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Jacob’s Ladder

Jacob’s Ladder
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2020-07-17 00:26
TransformationGeometric Construction
In collections Action Modular Origami
This example demonstrates a paper folding model from the book 'Action Modular Origami'. It involves geometric construction and transformation. Commands used include Mod, Point, Line, Intersect, Plane, PointIn, Vector, Translate, Mirror, etc. Suitable for middle school students and math enthusiasts interested in geometry and paper folding.

GeoGebra Commands & Parameters

  1. Mod(clock, flipclock) → clock2
  2. Point(rampcomp) → I
  3. Point(rampcomp) → H
  4. Line(H, I) → h
  5. Intersect(yAxis, xAxis) → A
  6. Point(xAxis) → C
  7. Point(zAxis) → B
  8. Plane(A, C, B) → a
  9. PointIn(a) → D
  10. Vector((0, 0, If[clock ≥ 14 ∧ clock ≤ 15, (fractionalPart(clock) * Distance[C, D]), 0])) → vLift3
  11. Vector((0, 0, If[clock2 ≥ 7 ∧ clock2 < 8, (fractionalPart(clock) * Distance[C, D]), 0])) → vLift2
  12. Vector((0, offset, 0)) → vOffset
  13. Plane(F, a) → c
  14. PointIn(a) → E
  15. Vector(A, E) → u
  16. Translate(Translate[Line[E, D], vLift], vOffset) → f
  17. Translate(Translate[Polygon[A, C, D, E], vLift], Vector[(0, offset, 0)]) → poly1
  18. Translate(Rotate[poly1, α, f], Vector[(-2 * vOffset)]) → poly1'
  19. Translate(poly1', Vector[(2 * u)]) → poly1''_1
  20. Translate(Translate[poly1''_1, Vector[(2 * u)]], Vector[(2 * vOffset)]) → poly4
  21. Translate(poly1, u) → poly1'_1
  22. Translate(poly1'_1, u) → poly2
  23. Mirror(poly1', a) → poly1''
  24. Translate(poly1'', u) → poly1'''
  25. Translate(poly2, u) → poly2'
  26. Translate(poly2', u) → poly2''
  27. Translate(poly1''', Vector[(2 * u)]) → poly3
  28. Translate(poly1''', Vector[(-2 * u)]) → poly5
  29. Translate(poly1, Vector[(-vOffset)]) → poly1'_2
  30. Translate(poly1'_1, Vector[(-vOffset)]) → poly6
  31. Translate(poly2, Vector[(-vOffset)]) → poly2'_1
  32. Translate(poly2', vLift) → poly2''_1
  33. Translate(poly2', Vector[(-vOffset)]) → poly2''_2
  34. Translate(poly2'', Vector[(-vOffset)]) → poly2'''
  35. Translate(poly5, Vector[(-vOffset)]) → poly5'
  36. Translate(poly4, Vector[(-vOffset)]) → poly4'
  37. Translate(poly2'', Vector[(-vOffset)]) → poly2'''_1
  38. Translate(poly2'', u) → poly2'''_2
  39. Translate(poly2'''_1, u) → poly7
  40. Mirror(poly5, c) → poly5'_1
  41. Mirror(poly1', c) → poly1''_2
  42. Mirror(poly1''', c) → poly8
  43. Mirror(poly1''_1, c) → poly9
  44. Mirror(poly3, c) → poly3'
  45. Mirror(poly4, c) → poly4'_1
  46. Mirror(poly5, c) → poly5'_2
  47. Mirror(poly5', c) → poly5''
  48. Mirror(poly4', c) → poly4''
  49. Translate(poly7, vOffset) → poly7'
  50. Point(fastramp) → G

AI Drawing Prompt Reference

Create a Jacob’s Ladder model, which consists of folded paper strips. Start by taking point C on the x-axis, point A on the y-axis, and point B on the z-axis. Then construct plane a through points A, C, and B. Next, take point D on plane a and construct vector vLift3 through points D and C. Use a series of translation, rotation, and mirroring operations to generate multiple folded strips, ultimately forming a ladder-like structure.
The prompt above was compiled from the original drawing commands and is for reference only.