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Square Slider (Centred Slide) Origami Animation

Square Slider (Centred Slide) Origami Animation
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2020-07-16 04:25
PolygonVectorTransformationGeometric ConstructionSlider Animation
① This example demonstrates a square slider model folded from paper, animated by a slider to show a centred sliding motion, illustrating dynamic geometric transformations. ② Core mathematical concepts include similarity transformations (dilation), translation, rotation, and polygon (square) construction, along with arithmetic, real numbers, probability, and perimeter. ③ Construction highlights: GeoGebra commands such as Dilate, Segment, Point, Polygon, Rotate, Intersect, Vector, and Translate are used to build multiple squares and their transformed copies (e.g., poly1, poly1', poly1'_1), with a slider controlling scaling and translation to achieve the centred slide animation. ④ Suitable for middle or high school mathematics, this example helps teach similarity transformations, combined rotations and translations, and the mathematical principles behind origami models, ideal for classroom demonstrations or exploratory activities.

GeoGebra Commands & Parameters

  1. Dilate(F, frac, E) → F'
  2. Segment(E, F) → f
  3. Point(xAxis) → B
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Rotate(A, 90°, OO) → A'
  6. Rotate(B, 90°, OO) → B'
  7. Rotate(C, 90°, OO) → C'
  8. Rotate(D, 90°, OO) → D'
  9. Polygon(A', B', C', D') → poly1', a', b', c', d'
  10. Rotate(A, 180°, OO) → A'_1
  11. Rotate(B, 180°, OO) → B'_1
  12. Rotate(C, 180°, OO) → C'_1
  13. Rotate(D, 180°, OO) → D'_1
  14. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1
  15. Rotate(A, 270°, OO) → A'_2
  16. Rotate(B, 270°, OO) → B'_2
  17. Rotate(C, 270°, OO) → C'_2
  18. Rotate(D, 270°, OO) → D'_2
  19. Polygon(A'_2, B'_2, C'_2, D'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2
  20. Intersect(a'_2, poly1'_2) → G, H
  21. Intersect(a'_1, a'_2) → I
  22. Polygon(I, A'_1, D'_2, A'_2) → poly2, i, a'_3, d'_3, a'_4
  23. Intersect(c'_1, a'_2) → J
  24. Polygon(J, D'_1, C'_2, B'_2) → poly3, j, d'_4, c'_3, b'_3
  25. Intersect(a'_4, a) → K
  26. Polygon(A'_2, K, A, D) → poly4, a'_5, k, a_1, d_1
  27. Vector(OO, E) → u
  28. Translate(A, u) → A'_3
  29. Translate(B, u) → B'_3
  30. Translate(C, u) → C'_3
  31. Translate(D, u) → D'_3
  32. Polygon(A'_3, B'_3, C'_3, D'_3) → poly1'_3, a'_6, b'_4, c'_4, d'_5
  33. Translate(A', u) → A''
  34. Translate(B', u) → B''
  35. Translate(C', u) → C''
  36. Translate(D', u) → D''
  37. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
  38. Translate(A'_1, u) → L
  39. Translate(B'_1, u) → M
  40. Translate(C'_1, u) → N
  41. Translate(D'_1, u) → O
  42. Polygon(L, M, N, O) → poly5, l, m, n, o
  43. Translate(I, u) → I'
  44. Translate(A'_1, u) → P
  45. Translate(D'_2, u) → Q
  46. Translate(A'_2, u) → R
  47. Polygon(I', P, Q, R) → poly2', i', p, q, r
  48. Translate(J, u) → J'
  49. Translate(D'_1, u) → S
  50. Translate(C'_2, u) → T
  51. Translate(B'_2, u) → U
  52. Polygon(J', S, T, U) → poly3', j', s, t, u_1

AI Drawing Prompt Reference

Draw a symmetric composition of four congruent squares centered on a common point, rotated at 0, 90, 180, and 270 degrees, each scaled about the center to create an origami-like sliding effect. Add a translation vector from the center to a point, and translate the entire rotated group along this vector to form a second overlapping set of squares. Finally, construct four small polygons using intersections of adjacent square edges, filling the gaps between rotated squares, resulting in a centered fold pattern controlled by a slider for scaling and translation.
The prompt above was compiled from the original drawing commands and is for reference only.