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Golden Spiral Construction

Golden Spiral Construction
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2019-05-10 19:42
CircleTrigonometrySequenceCoordinate GeometryGeometric Construction
This example demonstrates how to construct a golden spiral using a square and inscribed circles, involving the golden ratio, geometric construction, sequences and series, and coordinate geometry. It utilizes GeoGebra commands like Intersect, Point, Polygon, and CircleArc. Suitable for high school and above students to understand the geometric significance of the golden ratio.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Polygon(C, B, 4) → poly2, e, f, g, h, E, F
  5. Polygon(D, F, 4) → poly3, i, j, k, l, G, H
  6. Polygon(A, H, 4) → poly4, m, n, p, q, I, J
  7. Polygon(E, J, 4) → poly5, r, s, t, a_1, K, L
  8. Polygon(G, L, 4) → poly6, b_1, c_1, d_1, e_1, M, N
  9. Polygon(I, N, 4) → poly7, f_1, g_1, o, i_1, O, P
  10. Polygon(K, P, 4) → poly8, h_1, j_1, k_1, l_1, Q, R
  11. CircleArc(C, D, B) → p_1
  12. CircleArc(C, B, F) → q_1
  13. CircleArc(D, F, H) → r_1
  14. CircleArc(A, H, J) → s_1
  15. CircleArc(E, J, L) → t_1
  16. CircleArc(G, L, N) → c_2
  17. CircleArc(I, N, P) → d_2
  18. CircleArc(K, P, R) → e_2

AI Drawing Prompt Reference

Draw a square and inscribe four circles inside it, with each circle's radius increasing to form a spiral. Connect the midpoints of the square's sides as the centers of the circles, draw arcs between adjacent circle centers, and connect the endpoints of the arcs to form a spiral.
The prompt above was compiled from the original drawing commands and is for reference only.