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Box Q1 Geometric Construction

Box Q1 Geometric Construction
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2014-09-06 01:19
CirclePolygonVectorGeometric Construction
In collections Modeling Volume as a function of height
This example demonstrates how to construct a rectangle with an inscribed circle using GeoGebra, showcasing related geometric properties. Core math concepts include incircle, function graph, vector, rotation, polygon construction, etc. Construction highlights involve commands like Circle, Vector, Translate, Intersect, Rotate, Polygon, Segment, OrthogonalLine, newbox, Point, blackbox, Length. Suitable for high school mathematics teaching on geometric construction and properties of inscribed circles.

GeoGebra Commands & Parameters

  1. Circle(Origin, len - (2 * h)) → c
  2. Vector((width - (2 * h), 0)) → u
  3. Translate(A, u) → A'
  4. Intersect(c, xAxis) → B, C
  5. Rotate(C, α) → C'
  6. Vector(C') → v
  7. Translate(A, v) → A'_1
  8. Translate(A', v) → A''
  9. Polygon(A, A'_1, A'', A') → poly1, a, a'_1, a'', a'
  10. Vector((0, h)) → w
  11. Translate(A, w) → A'_2
  12. Translate(A', w) → A''_1
  13. Translate(A'_1, w) → D
  14. Translate(A'', w) → A'''
  15. Segment(A'_2, A) → b
  16. Segment(A''_1, A') → d
  17. Segment(D, A'_1) → e
  18. Segment(A''', A'') → f
  19. Polygon(A'_2, A''_1, A', A) → poly2, a'_2, a''_1, a'_3, a_1
  20. Polygon(D, A''', A'', A'_1) → poly3, d_1, a''', a''_2, a'_4
  21. Polygon(A''_1, A''', A'', A') → poly4, a''_3, a'''_1, a''_4, a'_5
  22. Polygon(D, A'_2, A, A'_1) → poly5, d_2, a'_6, a_2, a'_7
  23. Rotate(E, α) → E'
  24. Vector(E') → g
  25. Segment(W_1, A_2) → c_7
  26. Segment(A_2, Z_1) → d_7
  27. Segment(Z_1, V_1) → e_7
  28. Segment(V_1, W_1) → f_7
  29. Segment(Paper, U_1) → g_7
  30. Segment(U_1, S_1) → h_7
  31. Segment(S_1, T_1) → i_7
  32. Segment(T_1, Paper) → j_7
  33. OrthogonalLine(Z_1, g_7) → m_7
  34. OrthogonalLine(Z_1, h_7) → n_7
  35. OrthogonalLine(A_2, h_7) → a_8
  36. OrthogonalLine(W_1, i_7) → b_8
  37. Intersect(j_7, a_8) → B_2
  38. Intersect(i_7, b_8) → C_2
  39. Intersect(m_7, i_7) → D_2
  40. Intersect(h_7, a_8) → E_2
  41. Intersect(n_7, h_7) → F_2
  42. Intersect(m_7, g_7) → G_2
  43. Intersect(g_7, b_8) → H_2
  44. Intersect(n_7, j_7) → I_2
  45. Polygon(B_2, W_1, 4) → poly26, c_8, d_8, e_8, f_8, J_2, K_2
  46. Polygon(Paper, H_2, 4) → poly27, g_8, h_8, i_8, j_8, L_2, M_2
  47. Polygon(G_2, U_1, 4) → poly28, k_8, l_8, m_8, n_8, N_2, O_2
  48. Polygon(A_2, E_2, 4) → poly29, p_8, q_8, r_8, s_8, P_2, Q_2
  49. Polygon(V_1, Z_1, A_2, W_1) → poly31, v_1, z_1, a_9, w_1
  50. newbox(α, E, G) → n, p, c_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, J, q, H, poly6, poly7, r, s, t, b_1
  51. Intersect(r, i_1) → K
  52. Intersect(r, i_1) → L
  53. Intersect(r, e_1) → M
  54. Polygon(J, M, H, G) → poly8, j_2, m_1, h_2, g_2
  55. Polygon(B_2, W_1, V_1, I_2) → poly9, b_2, w_2, v_2, i_2
  56. Polygon(W_1, A_2, D_2, C_2) → poly10, w_3, a_3, d_3, c_2
  57. Point(w_3) → N
  58. Polygon(N, Z_1, F_2, E_2) → poly11, n_1, z_2, f_2, e_2
  59. Point(n_1) → O
  60. Point(w_2) → P
  61. Polygon(H_2, G_2, O, P) → poly12, h_3, g_3, o, p_1
  62. blackbox(α, E, Q) → poly13, poly14, r_1, s_1, t_1, k_2, l_2, m_2, n_2, p_2, q_2, r_2, poly15, s_2, t_2, i, j, k, l, m, l_1, q_1
  63. blackbox(α, E, R) → poly16, poly17, l_3, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_4, b_4, poly18, c_4, d_4, b_3, c_3, e_3, f_3, i_3, j_3, k_3
  64. Vector(S, T) → u_1
  65. Point(xAxis) → U
  66. OrthogonalLine(U, xAxis) → e_4
  67. Point(xAxis) → V
  68. OrthogonalLine(V, xAxis) → f_4
  69. Segment(U, V) → g_4
  70. Length(g_4) → o_1
  71. Translate(W, u_1) → W'
  72. Translate(W', u_1) → W''
  73. Vector(W', W'') → u_2

AI Drawing Prompt Reference

Draw a rectangle inscribed in a circle. Start by plotting the circle's center and radius, then create the rectangle's sides using rotations and vector translations to determine the vertices. Connect the vertices with line segments to form the rectangle and circle. Finally, show the perpendicular lines from the circle's center to the rectangle's sides, and the internal polygons formed by these lines, highlighting geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.