MathPlotAI Logo MathPlotAI

Step 3: Geometric Transformations with Unit Circle, Square, and Bar Chart

Step 3: Geometric Transformations with Unit Circle, Square, and Bar Chart
Loading the math board and drawing, please wait…
2015-12-09 07:47
CirclePolygonVectorTrigonometryTransformation
In collections Hands in the Air: Square Translation Tessellation
This example demonstrates the integration of a unit circle, square, and bar chart through geometric transformations, illustrating mathematical visualization. Key concepts include the unit circle, square geometry, bar chart representation, and transformations such as translation and vector operations. Construction highlights: using GeoGebra commands like Polygon to create polygons, Segment for lines, Vector for vectors, and Translate for shifts; objects include text, points, polygons (e.g., text1, A, B, poly1). Suitable for high school or college mathematics education, particularly in teaching trigonometry, geometric transformations, or data visualization.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(B, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(H, I) → i
  7. Segment(I, J) → j
  8. Segment(J, K) → k
  9. Segment(K, L) → l
  10. Segment(L, M) → m
  11. Segment(M, N) → n
  12. Segment(N, O) → p
  13. Segment(O, P) → q
  14. Segment(P, Q) → r
  15. Segment(Q, R) → s
  16. Segment(R, S) → t
  17. Segment(S, T) → a_1
  18. Segment(T, U) → b_1
  19. Segment(U, V) → c_1
  20. Segment(V, W) → d_1
  21. Segment(W, Z) → e_1
  22. Segment(Z, A_1) → f_1
  23. Segment(A_1, B_1) → g_1
  24. Segment(B_1, C_1) → h_1
  25. Segment(C_1, C) → i_1
  26. Vector(B, A) → u
  27. Translate(B, u) → B'
  28. Translate(C, u) → C'
  29. Segment(B', C') → b'
  30. Translate(B, u) → B'_1
  31. Translate(E, u) → E'
  32. Segment(B'_1, E') → e'
  33. Translate(E, u) → E'_1
  34. Translate(F, u) → F'
  35. Segment(E'_1, F') → f'
  36. Translate(F, u) → F'_1
  37. Translate(G, u) → G'
  38. Segment(F'_1, G') → g'
  39. Translate(G, u) → G'_1
  40. Translate(H, u) → H'
  41. Segment(G'_1, H') → h'
  42. Translate(H, u) → H'_1
  43. Translate(I, u) → I'
  44. Segment(H'_1, I') → i'
  45. Translate(I, u) → I'_1
  46. Translate(J, u) → J'
  47. Segment(I'_1, J') → j'
  48. Translate(J, u) → J'_1
  49. Translate(K, u) → K'
  50. Segment(J'_1, K') → k'
  51. Translate(K, u) → K'_1
  52. Translate(L, u) → L'
  53. Segment(K'_1, L') → l'
  54. Translate(L, u) → L'_1
  55. Translate(M, u) → M'
  56. Segment(L'_1, M') → m'
  57. Translate(M, u) → M'_1
  58. Translate(N, u) → N'
  59. Segment(M'_1, N') → n'
  60. Translate(N, u) → N'_1
  61. Translate(O, u) → O'
  62. Segment(N'_1, O') → p'
  63. Translate(O, u) → O'_1
  64. Translate(P, u) → P'
  65. Segment(O'_1, P') → q'
  66. Translate(P, u) → P'_1
  67. Translate(Q, u) → Q'
  68. Segment(P'_1, Q') → r'
  69. Translate(Q, u) → Q'_1
  70. Translate(R, u) → R'
  71. Segment(Q'_1, R') → s'
  72. Translate(R, u) → R'_1
  73. Translate(S, u) → S'
  74. Segment(R'_1, S') → t'
  75. Translate(S, u) → S'_1
  76. Translate(T, u) → T'
  77. Segment(S'_1, T') → j_1
  78. Translate(T, u) → T'_1
  79. Translate(U, u) → U'
  80. Segment(T'_1, U') → k_1
  81. Translate(U, u) → U'_1
  82. Translate(V, u) → V'
  83. Segment(U'_1, V') → l_1
  84. Translate(V, u) → V'_1
  85. Translate(W, u) → W'
  86. Segment(V'_1, W') → m_1
  87. Translate(W, u) → W'_1
  88. Translate(Z, u) → Z'
  89. Segment(W'_1, Z') → n_1
  90. Translate(Z, u) → Z'_1
  91. Translate(A_1, u) → D_1
  92. Segment(Z'_1, D_1) → p_1
  93. Translate(A_1, u) → E_1
  94. Translate(B_1, u) → F_1
  95. Segment(E_1, F_1) → q_1
  96. Translate(B_1, u) → G_1
  97. Translate(C_1, u) → H_1
  98. Segment(G_1, H_1) → r_1
  99. Translate(C_1, u) → I_1
  100. Translate(C, u) → C'_1
  101. Segment(I_1, C'_1) → s_1