积极 AI Logo 积极 AI

毕达哥拉斯定理动画演示 by Atli Guðnason

毕达哥拉斯定理动画演示 by Atli Guðnason
几何画板及绘图内容加载中，请稍等……
2015-10-27 21:29
测试改名0三角函数几何作图滑块动画轨迹
该范例通过动画演示毕达哥拉斯定理，即直角三角形斜边的平方等于两腰的平方和。核心数学概念包括直角三角形、勾股定理。构造过程中使用了半圆、交点、圆弧、点、线段、镜像、多边形、垂直线、旋转、中点、条件语句等命令。适合初中及以上学生学习和教师教学。

GeoGebra 命令及参数

  1. Semicircle(A4, A5) → c
  2. Intersect(c, LineBisector[A4, A5]) → A,
  3. CircleArc(Midpoint[A4, A5], A, A4) → r_1
  4. Point(r_1) → A6
  5. Segment(A6, A5) → b
  6. Mirror(A4, b) → A12
  7. Polygon(A6, A5, 4) → poly2, c_2, b_1, g, h, A9, A10
  8. OrthogonalLine(A12, h) → m
  9. Segment(A10, A5) → j
  10. Intersect(m, j) → A11
  11. Rotate(A6, 90*°, A5) → B8
  12. Segment(A4, A6) → a
  13. Segment(A5, A4) → d
  14. Polygon(A4, A6, 4) → poly1, a_1, c_1, e, f, A7, A8
  15. Segment(A4, A7) → i
  16. Mirror(A12, j) → A13
  17. Segment(A5, A12) → k_1
  18. Segment(A5, A13) → l
  19. Segment(A11, A13) → n
  20. Segment(A11, A12) → p
  21. Polygon(A5, A4, 4) → poly4, b_2, a_2, k, q, B12, B6
  22. Rotate(A11, 90*°, A5) → B7
  23. Midpoint(A4, B6) → O
  24. Rotate(B8, 90*°, O) → B10
  25. Rotate(B10, 90*°, O) → B11
  26. Rotate(B11, 90*°, O) → B13
  27. Rotate(B7, 180*°, O) → B9
  28. Segment(B13, B8) → r
  29. Segment(B8, B10) → s
  30. Segment(B11, B13) → d_1
  31. Segment(B11, A4) → e_1
  32. Segment(B13, B12) → f_1
  33. Segment(B8, B6) → g_1
  34. Segment(B10, A5) → h_1
  35. Segment(B7, A5) → j_1
  36. Segment(B9, B12) → p_1
  37. Segment(B10, B11) → q_1
  38. Polygon(C4, C5, C6, C7) → poly3, c2, c3, c4, c5
  39. Polygon(D4, D5, D6) → poly5, d4, d2, d3
  40. Polygon(E4, E5, E6) → poly6, e4, e2, e3
  41. Polygon(F4, F5, F6) → poly7, f4, f2, f3
  42. Polygon(G4, G5, G6) → poly8, g4, g2, g3
  43. Polygon(H4, H5, H6) → poly9, h4, h2, h3
  44. Polygon(I4, I5, I6) → poly10, i4, i2, i3
  45. If(time < C$2, C4, If[(C$2 ≤ time) ∧ (time < C$3), C4 - (time - C$2) * (C4 - C9) / (C$3 - C$2), C9]) → J4
  46. If(time < C$2, C5, If[(C$2 ≤ time) ∧ (time < C$3), C5 - (time - C$2) * (C5 - C10) / (C$3 - C$2), C10]) → J5
  47. If(time < C$2, C6, If[(C$2 ≤ time) ∧ (time < C$3), C6 - (time - C$2) * (C6 - C11) / (C$3 - C$2), C11]) → J6
  48. If(time < C$2, C7, If[(C$2 ≤ time) ∧ (time < C$3), C7 - (time - C$2) * (C7 - C12) / (C$3 - C$2), C12]) → J7
  49. If(time < D$2, D4, If[(D$2 ≤ time) ∧ (time < D$3), D4 - (time - D$2) * (D4 - D9) / (D$3 - D$2), D9]) → K4
  50. If(time < D$2, D5, If[(D$2 ≤ time) ∧ (time < D$3), D5 - (time - D$2) * (D5 - D10) / (D$3 - D$2), D10]) → K5
  51. If(time < D$2, D6, If[(D$2 ≤ time) ∧ (time < D$3), D6 - (time - D$2) * (D6 - D11) / (D$3 - D$2), D11]) → K6
