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Curry's Paradox: Version 4

Curry's Paradox: Version 4
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2023-05-13 09:54
PolygonFunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates Curry's Paradox, an intriguing phenomenon involving geometric transformations and area calculations. Key math concepts include geometric transformations (rotation), coordinate geometry, polygon area computation, and function graphs. Construction highlights involve commands/objects like Circle, Line, OrthogonalLine, Point, Intersect, Polygon, and Segment in GeoGebra. Suitable for high school and above learners to explore counterintuitive geometric problems.

GeoGebra Commands & Parameters

  1. Circle(D, 15) → e
  2. Circle(E, 11) → k
  3. Line(D, E) → h
  4. OrthogonalLine(E, h) → i
  5. Circle(A, 4) → c
  6. Point(c) → B
  7. Line(A, B) → f
  8. OrthogonalLine(B, f) → g
  9. Circle(B, 3) → d
  10. Intersect(d, g, 2) → C
  11. Polygon(A, B, C) → t1, c_1, a, b
  12. Polygon(D, E, G) → t2, g_1, d_1, e_1
  13. Segment(F, H) → j
  14. Segment(H, I) → l
  15. Segment(I, F) → m
  16. Circle(J, 11) → p
  17. Point(p) → K
  18. Line(J, K) → n
  19. OrthogonalLine(K, n) → q
  20. Circle(K, 3) → r
  21. Intersect(r, q, 2) → L
  22. OrthogonalLine(L, q) → s
  23. OrthogonalLine(J, n) → t
  24. Intersect(s, t) → M
  25. Polygon(J, M, L, K) → q1, j_1, m_1, l_1, k_1
  26. Circle(N, 4) → f_1
  27. Circle(O, 4) → h_1
  28. Circle(P, 3) → p_1
  29. Point(f_1) → Q
  30. Point(h_1) → R
  31. Point(p_1) → S
  32. Circle(Q, 1) → q_1
  33. Circle(R, 1) → r_1
  34. Circle(S, 1) → s_1
  35. Line(N, Q) → i_1
  36. Line(O, R) → n_1
  37. Line(P, S) → t_1
  38. OrthogonalLine(Q, i_1) → a_1
  39. OrthogonalLine(R, n_1) → b_1
  40. OrthogonalLine(S, t_1) → f_2
  41. Intersect(q_1, a_1, 2) → T
  42. Intersect(r_1, b_1, 2) → U
  43. Intersect(s_1, f_2, 2) → V
  44. OrthogonalLine(V, f_2) → g_2
  45. OrthogonalLine(P, t_1) → h_2
  46. Intersect(g_2, h_2) → W
  47. OrthogonalLine(U, b_1) → i_2
  48. OrthogonalLine(O, n_1) → j_2
  49. Intersect(i_2, j_2) → Z
  50. OrthogonalLine(N, i_1) → k_2
  51. OrthogonalLine(T, a_1) → l_2
  52. Intersect(k_2, l_2) → A_1
  53. Polygon(N, A_1, T, Q) → q2, n_2, m_2, t_2, q_2
  54. Polygon(O, Z, U, R) → q3, o, z_1, u, r_2
  55. Polygon(P, W, V, S) → q4, p_2, w, v, s_2

AI Drawing Prompt Reference

This is a geometric construction example showing a figure composed of circles, lines, and orthogonal lines. The figure includes a larger circle and smaller circles, connected by lines. Orthogonal lines create perpendicular relationships. The figure also includes triangles and line segments that are connected through intersection points. The overall construction involves rotation and coordinate geometry, demonstrating area calculations and function graph concepts. Suitable for high school and above learners to explore counterintuitive geometric problems.
The prompt above was compiled from the original drawing commands and is for reference only.