  39. Rotate(B1, (((s - 5) * 180))°, b_3) → B1'
  40. Rotate(B2, (((s - 5) * 180))°, b_3) → B2'
  41. Polygon(B', B1', B2') → driehoek4', b2', b', b1'
  42. Polygon(B2, B1, A2, A1, C1, C2, D1, D2) → veelhoek3, b2_3, b1_3, a2_4, a1_4, c1_2, c2_2, d1_5, d2_5
  43. Rotate(C1, (((-(s - 5)) * 180))°, c1) → C1'
  44. Rotate(E, (((-(s - 5)) * 180))°, c1) → E'
  45. Rotate(C2, (((-(s - 5)) * 180))°, c1) → C2'
  46. Polygon(C1', E', C2') → driehoek5', c2', c1', e'
  47. Rotate(DDB, 90°, M) → DDB'
  48. Rotate(DB, 90°, M) → DB'_1
  49. Segment(DDB', DB'_1) → j'
  50. Polygon(B1, DB'_1, B2) → driehoek5, b2_4, b1_4, db'_1
  51. Polygon(C1, DDB', C2) → driehoek6, c2_3, c1_3, ddb'
  52. Rotate(B1, (((-(s - 6)) * 45))°, M) → B1'_1
  53. Rotate(C1, (((-(s - 6)) * 45))°, M) → C1'_1
  54. Rotate(C2, (((-(s - 6)) * 45))°, M) → C2'_1
  55. Rotate(B2, (((-(s - 6)) * 45))°, M) → B2'_1
  56. Polygon(B1'_1, C1'_1, C2'_1, B2'_1) → vierhoek6', b1'_1, c1'_1, c2'_1, b2'_1
  57. Mirror(B2, M) → E1
  58. Mirror(B1, M) → E2
  59. Mirror(B, b2_2) → BB
  60. Mirror(BB, M) → EE
  61. CircleArc(B1, BB, B) → q
  62. CircleArc(C1, E, EE) → r

AI Drawing Prompt Reference

Draw an octagon and demonstrate its folding process through geometric transformations such as rotation, translation, and reflection. Start by constructing the octagon, then create vectors and segments. Next, use translation and rotation to transform the vertices of the octagon. Finally, apply reflection and circular arcs to further transform the vertices, showcasing the folding process.
The prompt above was compiled from the original drawing commands and is for reference only.