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平方数可视化

平方数可视化
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2019-10-18 10:07
函数数列几何作图滑块动画函数图像
①本范例通过动态演示展示平方数的几何表示，将自然数n的平方nsq用正方形面积可视化；②涉及的核心数学概念包括数列、函数、几何作图、连续性；③作图要点——使用Polygon（多边形）、Point（点）、Segment（线段）等GeoGebra命令构建正方形，通过滑块n控制正方形边长，并绘制条形图展示平方数增长趋势；④适合初中及以上数学学习者，用于理解数形结合思想及平方数特性。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Point(Circle[A1, n]) → E
  3. Segment(A1, E) → e
  4. Point(Circle[A2, n]) → F
  5. Segment(A2, F) → f
  6. Point(Circle[A3, n]) → G
  7. Segment(A3, G) → g
  8. Point(Circle[A4, n]) → H
  9. Segment(A4, H) → h
  10. Point(Circle[A5, n]) → I
  11. Segment(A5, I) → i
  12. Point(Circle[A6, n]) → J
  13. Segment(A6, J) → j
  14. Point(Circle[A7, n]) → K
  15. Segment(A7, K) → k
  16. Point(Circle[A8, n]) → L
  17. Segment(A8, L) → l
  18. Point(Circle[A9, n]) → M
  19. Segment(A9, M) → m
  20. Point(Circle[A10, n]) → N
  21. Segment(A10, N) → p
  22. Point(Circle[A11, n]) → O
  23. Segment(A11, O) → q
  24. Point(Circle[A12, n]) → P
  25. Segment(A12, P) → r
  26. Point(Circle[A13, n]) → Q
  27. Segment(A13, Q) → s
  28. Point(Circle[A14, n]) → R
  29. Segment(A14, R) → t
  30. Point(Circle[A15, n]) → S
  31. Segment(A15, S) → a_1
  32. Point(Circle[A16, n]) → T
  33. Segment(A16, T) → b_1
  34. Point(Circle[B1, n]) → U
  35. Segment(B1, U) → c_1
  36. Point(Circle[B2, n]) → V
  37. Segment(B2, V) → d_1
  38. Point(Circle[B3, n]) → W
  39. Segment(B3, W) → e_1
  40. Point(Circle[B4, n]) → Z
  41. Segment(B4, Z) → f_1
  42. Point(Circle[B5, n]) → A_1
  43. Segment(B5, A_1) → g_1
  44. Point(Circle[B6, n]) → B_1
  45. Segment(B6, B_1) → h_1
  46. Point(Circle[B7, n]) → C_1
  47. Segment(B7, C_1) → i_1
  48. Point(Circle[B8, n]) → D_1
  49. Segment(B8, D_1) → j_1
  50. Point(Circle[B9, n]) → E_1
  51. Segment(B9, E_1) → k_1
  52. Point(Circle[B10, n]) → F_1
  53. Segment(B10, F_1) → l_1
  54. Point(Circle[B11, n]) → G_1
  55. Segment(B11, G_1) → m_1
  56. Point(Circle[B12, n]) → H_1
  57. Segment(B12, H_1) → n_1
  58. Point(Circle[B13, n]) → I_1
  59. Segment(B13, I_1) → p_1
  60. Point(Circle[B14, n]) → J_1
  61. Segment(B14, J_1) → q_1
  62. Point(Circle[B15, n]) → K_1
  63. Segment(B15, K_1) → r_1
  64. Point(Circle[B16, n]) → L_1
  65. Segment(B16, L_1) → s_1