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生成所有勾股数三元组

生成所有勾股数三元组
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2020-02-21 21:48
数列解析几何几何作图
这个范例演示了如何生成所有勾股数三元组。它涉及勾股定理和数列的概念。通过使用GeoGebra命令如Sequence、Union、Point等，可以动态地展示不同m和n值下的勾股数三元组。适合初中及以上学生学习勾股定理和数列知识。

GeoGebra 命令及参数

  1. Sequence(Sequence[(-(j + (k * ί))^(2)), j, 1, m], k, 1, m) → l4
  2. Sequence(Sequence[(j + (k * ί))^(2), j, 1, m], k, 1, m) → l3
  3. Sequence(Parabola[(0, 0), x = (-2 * j^(2))], j, 1, m) → grid1
  4. Sequence(Parabola[(0, 0), x = (2 * j^(2))], j, 1, m) → grid2
  5. Union(l3, l4) → l5
  6. Point(l5) → P
  7. Segment(O, Q) → px
  8. Segment(P, Q) → py
  9. Segment(O, P) → pz
  10. Polygon(Q, Rotate[P, (((-sgn(x(P))) * sgn(y(P))) * π / 2), Q], Rotate[Q, ((sgn(x(P)) * sgn(y(P))) * π / 2), P], P) → Qy, f, g, l, p
  11. Polygon(O, Q, Rotate[O, ((sgn(x(P)) * sgn(y(P))) * π / 2), Q], Rotate[Q, ((sgn(x(P)) * sgn(y(P))) * ((-π)) / 2)]) → Qx, h, i, q, r
  12. Circle((0, 0), 1) → k
  13. Point(k) → P2
  14. Segment(Q1, (0, 0)) → px'
  15. Segment(Q1, P1) → py'
  16. Segment((0, 0), P1) → pz'
  17. Polygon(O, P, Rotate[O, (((-sgn(x(P))) * sgn(y(P))) * π / 2), P], Rotate[P, ((sgn(x(P)) * sgn(y(P))) * π / 2)]) → Qz, j, s, t, a
  18. Polygon(O, P1, Rotate[O, ((-π)) / 2, P1], Rotate[P1, π / 2]) → Qz1, o, p1, b, c
  19. Polygon(Q1, Rotate[P1, (((-sgn(x(P1))) * sgn(y(P1))) * π / 2), Q1], Rotate[Q1, ((sgn(x(P1)) * sgn(y(P1))) * π / 2), P1], P1) → Qy1, q1, d, e, f_1
  20. Polygon(O, Q1, Rotate[O, ((sgn(x(P1)) * sgn(y(P1))) * π / 2), Q1], Rotate[Q1, ((sgn(x(P1)) * sgn(y(P1))) * ((-π)) / 2)]) → Qx1, g_1, h_1, i_1, j_1
  21. Angle((10000, 0), O, P) → α
  22. Sequence(Sequence[(k + (j * ί))^(u), j, -10, 10], k, -10, 10) → l1
  23. Polygon((10.5, 10.5), (-10.5, 10.5), (-10.5, -10.5), (10.5, -10.5)) → v1, k_1, l_1, m_1, n_1