Logarithmic Spiral on an Equilateral Triangle

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Circle(A, sideLength / sqrt(3)) → c
3. Intersect(c, yAxis, 2) → B
4. Circle(B, sideLength) → d
5. Intersect(d, c) → C, D, ,
6. Segment(B, D) → f
7. Segment(D, C) → g
8. Segment(C, B) → h
9. Polygon(B, D, C) → t1, c_1, b, d_1
10. Rotate(B, 30°, A) → B'
11. Rotate(D, 30°, A) → D'
12. Rotate(C, 30°, A) → C'
13. Polygon(B', D', C') → triangle, c', b', d'
14. Intersect(xAxis, yAxis) → E
15. Length(Segment[B', C']) → a
16. CurveCartesian(((a / sqrt(3) * ℯ^(((-sqrt(3)) * θ))); θ), θ, 0, (2 * 3.141592653589793)) → curve1
17. OrthogonalLine(E, d') → j
18. Mirror(curve1, j) → i'
19. LineBisector(b') → k
20. LineBisector(c') → l
21. Mirror(i', l) → curve3
22. Mirror(i', k) → curve2
23. Rotate(curve1, (-(30°)), E) → curve1'
24. Rotate(curve3, (-(30°)), E) → curve3'
25. Rotate(curve2, (-(30°)), E) → curve2'
26. Point(curve2') → F
27. Point(curve3') → G
28. Point(curve1') → H
29. Polygon(F, G, H) → t2, h_1, f_1, g_1
30. Circle(G, 1) → p
31. Tangent(G, curve3') → i
32. Intersect(p, i) → I, J
33. Vector(G, J) → u
34. Tangent(H, curve1') → m
35. Circle(H, 1) → q
36. Intersect(q, m, 2) → K
37. Vector(H, K) → v
38. Tangent(F, curve2') → n
39. Circle(F, 1) → r
40. Intersect(r, n, 2) → L
41. Vector(F, L) → w