  52. If(time < E$2, E4, If[(E$2 ≤ time) ∧ (time < E$3), E4 - (time - E$2) * (E4 - E9) / (E$3 - E$2), E9]) → L4
  53. If(time < E$2, E5, If[(E$2 ≤ time) ∧ (time < E$3), E5 - (time - E$2) * (E5 - E10) / (E$3 - E$2), E10]) → L5
  54. If(time < E$2, E6, If[(E$2 ≤ time) ∧ (time < E$3), E6 - (time - E$2) * (E6 - E11) / (E$3 - E$2), E11]) → L6
  55. If(time < F$2, F4, If[(F$2 ≤ time) ∧ (time < F$3), F4 - (time - F$2) * (F4 - F9) / (F$3 - F$2), F9]) → M4
  56. If(time < F$2, F5, If[(F$2 ≤ time) ∧ (time < F$3), F5 - (time - F$2) * (F5 - F10) / (F$3 - F$2), F10]) → M5
  57. If(time < F$2, F6, If[(F$2 ≤ time) ∧ (time < F$3), F6 - (time - F$2) * (F6 - F11) / (F$3 - F$2), F11]) → M6
  58. If(time < G$2, G4, If[(G$2 ≤ time) ∧ (time < G$3), G4 - (time - G$2) * (G4 - G9) / (G$3 - G$2), G9]) → N4
  59. If(time < G$2, G5, If[(G$2 ≤ time) ∧ (time < G$3), G5 - (time - G$2) * (G5 - G10) / (G$3 - G$2), G10]) → N5
  60. If(time < G$2, G6, If[(G$2 ≤ time) ∧ (time < G$3), G6 - (time - G$2) * (G6 - G11) / (G$3 - G$2), G11]) → N6
  61. If(time < H$2, H4, If[(H$2 ≤ time) ∧ (time < H$3), H4 - (time - H$2) * (H4 - H9) / (H$3 - H$2), H9]) → O4
  62. If(time < H$2, H5, If[(H$2 ≤ time) ∧ (time < H$3), H5 - (time - H$2) * (H5 - H10) / (H$3 - H$2), H10]) → O5
  63. If(time < H$2, H6, If[(H$2 ≤ time) ∧ (time < H$3), H6 - (time - H$2) * (H6 - H11) / (H$3 - H$2), H11]) → O6
  64. If(time < I$2, I4, If[(I$2 ≤ time) ∧ (time < I$3), I4 - (time - I$2) * (I4 - I9) / (I$3 - I$2), I9]) → P4
  65. If(time < I$2, I5, If[(I$2 ≤ time) ∧ (time < I$3), I5 - (time - I$2) * (I5 - I10) / (I$3 - I$2), I10]) → P5
  66. If(time < I$2, I6, If[(I$2 ≤ time) ∧ (time < I$3), I6 - (time - I$2) * (I6 - I11) / (I$3 - I$2), I11]) → P6
  67. Polygon(J4, J5, J6, J7) → poly11, j4, j5, j6, j7
  68. Polygon(K4, K5, K6) → poly12, k6, k4, k5
  69. Polygon(L4, L5, L6) → poly13, l6, l4, l5
  70. Polygon(M4, M5, M6) → poly14, m6, m4, m5
  71. Polygon(N4, N5, N6) → poly15, n6, n4, n5
  72. Polygon(O4, O5, O6) → poly16, o6, o4, o5
  73. Polygon(P4, P5, P6) → poly17, p6, p4, p5
  74. Polygon(C9, C10, C11, C12) → poly18, c9, c10, c11, c12
  75. Polygon(D9, D10, D11) → poly19, d11, d9, d10
  76. Polygon(E9, E10, E11) → poly20, e11, e9, e10
  77. Polygon(F9, F10, F11) → poly21, f11, f9, f10
  78. Polygon(G9, G10, G11) → poly22, g11, g9, g10
  79. Polygon(H9, H10, H11) → poly23, h11, h9, h10
  80. Polygon(I9, I10, I11) → poly24, i11, i9, i10

AI 绘图提示语参考

绘制一个直角三角形ABC，其中AB为斜边。通过旋转和镜像操作，构造出三个与原三角形相似的小三角形，它们的面积分别等于直角三角形ABC的三个直角边的平方。使用滑块调整三角形的大小，观察面积关系的变化。
以上提示语为根据原始绘图命令整理而来，仅供参考。