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无言证明：勾股定理 by Steve Phelps

无言证明：勾股定理 by Steve Phelps
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2015-02-09 07:43
测试改名0向量解析几何
这个范例通过拖动点和滑块，展示了勾股定理的直观证明。它涉及矩形和向量等核心数学概念。通过构造矩形、旋转、平移等GeoGebra命令，动态展示了直角三角形斜边上的正方形面积等于两个直角边上的正方形面积之和。适合初中及以上学生学习几何证明。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  7. Polygon(A, C, 4) → poly3, j, k, l, m, J, K
  8. Intersect(b, m) → L
  9. Intersect(i, l) → M
  10. Polygon(A, G, F, L) → poly4, a_1, g_1, f_1, l_1
  11. Polygon(M, I, J) → poly5, j_1, m_1, i_1
  12. Polygon(J, C, H) → poly6, h_1, j_2, c_1
  13. Polygon(A, E, L) → poly7, l_2, a_2, e_1
  14. Polygon(E, M, J, C) → poly8, e_2, m_2, j_3, c_2
  15. If(n < 1, n, 1) → r1
  16. Rotate(A, (-(((r1 * 90))°)), A) → A'
  17. Rotate(G, (-(((r1 * 90))°)), A) → G'
  18. Rotate(F, (-(((r1 * 90))°)), A) → F'
  19. Rotate(L, (-(((r1 * 90))°)), A) → L'
  20. Polygon(A', G', F', L') → poly4', a', g', f', l'
  21. Dilate(J, If[1 ≤ n < 2, 2 - n, If[n ≥ 2, 0, 1]], C) → J'
  22. Vector(J, J') → u
  23. Translate(M, u) → M'
  24. Translate(I, u) → I'
  25. Translate(J, u) → J'_1
  26. Polygon(M', I', J'_1) → poly5', j'_1, m', i'
  27. Midpoint(A, J) → N
  28. Vector(A, L) → v
  29. Translate(C, v) → C'
  30. Vector(A, E) → w
  31. Translate(C, w) → C'_1
  32. Polygon(C, C', C'_1) → poly9, c'_1, c_3, c'
  33. Polygon(C', J, H, C'_1) → poly10, c'_2, j_4, h_2, c'_3
  34. Dilate(J, If[2 ≤ n < 3, 3 - n, If[n ≥ 3, 0, 1]], K) → J'_2
  35. Vector(J, J'_2) → p
  36. Translate(C', p) → C''
  37. Translate(J, p) → J'_3
  38. Translate(H, p) → H'
  39. Translate(C'_1, p) → O
  40. Polygon(C'', J'_3, H', O) → poly10', c'', j'_3, h', o
  41. If(3 ≤ n ≤ 4, n - 3, 0) → r2
  42. Rotate(C, (-(((r2 * 90))°)), J) → C'_2
  43. Rotate(C', (-(((r2 * 90))°)), J) → C''_1
  44. Rotate(C'_1, (-(((r2 * 90))°)), J) → P
  45. Polygon(C'_2, C''_1, P) → poly9', p_1, c'_4, c''_1