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奎里努斯悖论

奎里努斯悖论
几何画板及绘图内容加载中，请稍等……
2018-01-08 01:08
解析几何参数方程几何作图
这是一个有趣的悖论谜题，展示了面积和相似变换的概念。通过使用GeoGebra，我们可以构造出一系列的几何图形，包括圆、多边形和参数曲线。该范例涉及相似变换、面积计算和百分比等核心数学概念。适合初中及以上学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Point(Circle[O, 1 + o]) → P
  2. Segment(O, P) → g_1
  3. Segment(A, B) → f
  4. Polygon(A, B, 4) → poly1, g, h, i, j, C_1, D_1
  5. Segment(E, F) → k
  6. Segment(C, D) → l
  7. Segment(G, H) → m
  8. Polygon(E, F, 4) → poly2, n, p, q, r, I, J
  9. Polygon(C, D, 4) → poly3, s, t, a, b, K, L
  10. Polygon(G, H, 4) → poly4, c, d, e, f_1, M, N
  11. Point(Circle[Q, 1 + o]) → R
  12. Segment(Q, R) → h_1
  13. Point(Circle[S, 1 + o]) → T
  14. Segment(S, T) → i_1
  15. Point(Circle[U, 1 + o]) → V
  16. Segment(U, V) → j_1
  17. Point(Circle[W, 1 - o]) → Z
  18. Segment(W, Z) → k_1
  19. Point(Circle[A_1, 1 - o]) → B_1
  20. Segment(A_1, B_1) → l_1
  21. Point(Circle[E_1, 1 - o]) → F_1
  22. Segment(E_1, F_1) → m_1
  23. Point(Circle[G_1, 1 - o]) → H_1
  24. Polygon(O, P, P + u_1) → t1, p_1, i_2, j_2
  25. Segment(G_1, H_1) → n_1
  26. Polygon(Q, R, R + OrthogonalVector[h_1] / (1 + o)) → t2, q_1, r_1, k_2
  27. Polygon(S, T, T + OrthogonalVector[i_1] / (1 + o)) → t3, s_1, t_1, l_2
  28. Polygon(U, V, V + OrthogonalVector[j_1] / (1 + o)) → t4, a_1, m_2, n_2
  29. Polygon(W, Z, Z - OrthogonalVector[k_1] / (1 - o)) → t5, b_1, p_2, q_2
  30. Polygon(A_1, B_1, B_1 - OrthogonalVector[l_1] / (1 - o)) → t6, c_1, r_2, s_2
  31. Polygon(E_1, F_1, F_1 - OrthogonalVector[m_1] / (1 - o)) → t7, d_1, e_1, f_2
  32. Polygon(G_1, H_1, H_1 - OrthogonalVector[n_1] / (1 - o)) → t8, g_2, h_2, t_2
  33. Circle(I_1, (j_2 + f_2) / sqrt(2)) → c_2