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Square Spiral

Square Spiral
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2018-05-09 07:18
SequenceTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the generation of a square spiral. It involves concepts of geometric transformations and iteration. Using commands like Polygon, Segment, Dilate, and Rotate, a series of squares are constructed to form the spiral. Suitable for high school mathematics education, particularly in geometry and function graphing.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Segment(D, B) → j
  3. Segment(C, A) → k
  4. Intersect(j, k) → E
  5. Dilate(poly1, 5 / 6, E) → poly1'
  6. Rotate(poly1', (-(13°)), E) → poly1''
  7. Dilate(poly1'', 5 / 6, E) → poly1'''
  8. Rotate(poly1''', (-(13°)), E) → q1
  9. Dilate(q1, 5 / 6, E) → q1'
  10. Rotate(q1', (-(13°)), E) → q1''
  11. Dilate(q1'', 5 / 6, E) → q1'''
  12. Rotate(q1''', (-(13°)), E) → q2
  13. Dilate(q2, 5 / 6, E) → q2'
  14. Rotate(q2', (-(13°)), E) → q2''
  15. Dilate(q2'', 5 / 6, E) → q2'''
  16. Rotate(q2''', (-(13°)), E) → q3
  17. Dilate(q3, 5 / 6, E) → q3'
  18. Rotate(q3', (-(13°)), E) → q3''
  19. Dilate(q3'', 5 / 6, E) → q3'''
  20. Rotate(q3''', (-(13°)), E) → q4
  21. Dilate(q4, 5 / 6, E) → q4'
  22. Rotate(q4', (-(13°)), E) → q4''
  23. Dilate(q4'', 5 / 6, E) → q4'''
  24. Rotate(q4''', (-(13°)), E) → q5

AI Drawing Prompt Reference

Draw a square spiral by first creating a square ABCD, then using point E as the rotation center, shrink the square by 1/6 and rotate it 13 degrees counterclockwise, and repeat this process multiple times to form a spiral sequence of squares.
The prompt above was compiled from the original drawing commands and is for reference only.