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Missing Square Paradox (Curry) Part 2: Geometry and Slope

Missing Square Paradox (Curry) Part 2: Geometry and Slope
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2023-02-10 19:43
PolygonGeometric Construction
This example demonstrates the Missing Square Paradox in geometric figures, highlighting the relationship between area calculation and slope. Key mathematical concepts include area difference, slope, geometric construction, and parametric curves. Construction involves using GeoGebra commands like Polygon, Segment, Circle, Point, Line, OrthogonalLine, and Intersect. Suitable for high school students or college undergraduates learning geometry and mathematical analysis.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Polygon(J, K, L, O) → poly2, j, k, l, m
  3. Polygon(P, Q, F_1) → t2, p, q, r
  4. Segment(F_1, Q) → i_2
  5. Circle(B_1, 3) → d
  6. Point(d) → G
  7. Line(B_1, G) → f
  8. OrthogonalLine(G, f) → g
  9. Circle(G, 2) → e
  10. Intersect(e, g, 2) → H
  11. OrthogonalLine(H, g) → h
  12. OrthogonalLine(B_1, f) → i
  13. Intersect(h, i) → I
  14. Polygon(B_1, G, H, I) → q1, n, g_2, h_2, i_3
  15. Circle(D, 3) → c_1
  16. Point(c_1) → E
  17. Line(D, E) → m_1
  18. OrthogonalLine(E, m_1) → n_1
  19. Circle(E, 2) → d_1
  20. Intersect(d_1, n_1, 2) → F
  21. OrthogonalLine(F, n_1) → p_1
  22. OrthogonalLine(D, m_1) → e_1
  23. Intersect(p_1, e_1) → R
  24. Polygon(D, E, F, R) → q2, d_2, e_2, f_2, r_2
  25. Polygon(C_1, D_1, K_1, L_1) → q3, j_2, k_2, l_2, s_2
  26. Circle(N_1, 2) → c_2
  27. Point(c_2) → O_1
  28. Line(N_1, O_1) → t_2
  29. OrthogonalLine(O_1, t_2) → a_2
  30. Circle(O_1, 1) → c_3
  31. Intersect(c_3, a_2, 2) → P_1
  32. OrthogonalLine(P_1, a_2) → b_2
  33. OrthogonalLine(N_1, t_2) → f_3
  34. Intersect(b_2, f_3) → Q_1
  35. Polygon(N_1, O_1, P_1, Q_1) → q4, g_3, o_1, h_3, j_3
  36. Segment(S, T) → s
  37. Segment(T, U) → t
  38. Segment(U, S) → f_1
  39. Segment(V, W) → g_1
  40. Segment(W, Z) → h_1
  41. Segment(Z, A_1) → i_1
  42. Segment(A_1, E_1) → j_1
  43. Segment(E_1, V) → k_1
  44. Segment(A, B) → l_1
  45. Segment(B, C) → q_1
  46. Segment(A, C) → r_1
  47. Segment(P, Q) → s_1
  48. Segment(Q, F_1) → t_1
  49. Segment(P, F_1) → a_1
  50. Segment(J, K) → b_1
  51. Segment(K, L) → m_2
  52. Segment(L, O) → n_2
  53. Segment(O, J) → p_2
  54. Segment(B_1, G) → q_2
  55. Segment(G, H) → k_3
  56. Segment(H, I) → l_3
  57. Segment(I, B_1) → m_3
  58. Segment(D, E) → n_3
  59. Segment(E, F) → p_3
  60. Segment(F, R) → q_3
  61. Segment(R, D) → r_3
  62. Segment(N_1, O_1) → s_3
  63. Segment(O_1, P_1) → t_3
  64. Segment(P_1, Q_1) → a_3
  65. Segment(Q_1, N_1) → b_3
  66. Segment(C_1, D_1) → d_3
  67. Segment(K_1, D_1) → e_3
  68. Segment(K_1, L_1) → f_4
  69. Segment(C_1, L_1) → g_4

AI Drawing Prompt Reference

Draw a geometric figure composed of multiple quadrilaterals and triangles, including a square with a missing corner and two right-angled triangles. Start by drawing a square with a missing corner, then construct two right-angled triangles with their right angles touching the sides of the square. Use circles and perpendicular lines to generate a series of smaller triangles and quadrilaterals, forming a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.