Logarithmic Spiral for Pentagon

GeoGebra Commands & Parameters

1. CurveCartesian(((d / ((2 * sin(π / 5))) * ℯ^(((-θ) * tan(π / 5)))); θ), θ, 0, (2 * 3.141592653589793)) → r
2. Intersect(xAxis, yAxis) → A
3. Circle(A, d / ((2 * sin(π / 5)))) → c
4. Intersect(c, yAxis, 2) → B
5. Circle(B, d) → e
6. Intersect(e, c) → C, D, ,
7. Circle(D, d) → f
8. Intersect(f, c) → E, F, ,
9. Circle(C, d) → g
10. Intersect(g, c) → G, H, ,
11. Polygon(B, D, F, G, C) → poly1, b, d_1, f_1, g_1, c_1
12. Rotate(r, 90°, A) → r'
13. LineBisector(b) → h
14. Mirror(r', h) → r''
15. LineBisector(d_1) → i
16. LineBisector(f_1) → j
17. LineBisector(g_1) → k
18. LineBisector(c_1) → l
19. Mirror(r'', k) → r'''
20. Mirror(r''', i) → a
21. Mirror(a, l) → a'
22. Mirror(a, j) → a'_1
23. Mirror(a'_1, k) → m
24. Mirror(m, i) → m'
25. Mirror(m, l) → m'_1
26. Mirror(m, i) → m'_2
27. Mirror(k, h) → k'
28. Point(r''') → I
29. Point(a') → J
30. Point(a'_1) → K
31. Point(m'_2) → L
32. Point(m'_1) → M
33. Polygon(M, I, J, K, L) → poly2, m_1, i_1, j_1, k_1, l_1
34. Circle(M, 1) → p
35. Tangent(M, m'_1) → n
36. Intersect(p, n, 2) → N
37. Vector(M, N) → u
38. Circle(I, 1) → q
39. Tangent(I, r''') → s
40. Intersect(q, s, 2) → O
41. Vector(I, O) → v
42. Circle(J, 1) → t
43. Tangent(J, a') → h_1
44. Intersect(t, h_1, 2) → P
45. Vector(J, P) → w
46. Tangent(K, a'_1) → n_1
47. Circle(K, 1) → e_1
48. Intersect(e_1, n_1, 2) → Q
49. Vector(K, Q) → u_1
50. Circle(L, 1) → p_1
51. Tangent(L, m'_2) → q_1
52. Intersect(p_1, q_1, 2) → R
53. Vector(L, R) → v_1