MathPlotAI Logo MathPlotAI

Fibonacci Spiral 2

Fibonacci Spiral 2
Loading the math board and drawing, please wait…
2021-10-06 00:19
SequenceCoordinate GeometryGeometric Construction
In collections STEAM like Leonardo
This example demonstrates the construction of a Fibonacci spiral. It involves concepts of sequences and the golden ratio. Using GeoGebra commands such as Kwadrat, Point, CircleArc, etc., a Fibonacci spiral can be constructed. Suitable for middle school and above students to learn geometric construction and sequences.

GeoGebra Commands & Parameters

  1. Kwadrat(A, B) → q1, f, g, h, i
  2. Kwadrat(C, D) → q2, j, k, l, m
  3. Point(h) → E
  4. Kwadrat(C, E) → q3, n, p, q, r
  5. Point(p) → F
  6. Kwadrat(D, H) → q4, s, t, a, b
  7. Kwadrat(G, I) → q5, c, d, e, f_1
  8. Kwadrat(F, J) → q6, g_1, h_1, i_1, j_1
  9. Point(t) → K
  10. Point(i_1) → L
  11. Kwadrat(K, L) → q7, k_1, l_1, m_1, n_1
  12. Point(d) → M
  13. Point(m_1) → N
  14. Kwadrat(M, N) → q8, p_1, q_1, r_1, s_1
  15. Point(h_1) → O
  16. Point(r_1) → P
  17. Kwadrat(O, P) → q10, d_1, e_1, f_2, g_2
  18. Point(l_1) → Q
  19. Point(f_2) → R
  20. Kwadrat(Q, R) → q11, h_2, i_2, j_2, k_2
  21. Point(q_1) → S
  22. Point(j_2) → T
  23. Kwadrat(S, T) → q12, l_2, m_2, n_2, p_2
  24. CircleArc(A, C, B) → c_2
  25. CircleArc(A, B, E) → d_2
  26. CircleArc(C, E, H) → e_2
  27. CircleArc(D, H, I) → q_2
  28. CircleArc(G, I, J) → r_2
  29. CircleArc(F, J, L) → c_1
  30. CircleArc(K, L, N) → t_1
  31. CircleArc(M, N, P) → s_2
  32. CircleArc(O, P, R) → t_2
  33. CircleArc(Q, R, T) → c_3
  34. Point(n_2) → U
  35. CircleArc(S, T, U) → d_3
  36. Segment(P_1, Q_1) → a_1
  37. Segment(P_{3}, Q_{3}) → a_{3}

AI Drawing Prompt Reference

Draw a Fibonacci spiral. The figure consists of squares and arcs. Squares are arranged in a Fibonacci sequence, and arcs connect the diagonals of these squares. The construction order starts with a small square and gradually expands to form the spiral. Ensure the figure is clear, smooth, and proportionally coordinated.
The prompt above was compiled from the original drawing commands and is for reference only.