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Magic Star - Spiral Version

Magic Star - Spiral Version
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2020-07-16 03:43
TransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
This is an animation of a modular origami model from the book 'Action Modular Origami'. It demonstrates the step-by-step folding process of a magic star. The model involves geometric construction and transformation. It uses commands like Line, AngularBisector, Rotate, Intersect, Dilate, and Polygon in GeoGebra. Suitable for middle school and above students to learn geometric construction and transformation.

GeoGebra Commands & Parameters

  1. Line(A, C) → h
  2. Line(A, B) → g
  3. AngularBisector(h, g) → i, j
  4. Rotate(j, (-(22.5°)), D) → j'
  5. Rotate(g, 22.5°, A) → g'
  6. Intersect(j', g') → G
  7. Dilate(A, fac, G) → A'_1
  8. AngularBisector(B, C, A) → f
  9. Intersect(f, g) → E
  10. Line(E, i) → k
  11. Intersect(h, k) → F
  12. Polygon(A, F, E, C, D) → poly1, a, f_1, e, c, d
  13. Rotate(A, 45°, O) → A'
  14. Rotate(F, 45°, O) → F'
  15. Rotate(E, 45°, O) → E'
  16. Rotate(C, 45°, O) → C'
  17. Rotate(D, 45°, O) → D'
  18. Polygon(A', F', E', C', D') → poly1', a', f', e', c', d'
  19. Polygon(F', A, F, E, C, D, C', E') → poly2, l, m, n, p, q, r, s, t
  20. Intersect(k, j) → H
  21. Line(F', E') → b
  22. Intersect(b, k) → I
  23. If(fac ≥ sqrt(0.5), Polygon[H, I, F'], {}) → polySmall
  24. Intersect(xAxis, yAxis) → J
  25. Vector(A'_1, J) → u
  26. Translate(Sequence[Rotate[{poly2}, (n * 90°), O], n, 0, 3, 1], u) → listPoly1
  27. Translate(Sequence[Rotate[{polySmall}, (n * 90°), O], n, 1, 4, 1], u) → listSmall12
  28. Translate(Sequence[Rotate[{polySmall}, 45° + (n * 90°), O], n, 1, 4, 1], u) → listSmall1
  29. Translate(Sequence[Rotate[{poly2}, 45° + (n * 90°), O], n, 0, 3, 1], u) → listPoly2

AI Drawing Prompt Reference

Draw a rotating star pattern composed of pentagonal units symmetrically arranged around a central point. First construct a base pentagon with vertices determined by intersections of lines and angle bisectors, then rotate it by 45 degrees to create a second pentagon, overlapping to form star petals. Subsequently, rotate the entire petal assembly by 90, 180, and 270 degrees around the center, and translate copies to four directions to complete a full star array. Under certain conditions, small triangles appear at petal tips, toggling with a slider. The overall figure consists of nested polygons, giving a spiral unfolding visual effect.
The prompt above was compiled from the original drawing commands and is for reference only.