MathPlotAI Logo MathPlotAI

Dynamic Geometric Illustration by Tim Brzezinski (3)

Dynamic Geometric Illustration by Tim Brzezinski (3)
Loading the math board and drawing, please wait…
2017-12-10 11:39
VectorCoordinate GeometryCalculusGeometric Construction
This example dynamically demonstrates a problem posted by Antonio Gutierrez on Twitter, integrating geometry and arithmetic through adjustable illustrations. It covers core concepts like planes, pie charts, geometric constructions, arithmetic operations, and upper/lower sums or Riemann sums. The construction utilizes commands such as Point, Semicircle, Segment, Angle, Rotate, Ray, Intersect, Distance, Polygon, Midpoint, Circle, Dilate, CircleSector, Line, Vector, and Translate. Suitable for high school students and math enthusiasts exploring geometric transformations and integral concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → f
  6. Segment(C, B) → g
  7. Segment(B, A) → h
  8. Angle(B, A, C) → α
  9. Rotate(B, (2 * α / 3), A) → B'
  10. Angle(B, A, B') → β
  11. Ray(A, B') → i
  12. Intersect(g, i) → D
  13. Angle(C, B, A) → γ
  14. Rotate(A, γ, D) → A'
  15. Angle(A, D, A') → δ
  16. Ray(D, A') → j
  17. Intersect(h, xAxis) → E
  18. Intersect(h, j) → F
  19. Distance(D, F) → distanceDF
  20. Distance(D, C) → distanceDC
  21. Segment(A, D) → k
  22. Segment(D, F) → l
  23. Polygon(A, C, B) → t1, b, a, c_1
  24. Rotate(B, β / 2, A) → B'_1
  25. Angle(B, A, B'_1) → ε
  26. Ray(A, B'_1) → m
  27. Intersect(g, m) → G
  28. Segment(A, G) → n
  29. Intersect(l, n) → H
  30. Midpoint(A, H) → I
  31. Segment(A, I) → p
  32. Midpoint(l) → J
  33. Circle(A, (0.5 * p)) → d
  34. Circle(B, (0.25 * l)) → q
  35. Angle(A, C, B) → ζ
  36. Intersect(d, h) → K,
  37. Intersect(d, p) → L,
  38. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], I) → A'_1
  39. Segment(A, A'_1) → r
  40. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_2
  41. Segment(A, A'_2) → s
  42. Dilate(F, If[1 < o ≤ 2, 2 - o, 0], J) → F'
  43. Segment(F, F') → t
  44. Dilate(J, If[2 < o ≤ 3, 3 - o, 0], D) → J'
  45. Segment(J, J') → f_1
  46. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], C) → D'
  47. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'_1
  48. Segment(D, D') → g_1
  49. Segment(D, D'_1) → h_1
  50. Intersect(q, g) → M,
  51. Intersect(q, h) → N,
  52. Rotate(K, If[4 < o ≤ 5, ((o - 4) * ε), ε], A) → K'
  53. CircleSector(A, K, K') → d_1
  54. Rotate(d_1, If[6 < o ≤ 7, ((o - 6) * ε), ε], A) → e_1
  55. Rotate(e_1, If[8 < o ≤ 9, ((o - 8) * ε), ε], A) → k_1
  56. Rotate(M, If[11 < o ≤ 12, ((o - 10) * δ), δ], B) → M'
  57. Rotate(M, If[10 < o ≤ 11, ((o - 10) * δ), δ], B) → M'_1
  58. CircleSector(B, M, M'_1) → p_1
  59. Midpoint(D, B) → O
  60. Line(B, f_1) → i_1
  61. Circle(B, 1) → q_1
  62. Intersect(q_1, i_1, 1) → P
  63. Angle(A, B, P) → κ
  64. Dilate(B, If[11 < o ≤ 12, 12 - o, 0], O) → B'_2
  65. Vector(B, B'_2) → u
  66. Translate(p_1, u) → e
  67. Rotate(e, If[12 < o ≤ 13, ((o - 12) * κ), κ], O) → e'
  68. Dilate(O, If[13 < o ≤ 14, 14 - o, 0], D) → O'
  69. Vector(O, O') → v
  70. Translate(e', v) → e''
  71. Angle(C, D, F) → λ
  72. Rotate(D, If[15 < o ≤ 16, ((o - 15) * λ), λ], D) → D'_2
  73. Rotate(D', If[15 < o ≤ 16, ((o - 15) * λ), λ], D) → D''
  74. Segment(D'_2, D'') → j_1
  75. Dilate(D, If[16 < o ≤ 17, 17 - o, 0], J) → D'_3
  76. Vector(D, D'_3) → w
  77. Translate(D, w) → D'_4
  78. Translate(D', w) → D''_1
  79. Segment(D'_4, D''_1) → l_1
  80. Rotate(D'_4, If[17 < o ≤ 18, ((o - 17) * λ), λ], J) → Q
  81. Rotate(D''_1, If[17 < o ≤ 18, ((o - 17) * λ), λ], J) → R
  82. Segment(Q, R) → m_1