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Fibonacci Numbers and Spiral Demo

Fibonacci Numbers and Spiral Demo
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2020-11-04 02:48
PolygonSequenceGeometric Construction
This example demonstrates the construction of Fibonacci squares and the Fibonacci spiral using a GeoGebra applet, providing a quick visual representation without detailed construction steps. It involves core mathematical concepts like the Fibonacci sequence, geometric constructions, and polygon creation. The construction utilizes GeoGebra commands such as Point, Polygon, First, and CircleArc. Suitable for high school mathematics education or for enthusiasts exploring the geometric applications of the Fibonacci sequence.

GeoGebra Commands & Parameters

  1. Point(Circle[A, f]) → B
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Polygon(Corner[1], (x(Corner[1]) + 0.3 * Distance[Corner[1], Corner[2]], y(Corner[1])), (x(Corner[4]) + 0.3 * Distance[Corner[1], Corner[2]], y(Corner[4])), Corner[4]) → poly10, i_2, j_2, k_2, l_2
  4. First(Fibonacci, n + 1) → list1
  5. Element(list1, n - 1) → last
  6. Element(list1, n) → beforeLast
  7. Polygon((-22, 3), (-22, 4), (-21, 4), (-21, 3)) → poly2, g, h, i, j
  8. CircleArc((-21, 4), (-22, 4), (-21, 3)) → e
  9. Polygon((-22, 4), (-21, 4), (-21, 5), (-22, 5)) → poly3, l, m, p, q
  10. CircleArc((-21, 4), (-21, 5), (-22, 4)) → k
  11. Polygon((-21, 5), (-21, 3), (-19, 3), (-19, 5)) → poly4, s, t, a_1, b_1
  12. CircleArc((-21, 3), (-19, 3), (-21, 5)) → r
  13. Polygon((-19, 3), (-22, 3.0000000000000004), (-22, 4.440892098500626E-16), (-19, 0)) → poly5, d_1, e_1, f_1, g_1
  14. CircleArc((-22, 3.0000000000000004), (-22, 4.440892098500626E-16), (-19, 3)) → c_1
  15. Polygon((-22, 0), (-22, 5), (-27, 5), (-27, 0)) → poly6, i_1, j_1, k_1, l_1
  16. CircleArc((-22, 5), (-27, 5), (-22, 0)) → h_1
  17. Polygon((-27, 5), (-19, 5), (-19, 13), (-27, 13)) → poly7, m_1, n_1, q_1, r_1
  18. CircleArc((-19, 5), (-19, 13), (-27, 5)) → p_1
  19. Polygon((-19, 13), (-19, 0), (-6, 0), (-6, 13)) → poly8, t_1, a_2, b_2, c_2
  20. CircleArc((-19, 0), (-6, 0), (-19, 13)) → s_1

AI Drawing Prompt Reference

Draw a planar figure made of several adjacent squares/rectangular blocks placed next to each other, and connect corresponding corners with circular arcs so the overall shape resembles a Fibonacci spiral demo. Start by placing four corner points of a base square and draw one arc along its interior. Then extend the construction step by step to neighboring blocks on the right, keeping shared edges or corners between consecutive blocks. For each new block, add the circular arc determined by its corner triple. Assemble the blocks sequentially from left to right to obtain a continuous spiral-like arc outline.
The prompt above was compiled from the original drawing commands and is for reference only.