MathPlotAI Logo MathPlotAI

Fibonacci Spiral Construction

Fibonacci Spiral Construction
Loading the math board and drawing, please wait…
2021-10-06 00:16
PolygonSequenceGeometric Construction
In collections STEAM like Leonardo
This example demonstrates how to construct a Fibonacci spiral using the Fibonacci sequence and golden ratio. Key math concepts include the Fibonacci sequence, golden ratio, and geometric construction. GeoGebra commands used are Kwadrat (square) and CircleArc (arc). Suitable for high school geometry teaching to understand the Fibonacci sequence's natural manifestations.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a Fibonacci spiral constructed from a sequence of squares whose side lengths follow the Fibonacci sequence. Start with two small adjacent squares, then repeatedly add larger squares adjacent to the existing ones, each new square having a side length equal to the sum of the two previous squares, keeping all squares tightly packed. Inside each square, draw a quarter-circle arc centered at one corner with radius equal to the square's side, connecting diagonal points of successive squares, so that all arcs join smoothly into a continuous spiral. The overall shape exhibits golden ratio aesthetics.
The prompt above was compiled from the original drawing commands and is for reference only.