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Multiply by 4 with Dice: Random Rotation and Geometric Transformation

Multiply by 4 with Dice: Random Rotation and Geometric Transformation
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2020-02-09 13:36
CirclePolygonAngleProbability & StatisticsTransformation
① This example demonstrates how rolling a dice generates a random number, which is then used to rotate a polygon on a circle by an angle corresponding to that number, visually linking the arithmetic operation 'multiply by 4' with geometric rotation. ② Core math concepts include multiplication, random numbers, angles, rotation, polygons, and geometric transformations, with cosine functions used in coordinate calculations. ③ Construction highlights: GeoGebra commands such as Shuffle and Random generate dice outcomes, Element extracts values from lists, Circle and Point define points on the circumference, Rotate performs polygon rotation, Angle measures the rotation, Polygon and Midpoint build shapes, Textfield allows interactive input, and Intersect computes intersections; objects include points A through J, circles c, polygons p and q, and rotated copies. ④ Suitable for upper elementary to middle school students, this tool helps connect abstract multiplication with visual rotation and serves as an introduction to probability and geometric transformations.

GeoGebra Commands & Parameters

  1. Shuffle(positionlist) → pl, {(21, 15), (21, 21), (15, 22), (14, 16), (3, 22), (8, 15), (2, 16), (19.234824979926557, 9.296710623986465), (9, 21), (5, 10)}
  2. Element(pl, 1) → A
  3. Element(pl, 2) → B
  4. Element(pl, 3) → C
  5. Element(pl, 4) → D
  6. Element(pl, 5) → E
  7. Element(pl, 6) → F
  8. Element(pl, 7) → G
  9. Element(pl, 8) → H
  10. Element(pl, 9) → I
  11. Element(pl, 10) → J
  12. Circle(A, sd) → c
  13. Circle(B, sd) → d
  14. Circle(C, sd) → e
  15. Circle(D, sd) → f
  16. Circle(E, sd) → g
  17. Circle(J, sd) → h
  18. Circle(I, sd) → k
  19. Circle(H, sd) → p
  20. Circle(G, sd) → q
  21. Random(90, 270) → a1
  22. Circle(F, sd) → r
  23. Point(c) → K
  24. Point(d) → L
  25. Point(e) → M
  26. Point(f) → N
  27. Point(g) → O
  28. Rotate(K, a1°, A) → K'
  29. Angle(K, A, K') → α
  30. Polygon(A, K', 4) → poly1, i, j, l, m, P, Q
  31. Random(0, 360) → a2
  32. Random(0, 360) → a3
  33. Random(0, 360) → a4
  34. Random(0, 360) → a5
  35. Random(0, 360) → a6
  36. Random(0, 360) → a7
  37. Random(0, 360) → a8
  38. Random(0, 360) → a9
  39. Random(0, 360) → a10
  40. Point(r) → R
  41. Point(q) → S
  42. Point(p) → T
  43. Point(k) → U
  44. Point(h) → V
  45. Rotate(L, a2°, B) → L'
  46. Angle(L, B, L') → β
  47. Rotate(M, a3°, C) → M'
  48. Angle(M, C, M') → γ
  49. Rotate(N, a4°, D) → N'
  50. Angle(N, D, N') → δ
  51. Rotate(O, a5°, E) → O'
  52. Angle(O, E, O') → ε
  53. Rotate(R, a6°, F) → R'
  54. Angle(R, F, R') → ζ
  55. Rotate(S, a7°, G) → S'
  56. Angle(S, G, S') → η
  57. Rotate(T, a8°, H) → T'
  58. Angle(T, H, T') → θ
  59. Rotate(U, a9°, I) → U'
  60. Angle(U, I, U') → ι
  61. Rotate(V, a10°, J) → V'
  62. Angle(V, J, V') → κ
  63. Polygon(B, L', 4) → poly2, n, s, t, a, W, Z
  64. Polygon(C, M', 4) → poly3, b, f_1, g_1, h_1, A_1, B_1
  65. Polygon(D, N', 4) → poly4, i_1, j_1, k_1, l_1, C_1, D_1
  66. Polygon(E, O', 4) → poly5, m_1, n_1, p_1, q_1, E_1, F_1
  67. Polygon(F, R', 4) → poly6, r_1, s_1, t_1, a_1, G_1, H_1
