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爱因斯坦证明勾股定理

爱因斯坦证明勾股定理
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2015-11-23 09:10
测试改名0变换几何作图
这个范例展示了爱因斯坦如何证明勾股定理。它涉及的核心数学概念包括几何作图、变换和三角形。通过使用GeoGebra命令如Polygon、Dilate、Segment等，可以动态地展示勾股定理的证明过程。适合初中及以上学生学习几何证明。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(A, C, D, E) → poly2, a_1, c_1, d, e
  3. Dilate(A, r, F) → A'
  4. Dilate(C, r, F) → C'
  5. Dilate(D, r, F) → D'
  6. Dilate(E, r, F) → E'
  7. Polygon(A', C', D', E') → poly2', a', c', d', e'
  8. Dilate(A, r, F) → A'_1
  9. Dilate(B, r, F) → B'
  10. Dilate(C, r, F) → C'_1
  11. Polygon(A'_1, B', C'_1) → poly1', c'_1, a'_1, b'
  12. rttri(G, H) → I, poly3
  13. subright(H, I, G) → f, g, J
  14. Segment(I, G) → h
  15. Segment(G, H) → i
  16. Segment(I, H) → j
  17. Angle(I, J, G) → α
  18. Angle(H, G, I) → γ
  19. Polygon(G, J, I) → poly7, i_3, g_3, j_1
  20. Polygon(G, J, H) → poly8, h_3, g_4, j_2
  21. Angle(G, I, J) → ζ
  22. Angle(J, G, I) → η
  23. Angle(J, H, G) → θ
  24. Angle(H, G, J) → ι
  25. Polygon(I, H, 4) → poly4, k, l, m, n, K, L
  26. Polygon(G, I, 4) → poly5, p, q, s, t, M, N
  27. Polygon(H, G, 4) → poly6, b_1, d_1, e_1, f_1, O, P
  28. Polygon(H, Q, R, S, T, U, V, I) → poly9, h_1, q_1, r_1, s_1, t_1, u, v, i_1
  29. Intersect(LineBisector[Segment[H, I]], LineBisector[Segment[I, I + ((G - I) * Distance[H, I] / Distance[I, G])]]) → W
  30. Dilate(Polygon[Rotate[H, Angle[H, W, I], W], Rotate[Q, Angle[H, W, I], W], Rotate[R, Angle[H, W, I], W], Rotate[S, Angle[H, W, I], W], Rotate[T, Angle[H, W, I], W], Rotate[U, Angle[H, W, I], W], Rotate[V, Angle[H, W, I], W], Rotate[I, Angle[H, W, I], W]], Distance[G, I] / Distance[I, H], I) → poly10
  31. Intersect(LineBisector[Segment[H, I]], LineBisector[Segment[H, H + ((G - H) * Distance[H, I] / Distance[H, G])]]) → Z
  32. Dilate(Polygon[Rotate[H, Angle[I, Z, H], Z], Rotate[Q, Angle[I, Z, H], Z], Rotate[R, Angle[I, Z, H], Z], Rotate[S, Angle[I, Z, H], Z], Rotate[T, Angle[I, Z, H], Z], Rotate[U, Angle[I, Z, H], Z], Rotate[V, Angle[I, Z, H], Z], Rotate[I, Angle[I, Z, H], Z]], Distance[G, H] / Distance[I, H], H) → poly11