How Many Radii? Circumference Illustrator

How Many Radii? Circumference Illustrator
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2023-01-31 01:00
This example demonstrates the relationship between the radius and circumference of a circle. Key mathematical concepts include the formula for circumference, the relationship between radius and diameter, and geometric construction techniques. Construction involves using GeoGebra commands such as Segment, Rotate, CircleArc, Circle, etc. Suitable for middle or high school mathematics to understand basic circle properties and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment((0, 0), (r, 0)) → f
  2. Rotate((r, 0), 1, (0, 0)) → A
  3. Rotate((r, 0), 2, (0, 0)) → B
  4. Rotate((r, 0), 3, (0, 0)) → C
  5. Rotate((r, 0), 4, (0, 0)) → D
  6. Rotate((r, 0), 5, (0, 0)) → E
  7. Rotate((r, 0), -1, (0, 0)) → F
  8. Rotate(f, If[0 < a ≤ 1, ((-a) * pi / 2), ((-pi)) / 2], (r, 0)) → f'
  9. Rotate(G, If[1.5 < a ≤ 2.5, a - 1.5, 1], (0, 0)) → G'
  10. CircleArc((0, 0), G, G') → c
  11. Circle(G', r - c) → d
  12. Line((0, 0), G') → g
  13. OrthogonalLine(G', g) → h
  14. Intersect(d, h, 2) → H
  15. Segment(G', H) → i
  16. Dilate(G, If[3 < a ≤ 4, 4 - a, 0], A) → G'_{1}
  17. Vector(G, G'_{1}) → u
  18. Translate(f, u) → f'_{1}
  19. Line((0, 0), A) → j
  20. OrthogonalLine(A, j) → k
  21. Point(p) → I
  22. Point(k) → J
  23. Angle(J, A, I) → α
  24. Rotate(f'_{1}, If[3 < a ≤ 4, ((-(a - 3)) * α), (-α)], G'_{1}) → l
  25. Rotate(A, If[4 < a ≤ 5, a - 4, 1], (0, 0)) → A'
  26. CircleArc((0, 0), A, A') → e
  27. Circle(A', r - e) → q
  28. Line((0, 0), A') → m
  29. OrthogonalLine(A', m) → n
  30. Intersect(q, n, 2) → K
  31. Segment(A', K) → s
  32. Dilate((0, 0), If[5.5 < a ≤ 6.5, 6.5 - a, 0], B) → L
  33. Vector(M, L) → v
  34. Translate(f, v) → f'_{2}
  35. Line(M, B) → b
  36. OrthogonalLine(B, b) → f_1
  37. Point(t) → N
  38. Point(f_1) → O
  39. Angle(O, B, N) → β
  40. Rotate(f'_{2}, If[5.5 < a ≤ 6.5, ((-(a - 5.5)) * β), (-β)], L) → g_1
  41. Rotate(B, If[6.5 < a ≤ 7.5, a - 6.5, 1], (0, 0)) → B'
  42. CircleArc(M, B, B') → c_1
  43. Line(M, B') → h_1
  44. OrthogonalLine(B', h_1) → i_1
  45. Circle(B', r - c_1) → d_1
  46. Intersect(d_1, i_1, 2) → P
  47. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], C) → M'
  48. Vector(M, M') → w
  49. Translate(f, w) → f'_{3}
  50. Line(M, C) → k_1
  51. OrthogonalLine(C, k_1) → l_1
  52. Point(p_1) → Q
  53. Point(l_1) → R
  54. Angle(R, C, Q) → γ
  55. Rotate(f'_{3}, If[8 < a ≤ 9, ((-(a - 8)) * γ), (-γ)], M') → m_1
  56. Rotate(C, If[9 < a ≤ 10, a - 9, 1], M) → C'
  57. CircleArc(M, C, C') → e_1
  58. Line(M, C') → n_1
  59. OrthogonalLine(C', n_1) → q_1
  60. Circle(C', r - e_1) → r_1
  61. Intersect(r_1, q_1) → S, B_1
  62. Intersect(d_1, i_1, 1) → T
  63. Dilate(M, If[10.5 < a ≤ 11.5, 11.5 - a, 0], D) → M'_{1}
  64. Vector(M, M'_{1}) → u_1
  65. Translate(f, u_1) → f'_{4}
  66. Line(M, D) → a_1
  67. OrthogonalLine(D, a_1) → b_1
  68. Point(b_1) → U
  69. Point(t_1) → V
  70. Angle(U, D, V) → δ
  71. Rotate(f'_{4}, If[10.5 < a ≤ 11.5, ((-(a - 10.5)) * δ), (-δ)], M'_{1}) → f_2
  72. Rotate(D, If[11.5 < a ≤ 12.5, a - 11.5, 1], M) → D'
  73. CircleArc(M, D, D') → c_2
  74. Line(M, D') → g_2
  75. OrthogonalLine(D', g_2) → h_2
  76. Circle(D', r - c_2) → d_2
  77. Intersect(d_2, h_2, 2) → W
  78. Segment(D', W) → i_2
  79. Intersect(d_2, h_2, 1) → Z
  80. Rotate(M, If[13 < a ≤ 14, ((a - 13) * pi / 2), pi / 2], G) → M'_{2}
  81. Segment(G, M'_{2}) → j_2
  82. If(x(P) ≤ x(T), P, T) → A_1
  83. Segment(B', A_1) → j_1
  84. If(y(B_1) < y(S), B_1, S) → C_1
  85. Segment(C', C_1) → s_1
  86. Rotate(G, If[14 < a ≤ 15, (-(a - 14)), -1], M) → G'_{2}
  87. CircleArc(M, G'_{2}, G) → e_2
  88. Line(M, G'_{2}) → k_2
  89. Circle(G'_{2}, r - e_2) → p_2
  90. OrthogonalLine(G'_{2}, k_2) → l_2
  91. Intersect(p_2, l_2) → D_1, E_1
  92. If(y(D_1) ≤ y(E_1), D_1, E_1) → F_1
  93. Segment(G'_{2}, F_1) → m_2
  94. Rotate(D, 1, M) → D'_{1}
  95. Rotate(G, 0.5) → G'_{3}
  96. Rotate(G, 1.5) → G'_{4}
  97. Rotate(G, 2.5) → G'_{5}
  98. Rotate(G, 3.5) → G'_{6}
  99. Rotate(G, 4.5) → G'_{7}
  100. Rotate(G, -0.5) → G'_{8}

AI Drawing Prompt Reference

Draw a circle to illustrate the relationship between its radius and circumference. Start by drawing a radius from the center, then rotate this radius multiple times around the center to create several points. Connect these points to show the circumference of the circle. Also, draw the diameter of the circle and label the relationship between the radius and diameter. Use arcs and circles to emphasize the concept of circumference, and add auxiliary lines to demonstrate angle relationships.
The prompt above was compiled from the original drawing commands and is for reference only.