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中国古代几何证明演示

中国古代几何证明演示
几何画板及绘图内容加载中，请稍等……
2015-01-24 18:57
测试改名0解析几何几何作图
这是一个互动演示，展示了中国古代的几何证明方法，特别是勾股定理的视觉证明。该演示涉及勾股定理、旋转和平移等核心概念。通过使用GeoGebra命令如Segment、Point、Polygon、Rotate和Translate，可以清晰地展示几何图形的构造过程。适合初中及以上学生学习几何证明和勾股定理。

GeoGebra 命令及参数

  1. Segment((0, 0), (2.25, 0)) → r
  2. Segment((0, 1), (2.25, 1)) → s
  3. Segment((1.25, 0), (1.25, 1)) → b_1
  4. Segment((2.25, 0), (2.25, 1)) → c_1
  5. Point(Segment[B, C]) → E
  6. Polygon(E, B, Rotate[E, 1.5707963267948966, (0.5, 0.5)]) → polygon1, a, b, c
  7. Rotate(polygon1, 1.5707963267948966, (0.5, 0.5)) → polygon1'
  8. Rotate(polygon1', 1.5707963267948966, (0.5, 0.5)) → polygon1''
  9. Rotate(polygon1'', 1.5707963267948966, (0.5, 0.5)) → polygon1'''
  10. Polygon(E, Rotate[E, 1.5707963267948966, (0.5, 0.5)], Rotate[E, 3.141592653589793, (0.5, 0.5)], Rotate[E, 4.71238898038469, (0.5, 0.5)]) → polygon3, e, d, f, g
  11. Segment((1.25 + a, a), (2.25, 0)) → q
  12. Segment((0, 0), (0, 1)) → t
  13. Translate(c, (1.25, 0)) → c'
  14. Translate(polygon1, (1.25, -0.008489327809275027)) → polygon1'_1
  15. Translate(polygon1'', (0.25 + a, a)) → polygon1'''_1
  16. Translate(polygon1', (1.25 + a, 0)) → polygon1''_1
  17. Translate(polygon1''', (1.25, (-b))) → polygon2
  18. Polygon((1.25, 0), (1.25, a), (1.25 + a, a), (1.25 + a, 0)) → polygon4, h, i, j, k
  19. Polygon((1.25 + a, a), (1.25 + a, 1), (2.25, 1), (2.25, a)) → polygon5, l, m, n, p
  20. Segment((1, 0), (1, 1)) → a_1