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正方形交点演示

正方形交点演示
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2017-09-11 10:13
多边形解析几何几何作图
①本范例演示两个正方形相交时形成的几何图形与交点位置变化；②涉及核心数学概念包括多边形、交点、中点、线段、圆、坐标系等；③构造要点：使用Point, Polygon, Midpoint, Circle, Intersect, Line, OrthogonalLine, Segment等命令创建正方形、交点、中点圆、中线等对象；④适合高中数学教学，用于理解多边形交点、几何变换及坐标系应用。

GeoGebra 命令及参数

  1. Point(xAxis) → A_1
  2. Polygon(A_1, B_1, 4) → poly1, f, g, h, i, C_1, D_1
  3. Midpoint(A_1, C_1) → D
  4. Circle(D, 4) → c
  5. Point(c) → F
  6. Polygon(D, F, 4) → poly2, j, k, l, m, G, H
  7. Intersect(h, m) → I
  8. Intersect(g, j) → J
  9. Polygon(D, I, C_1, J) → poly3, e, i_1, c_1, j_1
  10. Line(D, C) → p
  11. Intersect(c, p) → P, Q
  12. Intersect(poly1, poly2) → E, B, Intersect[poly1, poly2]_1, Intersect[poly1, poly2]_2
  13. Line(A_1, D) → n
  14. Intersect(p, n) → K
  15. Polygon(E, C, B, K) → poly4, r, m_1, s, k_1
  16. Polygon(B, A_1, E, K) → poly5, s_1, a, r_1, k_2
  17. Polygon(D_1, B, K, E) → poly6, d, s_2, k_3, r_2
  18. OrthogonalLine(K, n) → q
  19. Line(D_1, A_1) → t
  20. OrthogonalLine(K, t) → b
  21. Intersect(b, poly1) → L, N
  22. Intersect(poly2, poly1) → O, T, Intersect[poly2, poly1]_1, Intersect[poly2, poly1]_2
  23. Polygon(K, N, O) → poly7, o, k_4, n_1
  24. Line(K, t) → f_1
  25. Intersect(f_1, poly1) → U, V
  26. Polygon(K, U, T) → poly8, t_1, k_5, u
  27. Polygon(K, V, E) → poly9, r_3, k_6, v
  28. Polygon(K, N, B) → poly10, s_3, k_7, n_2
  29. Polygon(K, V, E) → poly11, r_4, k_8, v_1
  30. Polygon(L, B, K) → poly12, k_9, l_1, s_4
  31. Polygon(E, K, U) → poly13, u_1, r_5, k_{10}
  32. Polygon(K, L, B) → poly14, s_5, k_{11}, l_2
  33. Segment(A, B) → g_1
  34. Segment(B, C) → h_1