  68. Polygon(G, S', 4) → poly7, b_1, c_1, d_1, e_1, I_1, J_1
  69. Polygon(H, T', 4) → poly8, f_2, g_2, h_2, i_2, K_1, L_1
  70. Polygon(I, U', 4) → poly9, j_2, k_2, l_2, m_2, M_1, N_1
  71. Polygon(J, V', 4) → poly10, n_2, p_2, q_2, r_2, O_1, P_1
  72. Circle(J, O_1) → c_2
  73. Circle(H, K_1) → d_2
  74. Circle(G, I_1) → e_2
  75. Circle(F, G_1) → s_2
  76. Circle(E, E_1) → t_2
  77. Circle(D, C_1) → c_3
  78. Circle(C, A_1) → d_3
  79. Circle(B, W) → e_3
  80. Circle(I, M_1) → f_3
  81. Circle(A, P) → g_3
  82. Midpoint(K', Q) → Q_1
  83. Midpoint(Q_1, Q) → R_1
  84. Midpoint(K', Q_1) → S_1
  85. Midpoint(B, W) → T_1
  86. Midpoint(T_1, W) → U_1
  87. Midpoint(B, T_1) → V_1
  88. Midpoint(C, A_1) → W_1
  89. Midpoint(C, W_1) → Z_1
  90. Midpoint(W_1, A_1) → A_2
  91. Midpoint(D, C_1) → B_2
  92. Midpoint(D, B_2) → C_2
  93. Midpoint(B_2, C_1) → D_2
  94. Midpoint(E, E_1) → E_2
  95. Midpoint(E_2, E_1) → F_2
  96. Midpoint(E, E_2) → G_2
  97. Midpoint(F, G_1) → H_2
  98. Midpoint(H_2, G_1) → I_2
  99. Midpoint(F, H_2) → J_2
  100. Midpoint(G, I_1) → K_2
  101. Midpoint(G, K_2) → L_2
  102. Midpoint(I_1, K_2) → M_2
  103. Midpoint(H, K_1) → N_2
  104. Midpoint(H, N_2) → O_2
  105. Midpoint(N_2, K_1) → P_2
  106. Midpoint(J, O_1) → Q_2
  107. Midpoint(J, Q_2) → R_2
  108. Midpoint(Q_2, O_1) → S_2
  109. Midpoint(M_1, I) → T_2
  110. Midpoint(M_1, T_2) → U_2
  111. Midpoint(T_2, I) → V_2
  112. Element(dl, dsl) → dn
  113. Textfield(kiddice) → InputBox1
  114. Textfield(kiddots) → InputBox2
  115. Element(dl, dsl) → dice
  116. Intersect(j, l) → E_3
  117. Intersect(t, a) → F_3
  118. Intersect(g_1, h_1) → G_3
  119. Intersect(k_1, l_1) → H_3
  120. Intersect(p_1, q_1) → I_3
  121. Intersect(t_1, a_1) → J_3
  122. Intersect(d_1, e_1) → K_3
  123. Intersect(h_2, i_2) → L_3
  124. Intersect(l_2, m_2) → M_3
  125. Intersect(n_2, p_2) → N_3
  126. Intersect(q_2, r_2) → O_3
  127. Midpoint(A, Q_1) → P_3
  128. Midpoint(Q_1, E_3) → Q_3
  129. Midpoint(F_3, T_1) → R_3
  130. Midpoint(L', T_1) → S_3
  131. Midpoint(M', W_1) → T_3
  132. Midpoint(W_1, G_3) → U_3
  133. Midpoint(H_3, B_2) → V_3
  134. Midpoint(B_2, N') → W_3
  135. Midpoint(E_2, I_3) → Z_3
  136. Midpoint(E_2, O') → A_4
  137. Midpoint(R', H_2) → B_4
  138. Midpoint(H_2, J_3) → C_4
  139. Midpoint(K_2, S') → D_4
  140. Midpoint(K_3, K_2) → E_4
  141. Midpoint(L_3, N_2) → F_4
  142. Midpoint(N_2, T') → G_4
  143. Midpoint(U', T_2) → H_4
  144. Midpoint(T_2, M_3) → I_4
  145. Midpoint(N_3, Q_2) → J_4
  146. Midpoint(Q_2, O_3) → K_4

AI Drawing Prompt Reference

Place ten random points on the canvas. Draw equal-sized circles centered at eight of these points. Use the remaining two points as rotation centers and starting points for random angles. Pick a point on the first circle, rotate it around its center by a random angle between 90 and 270 degrees, forming a rotated point. Connect the center and the two points to show the angle. Construct a regular quadrilateral using the center and the rotated point as vertices. For each of the other circles, pick a point and rotate it around its center by a random angle between 0 and 360 degrees, measuring each rotation angle. The final drawing includes all circles, points, rotated points, angles, and the quadrilateral, illustrating random rotation and geometric transformation.
The prompt above was compiled from the original drawing commands and is for reference only.