MathPlotAI Logo MathPlotAI

Spiral Generated from Polygons

Spiral Generated from Polygons
Loading the math board and drawing, please wait…
2014-08-03 21:44
PolygonSequence
In collections Symmetry, Transformation and Tessellation Dilation Animations
This example demonstrates the generation of a spiral through repeated rotation and dilation. Key mathematical concepts include rotation, dilation, and polygons. It uses commands like Polygon, Rotate, and Sequence in GeoGebra. Suitable for high school mathematics, particularly for geometric construction and transformation topics.

GeoGebra Commands & Parameters

  1. Polygon(B, C, D, E, F, G, H, I) → s1, b, c, d, e, f, g, h, i
  2. Rotate(B, 72*°, A) → B'
  3. Rotate(C, 72*°, A) → C'
  4. Rotate(D, 72*°, A) → D'
  5. Rotate(E, 72*°, A) → E'
  6. Rotate(F, 72*°, A) → F'
  7. Rotate(G, 72*°, A) → G'
  8. Rotate(H, 72*°, A) → H'
  9. Rotate(I, 72*°, A) → I'
  10. Polygon(B', C', D', E', F', G', H', I') → s2, b', c', d', e', f', g', h', i'
  11. Rotate(B', 72*°, A) → B''
  12. Rotate(C', 72*°, A) → C''
  13. Rotate(D', 72*°, A) → D''
  14. Rotate(E', 72*°, A) → E''
  15. Rotate(F', 72*°, A) → F''
  16. Rotate(G', 72*°, A) → G''
  17. Rotate(H', 72*°, A) → H''
  18. Rotate(I', 72*°, A) → I''
  19. Polygon(B'', C'', D'', E'', F'', G'', H'', I'') → s3, b'', c'', d'', e'', f'', g'', h'', i''
  20. Rotate(B'', 72*°, A) → B'''
  21. Rotate(C'', 72*°, A) → C'''
  22. Rotate(D'', 72*°, A) → D'''
  23. Rotate(E'', 72*°, A) → E'''
  24. Rotate(F'', 72*°, A) → F'''
  25. Rotate(G'', 72*°, A) → G'''
  26. Rotate(H'', 72*°, A) → H'''
  27. Rotate(I'', 72*°, A) → I'''
  28. Polygon(B''', C''', D''', E''', F''', G''', H''', I''') → s4, b''', c''', d''', e''', f''', g''', h''', i'''
  29. Rotate(B''', 72*°, A) → B''''
  30. Rotate(C''', 72*°, A) → C''''
  31. Rotate(D''', 72*°, A) → D''''
  32. Rotate(E''', 72*°, A) → E''''
  33. Rotate(F''', 72*°, A) → F''''
  34. Rotate(G''', 72*°, A) → G''''
  35. Rotate(H''', 72*°, A) → H''''
  36. Rotate(I''', 72*°, A) → I''''
  37. Polygon(B'''', C'''', D'''', E'''', F'''', G'''', H'''', I'''') → s5, b'''', c'''', d'''', e'''', f'''', g'''', h'''', i''''
  38. Sequence(Rotate[Polygon[Dilate[B, r^(n), A], Dilate[C, r^(n), A], Dilate[D, r^(n), A], Dilate[E, r^(n), A], Dilate[F, r^(n), A], Dilate[G, r^(n), A], Dilate[H, r^(n), A], Dilate[I, r^(n), A]], (t * n), A], n, 1, 10) → list1
  39. Sequence(Rotate[Polygon[Dilate[B', r^(n), A], Dilate[C', r^(n), A], Dilate[D', r^(n), A], Dilate[E', r^(n), A], Dilate[F', r^(n), A], Dilate[G', r^(n), A], Dilate[H', r^(n), A], Dilate[I', r^(n), A]], (t * n), A], n, 1, 10) → list2
  40. Sequence(Rotate[Polygon[Dilate[B'', r^(n), A], Dilate[C'', r^(n), A], Dilate[D'', r^(n), A], Dilate[E'', r^(n), A], Dilate[F'', r^(n), A], Dilate[G'', r^(n), A], Dilate[H'', r^(n), A], Dilate[I'', r^(n), A]], (t * n), A], n, 1, 10) → list3
  41. Sequence(Rotate[Polygon[Dilate[B''', r^(n), A], Dilate[C''', r^(n), A], Dilate[D''', r^(n), A], Dilate[E''', r^(n), A], Dilate[F''', r^(n), A], Dilate[G''', r^(n), A], Dilate[H''', r^(n), A], Dilate[I''', r^(n), A]], (t * n), A], n, 1, 10) → list4
  42. Sequence(Rotate[Polygon[Dilate[B'''', r^(n), A], Dilate[C'''', r^(n), A], Dilate[D'''', r^(n), A], Dilate[E'''', r^(n), A], Dilate[F'''', r^(n), A], Dilate[G'''', r^(n), A], Dilate[H'''', r^(n), A], Dilate[I'''', r^(n), A]], (t * n), A], n, 1, 10) → list5

AI Drawing Prompt Reference

Draw an octagon with eight vertices, then rotate and gradually enlarge it around a central point to form a spiral sequence of shapes. First, draw an octagon, then rotate and enlarge it by 72 degrees around the center point, repeating this process multiple times to form a sequence of rotated and enlarged octagons, ultimately creating a spiral sequence of shapes.
The prompt above was compiled from the original drawing commands and is for reference only.