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勾股定理无字证明 by Ben Sparks

勾股定理无字证明 by Ben Sparks
几何画板及绘图内容加载中，请稍等……
2020-07-11 00:57
测试改名0解析几何最值优化几何作图
①本范例通过动态演示证明勾股定理，即直角三角形两直角边的平方和等于斜边的平方；②涉及核心数学概念：勾股定理、几何变换、解析几何；③作图要点：使用 GeoGebra 命令如点、线段、旋转、正交线、多边形等构建图形并展示定理；④适合高中数学教学或数学爱好者探索几何证明。

GeoGebra 命令及参数

  1. Point(xAxis) → G_1
  2. Point(yAxis) → H_1
  3. Intersect(xAxis, yAxis) → A
  4. Ray(A, H_1) → s
  5. Ray(A, G_1) → r
  6. Point(r) → B
  7. Point(s) → C
  8. Segment(B, C) → f
  9. Rotate(B, 90°, C) → B'
  10. Rotate(C, 90°, C) → C'
  11. Segment(B', C') → f'
  12. Rotate(B', 90°, B') → E
  13. Rotate(C', 90°, B') → C''
  14. Segment(E, C'') → f''
  15. Rotate(E, 90°, C'') → B'''
  16. Rotate(C'', 90°, C'') → G
  17. Segment(B''', G) → f'''
  18. Segment(A, C) → g
  19. Segment(A, B) → h
  20. OrthogonalLine(B', yAxis) → i
  21. OrthogonalLine(C'', xAxis) → j
  22. Intersect(i, j) → F
  23. Intersect(i, yAxis) → D
  24. Intersect(j, xAxis) → H
  25. Segment(C, D) → k
  26. Segment(D, B') → l
  27. Segment(B', F) → m
  28. Segment(F, C'') → n
  29. Segment(C'', H) → p
  30. Segment(H, B) → q
  31. Polygon(A, B, C) → t1, a, a_1, b
  32. Polygon(C, E, D) → t2, d, c_1, e
  33. Rotate(C, (-α), C) → C'_1
  34. Rotate(E, (-α), C) → E'
  35. Rotate(D, (-α), C) → D'
  36. Polygon(C'_1, E', D') → t2', d', c'_1, e'
  37. Polygon(E, F, G) → t3, g_1, e_1, f_1
  38. Polygon(G, H, B) → t4, b_1, g_2, h_1
  39. Rotate(E, α, G) → E'_1
  40. Rotate(F, α, G) → F'
  41. Rotate(G, α, G) → G'
  42. Polygon(E'_1, F', G') → t3', g', e'_1, f'_1
  43. OrthogonalLine(N, l) → t_1
  44. Segment(N, I) → c
  45. Angle(B, A, C) → β
  46. Midpoint(e') → J
  47. Midpoint(e'_1) → K
  48. Midpoint(g) → L
  49. Midpoint(f) → M
  50. Midpoint(h) → O