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Animation 166: Geometric Transformations via Rotation and Translation

Animation 166: Geometric Transformations via Rotation and Translation
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2017-01-18 06:09
PolygonVectorTransformationGeometric ConstructionSlider Animation
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①This GeoGebra example demonstrates a dynamic animation of polygons undergoing combined geometric transformations such as rotation, translation, and dilation, showing how shapes move and change over time. ②Core mathematical concepts include geometric transformations (rotation, translation, homothety), vector operations, construction of polygons and circles, and parameter-driven dynamic processes. ③Construction highlights: from the summary, commands like Rotate, Angle, Ray, Point, Intersect, Polygon, Segment, Min, Circle, CircleSector, Dilate, Vector, and Translate are used, involving objects such as points A, B, C, D, E, F, polygon poly1, circles and sectors, plus auxiliary segments and vectors, all controlled by sliders or angle parameters. ④Suitable for middle/high school geometry or dynamic mathematics instruction, helping students visualize transformation composition and properties, and useful for teachers creating interactive lessons.

GeoGebra Commands & Parameters

  1. Rotate(A, 108°, B) → A'
  2. Angle(A, B, A') → α
  3. Ray(B, A) → f
  4. Ray(B, A') → g
  5. Point(f) → C
  6. Rotate(B, (-(108°)), C) → B'
  7. Angle(B', C, B) → β
  8. Ray(C, B') → h
  9. Point(h) → D
  10. Rotate(C, (-(108°)), D) → C'
  11. Angle(C', D, C) → γ
  12. Ray(D, C') → i
  13. Point(i) → E
  14. Rotate(D, (-(108°)), E) → D'
  15. Angle(D', E, D) → δ
  16. Ray(E, D') → j
  17. Intersect(g, j) → F
  18. Polygon(F, B, C, D, E) → poly1, f_1, b, c, d, e
  19. Segment(F, E) → k
  20. Segment(E, D) → l
  21. Segment(D, C) → m
  22. Segment(C, B) → n
  23. Segment(B, F) → p
  24. Min(list) → a
  25. Circle(B, (0.2 * a)) → q
  26. Intersect(q, p) → H,
  27. Intersect(q, n) → I,
  28. CircleSector(B, I, H) → r
  29. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], C) → B'_1
  30. Vector(B, B'_1) → u
  31. Translate(r, u) → r'
  32. Rotate(r', If[1 < o ≤ 2, (((o - 1) * 2) * π / 5), (2 * π / 5)], C) → r''
  33. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'_1
  34. Vector(C, C'_1) → v
  35. Translate(r'', v) → r'''
  36. Rotate(r''', If[3 < o ≤ 4, (((o - 3) * 2) * π / 5), (2 * π / 5)], D) → s
  37. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], E) → D'_1
  38. Vector(D, D'_1) → w
  39. Translate(s, w) → s'
  40. Rotate(s', If[5 < o ≤ 6, (((o - 5) * 2) * π / 5), (2 * π / 5)], E) → s''
  41. Dilate(E, If[6 < o ≤ 7, 7 - o, 0], F) → E'
  42. Vector(E, E') → t
  43. Translate(s'', t) → s'''
  44. Rotate(s''', If[7 < o ≤ 8, (((o - 7) * 2) * π / 5), (2 * π / 5)], F) → c_1

AI Drawing Prompt Reference

Create an animated geometric transformation showing a polygon undergoing combined rotations, translations, and scalings. The polygon rotates around a point at specific angles, translates, and scales, forming a new shape over time. Use vectors and parameters to dynamically demonstrate the continuous transformation and geometric properties, including angle changes and shape evolution.
The prompt above was compiled from the original drawing commands and is for reference only.