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Square Spiral Maria

Square Spiral Maria
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2018-05-12 05:57
PolygonSequenceTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the generation of a square spiral. It involves key mathematical concepts such as geometric construction, transformation, and sequences. Using commands like Polygon, Dilate, and Rotate, a series of squares are constructed to form a spiral pattern. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(A, C) → E
  3. Dilate(poly1, 5 / 6, E) → poly1'
  4. Rotate(poly1', (-(12°)), E) → poly1''
  5. Dilate(poly1'', 5 / 6, E) → poly1'''
  6. Rotate(poly1''', (-(12°)), E) → q1
  7. Dilate(q1, 5 / 6, E) → q1'
  8. Rotate(q1', (-(12°)), E) → q1''
  9. Dilate(q1'', 5 / 6, E) → q1'''
  10. Rotate(q1''', (-(13°)), E) → q2
  11. Dilate(q2, 5 / 6, E) → q2'
  12. Rotate(q2', (-(12°)), E) → q2''
  13. Dilate(q2'', 5 / 6, E) → q2'''
  14. Rotate(q2''', -12°, E) → q3
  15. Dilate(q3, 5 / 6, E) → q3'
  16. Rotate(q3', (-(12°)), E) → q3''
  17. Dilate(q3'', 5 / 6, E) → q3'''
  18. Rotate(q3''', (-(12°)), E) → q4
  19. Dilate(q4, 5 / 6, E) → q4'
  20. Rotate(q4', (-(12°)), E) → q4''
  21. Dilate(q4'', 5 / 6, E) → q4'''
  22. Rotate(q4''', (-(12°)), E) → q5
  23. Dilate(q5, 5 / 6, E) → q5'
  24. Rotate(q5', (-(12°)), E) → q5''
  25. Dilate(q5'', 5 / 6, E) → q5'''
  26. Rotate(q5''', (-(12°)), E) → q6
  27. Dilate(q6, 5 / 6, E) → q6'
  28. Rotate(q6', (-(12°)), E) → q6''
  29. Dilate(q6'', 5 / 6, E) → q6'''
  30. Rotate(q6''', (-(12°)), E) → q7
  31. Dilate(q7, 5 / 6, E) → q7'
  32. Rotate(q7', (-(12°)), E) → q7''
  33. Dilate(q7'', 5 / 6, E) → q7'''
  34. Rotate(q7''', (-(12°)), E) → q8

AI Drawing Prompt Reference

Draw a square spiral centered at point E. Start by creating a square, then dilate it to 5/6 of its size and rotate it -12 degrees around E. Repeat this process multiple times, each time dilating and rotating, to form a spiral sequence of squares.
The prompt above was compiled from the original drawing commands and is for reference only.