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两多项式的乘积 - 可视化

两多项式的乘积 - 可视化
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2016-03-24 02:29
三角函数解析几何最值优化几何作图
所属专题 Geom. & Alg.: Quadratics
①本范例通过可视化面积模型演示了两个三项式的乘积；②涉及的核心数学概念包括多项式乘法、面积计算、几何表示；③作图要点：使用了 Ray（射线）、OrthogonalLine（垂线）、Circle（圆）、Intersect（交点）、Polygon（多边形）、PointIn（点在对象内）等 GeoGebra 命令/对象；④适合高中数学教学，用于理解多项式乘法的几何意义和优化问题。

GeoGebra 命令及参数

  1. Ray(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Circle(A, VA) → c
  4. Intersect(c, b) → C, D
  5. Circle(D, VB) → d
  6. Intersect(d, b) → E, F
  7. Circle(F, VC) → e
  8. Intersect(e, b, 2) → G
  9. Circle(A, HA) → f
  10. Intersect(f, a, 1) → H
  11. Circle(H, HB) → g
  12. Intersect(g, a, 2) → I
  13. Circle(I, HC) → h
  14. Intersect(h, a, 2) → J
  15. OrthogonalLine(G, b) → i
  16. OrthogonalLine(F, b) → j
  17. OrthogonalLine(D, b) → k
  18. OrthogonalLine(H, a) → l
  19. OrthogonalLine(I, a) → m
  20. OrthogonalLine(J, a) → n
  21. Intersect(i, l) → K
  22. Intersect(m, i) → L
  23. Intersect(i, n) → M
  24. Intersect(j, l) → N
  25. Intersect(j, m) → O
  26. Intersect(j, n) → P
  27. Intersect(k, l) → Q
  28. Intersect(k, m) → R
  29. Intersect(k, n) → S
  30. Polygon(A, D, Q, H) → VAxHA, a_1, d_1, q, h_1
  31. Polygon(Q, R, I, H) → VAxHB, q_1, r, i_1, h_2
  32. Polygon(R, S, J, I) → VAxHC, r_1, s, j_1, i_2
  33. Polygon(D, F, N, Q) → VBxHA, d_2, f_1, n_1, q_2
  34. Polygon(N, O, R, Q) → VBxHB, n_2, o, r_2, q_3
  35. Polygon(O, P, S, R) → VBxHC, o_1, p, s_1, r_3
  36. Polygon(G, K, N, F) → VCxHA, g_1, k_1, n_3, f_2
  37. Polygon(K, L, O, N) → VCxHB, k_2, l_1, o_2, n_4
  38. Polygon(L, M, P, O) → VCxHC, l_2, m_1, p_1, o_3
  39. PointIn(VCxHC) → Pointpoly9
  40. PointIn(VCxHA) → Pointpoly7
  41. PointIn(VCxHB) → Pointpoly8
  42. PointIn(VBxHA) → Pointpoly4
  43. PointIn(VBxHB) → Pointpoly5
  44. PointIn(VBxHC) → Pointpoly6
  45. PointIn(VAxHA) → Pointpoly1
  46. PointIn(VAxHB) → Pointpoly2
  47. PointIn(VAxHC) → Pointpoly3