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Fibonacci Spiral 5: Geometric Construction and Sequence Relationship

Fibonacci Spiral 5: Geometric Construction and Sequence Relationship
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2021-10-13 01:04
CircleSequenceGeometric Construction
In collections STEAM like Leonardo
This example demonstrates the construction of the Fibonacci spiral, involving sequences, geometric construction, and circle arcs. Key concepts include the Fibonacci sequence, arc generation, and spiral formation. Construction points include using GeoGebra commands like Kwadrat and CircleArc, and objects such as A, B, C. Suitable for middle school and above, to understand the connection between geometry and sequences.

GeoGebra Commands & Parameters

  1. Kwadrat(A, B) → C, q1, f, g, h, i, D
  2. Kwadrat(D, C) → E, q2, j, k, l, m, F
  3. Kwadrat(A, F) → G, q3, n, p, q, r, H
  4. Kwadrat(B, H) → I, q4, s, t, a, b, J
  5. CircleArc(D, A, C) → c
  6. CircleArc(D, C, F) → d
  7. CircleArc(A, F, H) → e
  8. CircleArc(B, H, J) → c_1
  9. Kwadrat(E, J) → K, q5, f_1, g_1, h_1, i_1, L
  10. CircleArc(E, J, L) → d_1
  11. Kwadrat(G, L) → M, q6, j_1, k_1, l_1, m_1, N
  12. Kwadrat(I, N) → O, q7, n_1, p_1, q_1, r_1, P
  13. CircleArc(G, L, N) → e_1
  14. CircleArc(I, N, P) → s_1

AI Drawing Prompt Reference

Draw a Fibonacci spiral by first creating a series of squares, then drawing arcs with the side lengths of adjacent squares as radii, centered at the vertices of the squares. The arcs should connect the vertices of the squares to form each circle of the spiral, with the squares increasing in size sequentially.
The prompt above was compiled from the original drawing commands and is for reference only.