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Visualization of Equivalent Fractions

Visualization of Equivalent Fractions
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2019-01-25 15:34
CircleVectorTrigonometryGeometric ConstructionSlider Animation
This example dynamically demonstrates the geometric representation of equivalent fractions. It involves core math concepts like fractions, geometric visualization, and similar triangles. Constructed using commands such as Point, Circle, OrthogonalLine, Intersect, Rotate, CircleSector, Segment, Vector, Translate, Polygon, and Slider for interactive learning. Suitable for middle school and above, focusing on visualizing fraction relationships.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 3) → e
  3. OrthogonalLine(A, xAxis) → f
  4. Intersect(e, f, 2) → C
  5. Rotate(C, (360 * ° / Slider), A) → C'
  6. Rotate(C', (360 * ° / Slider), A) → C''
  7. Rotate(C'', (360 * ° / Slider), A) → C'''
  8. Rotate(C''', (360 * ° / Slider), A) → D
  9. Rotate(D, (360 * ° / Slider), A) → D'
  10. Rotate(D', (360 * ° / Slider), A) → D''
  11. Rotate(D'', (360 * ° / Slider), A) → D'''
  12. Rotate(D''', (360 * ° / Slider), A) → E
  13. Rotate(E, (360 * ° / Slider), A) → E'
  14. Rotate(E', (360 * ° / Slider), A) → E''
  15. Rotate(E'', (360 * ° / Slider), A) → E'''
  16. Rotate(E''', (360 * ° / Slider), A) → F
  17. Rotate(F, (360 * ° / Slider), A) → F'
  18. Rotate(F', (360 * ° / Slider), A) → F''
  19. Rotate(F'', (360 * ° / Slider), A) → F'''
  20. Rotate(F''', (360 * ° / Slider), A) → G
  21. Rotate(G, (360 * ° / Slider), A) → G'
  22. Rotate(G', (360 * ° / Slider), A) → G''
  23. Rotate(G'', (360 * ° / Slider), A) → G'''
  24. CircleSector(A, C, C') → g
  25. CircleSector(A, C', C'') → h
  26. CircleSector(A, C'', C''') → k
  27. CircleSector(A, C''', D) → p
  28. CircleSector(A, D, D') → q
  29. CircleSector(A, D', D'') → r
  30. CircleSector(A, D'', D''') → s
  31. CircleSector(A, D''', E) → t
  32. CircleSector(A, E, E') → c_1
  33. CircleSector(A, E', E'') → d_1
  34. CircleSector(A, E'', E''') → e_1
  35. CircleSector(A, E''', F) → f_1
  36. CircleSector(A, F, F') → g_1
  37. CircleSector(A, F', F'') → h_1
  38. CircleSector(A, F'', F''') → k_1
  39. CircleSector(A, F''', G) → p_1
  40. CircleSector(A, G, G') → q_1
  41. CircleSector(A, G', G'') → r_1
  42. CircleSector(A, G'', G''') → s_1
  43. CircleSector(A, G''', C) → t_1
  44. Segment(A, C) → i
  45. Segment(A, C') → j
  46. Segment(A, C'') → l
  47. Segment(A, C''') → m
  48. Segment(A, D) → n
  49. Segment(A, D') → a_1
  50. Segment(A, D'') → b_1
  51. Segment(A, D''') → i_1
  52. Segment(A, E) → j_1
  53. Segment(A, E') → l_1
  54. Segment(A, E'') → m_1
  55. Segment(A, E''') → n_1
  56. Segment(A, F) → a_2
  57. Segment(A, F') → b_2
  58. Segment(A, F'') → c_2
  59. Segment(A, F''') → d_2
  60. Segment(A, G) → e_2
  61. Segment(A, G') → f_2
  62. Segment(A, G'') → g_2
  63. Segment(A, G''') → h_2
  64. Intersect(e, xAxis, 1) → H
  65. Intersect(e, xAxis, 2) → I
  66. OrthogonalLine(H, xAxis) → i_2
  67. OrthogonalLine(I, xAxis) → j_2
  68. OrthogonalLine(J, i_2) → k_2
  69. OrthogonalLine(K, i_2) → l_2
  70. Intersect(j_2, k_2) → L
  71. Intersect(j_2, l_2) → M
  72. Segment(J, L) → m_2
  73. Segment(K, M) → n_2
  74. Segment(K, J) → p_2
  75. Segment(M, L) → q_2
  76. Vector(J, L) → u
  77. Translate(i_2, Vector[u / Slider]) → r_2
  78. Translate(i_2, Vector[(u * 2 / Slider)]) → s_2
  79. Translate(i_2, Vector[(u * 18 / Slider)]) → t_2
  80. Translate(i_2, Vector[(u * 19 / Slider)]) → a_3
  81. Translate(i_2, Vector[(u * 17 / Slider)]) → b_3
  82. Translate(i_2, Vector[(u * 16 / Slider)]) → c_3
