MathPlotAI Logo MathPlotAI

Geometric Demonstration of Equation A

Geometric Demonstration of Equation A
Loading the math board and drawing, please wait…
2017-05-10 11:59
Coordinate GeometrySolid GeometryGeometric Construction
In collections Solving equations by balancing
This example dynamically demonstrates the geometric relationship between a cube and its circumscribed circle. Core math concepts include volume, cube, circumscribed circle, real numbers, difference, and slope. The construction utilizes GeoGebra commands and objects such as angle, polygon, point, segment, circle, line, intersect, rotate, PointIn, If, and Textfield. Suitable for high school and above students to understand the application of solid geometry and analytical geometry.

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