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Equation C: Interactive Exploration of Conic Sections and Rotation Logic

Equation C: Interactive Exploration of Conic Sections and Rotation Logic
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2017-05-10 12:17
AngleGeometric ConstructionSlider Animation
In collections Solving equations by balancing
①This example demonstrates an interactive geometric construction combining conic sections, rotation, and logical conditions, where dynamic sliders and text inputs control the figure and display real-time angle and coordinate information. ②Core mathematical concepts include conic sections (circles, ellipses), rotational geometry, angle measurement, logical conditions (If statements), and point loci/position relationships. ③Construction highlights: GeoGebra commands such as Angle, Polygon, Point, Segment, Circle, Line, Intersect, Rotate, PointIn, If, and Textfield are used to build multiple auxiliary points (e.g., A_1, M2, K2) and their rotated counterparts, with conditional checks (like sign_xm2) controlling visibility, and text fields for parameter input. ④Suitable for high school or college-level analytic geometry, geometric transformations, and dynamic mathematics teaching, ideal for exploring combined applications of conic sections and rotational symmetry.

GeoGebra Commands & Parameters

  1. Angle(angle_c, angle_b, angle_a) → anglemeasure
  2. Polygon(C_1, C_2, 4) → x_c, c_1, c_2, c_3, c_4, C_3, C_4
  3. Polygon(A_1, A_2, 4) → x_a, a_1, a_2, a_4, a_3, A_3, A_4
  4. Polygon(P_1, P_2, 4) → x_P, p_1, p_2, p_4, p_3, P_3, P_4
  5. Point(xAxis) → foot1
  6. Segment(fulcrum, foot1) → leg_b
  7. Point(xAxis) → foot2
  8. Segment(fulcrum, foot2) → leg_a
  9. Circle(fulcrum, 4) → circle
  10. Line(fulcrum, xAxis) → parallel
  11. Intersect(circle, parallel, 2) → balance1
  12. Intersect(circle, parallel, 1) → balance2
  13. Segment(balance1, balance2) → balance
  14. Segment(angle_a, angle_b) → anglesegment_a
  15. Segment(angle_b, angle_c) → anglesegment_b
  16. Rotate(balance1, tip, fulcrum) → balance1'
  17. Rotate(balance2, tip, fulcrum) → balance2'
  18. Segment(balance1', balance2') → balance'
  19. PointIn(x_c) → A
  20. PointIn(x_P) → C
  21. PointIn(x_a) → P
  22. If(equal > tipequal, ">", If[equal < tipequal, "<", "="]) → sign
  23. Circle(O, 0.25) → o
  24. Circle(D, 0.25) → d
  25. Polygon(Q_1, Q_2, 4) → x_Q, q_3, q_1, q_2, q_4, Q_3, Q_4
  26. PointIn(x_Q) → Q
  27. Polygon(F_1, F_2, 4) → x_F, f_2, f_1, f_3, f_4, F_3, F_4
  28. Polygon(E_1, E_2, 4) → x_E, e_2, e_1, e_3, e_4, E_4, E_3
  29. PointIn(x_F) → E
  30. PointIn(x_E) → F
  31. Polygon(H_1, H_2, 4) → x_H, h_2, h_1, h_3, h_4, H_3, H_4
  32. Polygon(G_1, G_2, 4) → x_G, g_2, g_1, g_3, g_4, G_3, G_4
  33. PointIn(x_H) → H
  34. PointIn(x_G) → G
  35. Polygon(J_1, J_2, 4) → x_J, j_2, j_1, j_3, j_4, J_3, J_4
  36. Polygon(I_1, I_2, 4) → x_I, i_2, i_1, i_3, i_4, I_3, I_4
  37. PointIn(x_J) → I
  38. PointIn(x_I) → J
  39. Circle(K, 0.25) → k
  40. Circle(L, 0.25) → l
  41. Circle(S, 0.25) → s
  42. Circle(U, 0.25) → u
  43. Circle(R, 0.25) → r
  44. Circle(T, 0.25) → t
  45. Circle(W, 0.25) → w
  46. Circle(V, 0.25) → v
  47. Circle(Y, 0.25) → y_1
  48. Circle(X, 0.25) → x_1
  49. Circle(Z2, 0.25) → z2
  50. Circle(Z, 0.25) → z
  51. Polygon(M_1, M_2, 4) → x_M, m_2, m_1, m_3, m_4, P_7, P_8
  52. PointIn(x_M) → M
  53. Polygon(C'_1, C'_2, 4) → x_{C'}, c'_2, c'_1, c'_3, c'_4, Q_7, Q_8
  54. PointIn(x_{C'}) → C'
  55. Polygon(A'_1, A'_2, 4) → x_{A'}, a'_2, a'_1, a'_3, a'_4, P_{11}, P_{12}
  56. PointIn(x_{A'}) → A'
  57. Polygon(D'_1, D'_2, 4) → x_{D'}, d'_2, d'_1, d'_3, d'_4, Q_{12}, Q_{13}
  58. PointIn(x_{D'}) → D'
  59. Polygon(B'_1, B'_2, 4) → x_{B'}, b'_2, b'_1, b'_3, b'_4, P_{15}, P_{16}
  60. PointIn(x_{B'}) → B'
  61. Polygon(E'_1, E'_2, 4) → x_{E'}, e'_2, e'_1, e'_3, e'_4, Q_{17}, Q_{18}
  62. PointIn(x_{E'}) → E'
  63. Circle(N, 0.25) → n
  64. Circle(B, 0.25) → b
  65. Circle(J2, 0.25) → j'
  66. Circle(L2, 0.25) → l'
  67. Circle(K2, 0.25) → k'
  68. Circle(M2, 0.25) → m'
  69. Polygon(I'_2, I'_1, 4) → x_2, i'_2, i'_1, i'_3, i'_4, P_6, P_{10}
  70. PointIn(x_2) → I'
  71. Polygon(G'_2, G'_1, 4) → x_3, g'_2, g'_1, g'_3, g'_4, Q_6, Q_{10}
  72. PointIn(x_3) → G'
  73. Polygon(F'_2, F'_1, 4) → x_4, f'_2, f'_1, f'_3, f'_4, P_5, P_9
  74. PointIn(x_4) → F'
  75. Polygon(H'_2, H'_1, 4) → x_5, h'_2, h'_1, h'_3, h'_4, Q_5, Q_9
  76. PointIn(x_5) → H'
  77. Textfield(unknown) → answer

AI Drawing Prompt Reference

Create an interactive geometric figure combining conic sections and rotation. Start by drawing a circle centered at the origin, then draw a line parallel to the x-axis. Pick a point on the circle and another on the line, and connect them with a line segment. Rotate these points around the circle's center to form new points. Use these points and lines to construct additional shapes such as triangles, segments, circles, and their centers. Finally, adjust the visibility of the shapes based on angle and coordinate information, and display real-time angle and coordinate values.
The prompt above was compiled from the original drawing commands and is for reference only.