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无字证明 by Steve Phelps (3)

无字证明 by Steve Phelps (3)
几何画板及绘图内容加载中，请稍等……
2015-02-03 22:16
测试改名0圆三角函数几何作图滑块动画
①本范例通过拖动点和滑块演示勾股定理的几何证明；②涉及核心数学概念：勾股定理、球体、直角三角形、等边三角形、单位圆、四边形；③作图要点：使用 GeoGebra 命令如 Point, Mirror, CircleArc, Polygon, Segment, OrthogonalLine, Dilate, Intersect, Rotate 等构建几何图形；④适合高中数学教学，用于直观理解勾股定理的证明过程。

GeoGebra 命令及参数

  1. If(o ≤ 1, o, 1) → scalefactor
  2. Point(yAxis) → B
  3. Point(xAxis) → A
  4. Mirror(A, B) → A'
  5. CircleArc(B, C, A) → c
  6. Point(c) → D
  7. Polygon(D, A', 4) → poly1, e, f, g, h, E, F
  8. Segment(A, D) → a
  9. Segment(D, A') → b
  10. Segment(A, A') → d
  11. Polygon(A', A, 4) → poly2, i, j, k, l, G, H
  12. Polygon(A, D, 4) → poly3, m, n, p, q, I, J
  13. OrthogonalLine(D, i) → r
  14. Dilate(F, 1 - scalefactor, A) → F'
  15. Polygon(F', A', E) → poly4, b_1, c_1, d_1
  16. Intersect(r, k) → M
  17. Segment(D, M) → a_1
  18. If(1 < o ≤ 2, o - 1, 1) → rotatefactor
  19. Rotate(F', ((rotatefactor * 90))°, A') → F''
  20. Rotate(A', ((rotatefactor * 90))°, A') → A''
  21. Rotate(E, ((rotatefactor * 90))°, A') → E'
  22. Polygon(F'', A'', E') → poly4', e', f'', a''
  23. Intersect(i, a_1) → K
  24. If(o > 2, 3 - o, 1) → scalefactor2
  25. Dilate(D, scalefactor2, K) → D'
  26. Polygon(D', A', H) → poly5, h_1, d', a'
  27. Dilate(I, 1 - scalefactor, A') → I'
  28. Polygon(J, I', A) → poly6, a_2, j_1, i'
  29. Rotate(J, (-(((rotatefactor * 90))°)), A) → J'
  30. Rotate(I', (-(((rotatefactor * 90))°)), A) → I''
  31. Rotate(A, (-(((rotatefactor * 90))°)), A) → A'_1
  32. Polygon(J', I'', A'_1) → poly6', a'_1, j', i''
  33. Polygon(A, D', G) → poly7, g_1, a_3, d'_1