  83. Translate(i_2, Vector[(u * 15 / Slider)]) → d_3
  84. Translate(i_2, Vector[(u * 14 / Slider)]) → e_3
  85. Translate(i_2, Vector[(u * 13 / Slider)]) → f_3
  86. Translate(i_2, Vector[(u * 12 / Slider)]) → h_3
  87. Translate(i_2, Vector[(u * 11 / Slider)]) → i_3
  88. Translate(i_2, Vector[(u * 10 / Slider)]) → j_3
  89. Translate(i_2, Vector[(u * 9 / Slider)]) → k_3
  90. Translate(i_2, Vector[(u * 8 / Slider)]) → l_3
  91. Translate(i_2, Vector[(u * 7 / Slider)]) → m_3
  92. Translate(i_2, Vector[(u * 6 / Slider)]) → n_3
  93. Translate(i_2, Vector[(u * 5 / Slider)]) → p_3
  94. Translate(i_2, Vector[(u * 4 / Slider)]) → q_3
  95. Translate(i_2, Vector[(u * 3 / Slider)]) → r_3
  96. Intersect(r_2, n_2) → N
  97. Intersect(r_2, m_2) → O
  98. Intersect(s_2, m_2) → P
  99. Intersect(r_3, m_2) → Q
  100. Intersect(q_3, m_2) → R
  101. Intersect(p_3, m_2) → S
  102. Intersect(n_3, m_2) → T
  103. Intersect(m_3, m_2) → U
  104. Intersect(l_3, m_2) → V
  105. Intersect(k_3, m_2) → W
  106. Intersect(j_3, m_2) → Z
  107. Intersect(i_3, m_2) → A_1
  108. Intersect(h_3, m_2) → B_1
  109. Intersect(m_2, f_3) → D_1
  110. Intersect(e_3, m_2) → E_1
  111. Intersect(d_3, m_2) → F_1
  112. Intersect(c_3, m_2) → G_1
  113. Intersect(b_3, m_2) → H_1
  114. Intersect(t_2, m_2) → I_1
  115. Intersect(a_3, m_2) → J_1
  116. Intersect(a_3, n_2) → K_1
  117. Intersect(t_2, n_2) → L_1
  118. Intersect(b_3, n_2) → M_1
  119. Intersect(c_3, n_2) → N_1
  120. Intersect(d_3, n_2) → O_1
  121. Intersect(e_3, n_2) → P_1
  122. Intersect(n_2, h_3) → R_1
  123. Intersect(i_3, n_2) → S_1
  124. Intersect(j_3, n_2) → T_1
  125. Intersect(k_3, n_2) → U_1
  126. Intersect(l_3, n_2) → V_1
  127. Intersect(m_3, n_2) → W_1
  128. Intersect(n_3, n_2) → Z_1
  129. Intersect(p_3, n_2) → A_2
  130. Intersect(q_3, n_2) → B_2
  131. Intersect(r_3, n_2) → C_2
  132. Intersect(s_2, n_2) → D_2
  133. Intersect(f_3, n_2) → C_1
  134. Polygon(J, O, N, K) → poly1, j_4, o, n_4, k_4
  135. Polygon(N, D_2, P, O) → poly2, n_5, d_4, p_4, o_1
  136. Polygon(D_2, C_2, Q, P) → poly3, d_5, c_4, q_4, p_5
  137. Polygon(C_2, B_2, R, Q) → poly4, c_5, b_4, r_4, q_5
  138. Polygon(A_2, B_2, R, S) → poly5, a_4, b_5, r_5, s_3
  139. Polygon(A_2, Z_1, T, S) → poly6, a_5, z_1, t_3, s_4
  140. Polygon(Z_1, W_1, U, T) → poly7, z_2, w_1, u_1, t_4
  141. Polygon(W_1, V_1, V, U) → poly8, w_2, v_1, v, u_2
  142. Polygon(V_1, U_1, W, V) → poly9, v_2, u_3, w, v_3
  143. Polygon(U_1, T_1, Z, W) → poly10, u_4, t_5, z, w_3
  144. Polygon(T_1, S_1, A_1, Z) → poly11, t_6, s_5, a_6, z_3
  145. Polygon(S_1, R_1, B_1, A_1) → poly12, s_6, r_6, b_6, a_7
  146. Polygon(R_1, C_1, D_1, B_1) → poly13, r_7, c_6, d_6, b_7
  147. Polygon(C_1, P_1, E_1, D_1) → poly14, c_7, p_6, e_4, d_7
  148. Polygon(P_1, O_1, F_1, E_1) → poly15, p_7, o_2, f_4, e_5
  149. Polygon(O_1, N_1, G_1, F_1) → poly16, o_3, n_6, g_3, f_5
  150. Polygon(M_1, N_1, G_1, H_1) → poly17, m_4, n_7, g_4, h_4
  151. Polygon(M_1, L_1, I_1, H_1) → poly18, m_5, l_4, i_4, h_5
  152. Polygon(L_1, K_1, J_1, I_1) → poly19, l_5, k_5, j_5, i_5
  153. Polygon(K_1, M, L, J_1) → poly20, k_6, m_6, l_6, j_6

AI Drawing Prompt Reference

Draw a circle and create a horizontal line from its center. Find a point on the circle that intersects the line at a certain angle. Rotate this point around the center multiple times, with each rotation angle controlled by a slider, forming several sectors. Connect the center to these points with line segments to display the sector areas, visually demonstrating the geometric representation of fractions and rotational relationships.
The prompt above was compiled from the original drawing commands and is for reference only.