积极 AI Logo 积极 AI

方程（第三级）——多对象综合几何与代数演示

方程（第三级）——多对象综合几何与代数演示
几何画板及绘图内容加载中，请稍等……
2016-04-11 00:41
多边形数列解析几何几何作图
①本范例演示了一个包含椭圆、多边形、线段、交点、中点及文本框的复合几何图形，并配以方程相关的交互操作，属于第三级难度练习。②核心数学概念涵盖方程求解、椭圆与多边形几何性质、点与线段关系、组合计数以及标准差等统计量，同时涉及不定积分与平面概念，是一个多主题融合的综合性范例。③作图要点：从构造摘要可见，使用了If条件判断、Ellipse椭圆、Segment线段、Intersect交点、Point点、Polygon多边形、Midpoint中点、Sequence序列以及Textfield文本框等GeoGebra命令，构建了dr、u、ul、r、dl、pul、mul、fmul、UL、fmur、mur、pur、ur、fmr、mr、pr、l、fml、L、ml、pl、R、UR、B、c、d、a、A、b、C、A'、C'、e、f、g、D、E、poly2、i、j等众多对象，体现了复杂的几何构造与代数联动。④适合高中或大学低年级学生用于探究方程与几何图形的综合应用，也可作为教师制作交互式数学课件的参考范例，帮助学生在动态操作中理解代数与几何的相互联系。

GeoGebra 命令及参数

  1. If((u * UL) ≟ R, 0, If[(u * UL) ≥ R, -1, 1]) → B
  2. Ellipse((-3, B), (-7, B), 2.25) → c
  3. Ellipse((3, (-B)), (7, (-B)), 2.25) → d
  4. Segment((-5, B), (-5, -3)) → a
  5. Intersect(c, a) → A,
  6. Segment((5, (-B)), (5, -3)) → b
  7. Intersect(d, b) → C,
  8. Segment(A, A') → e
  9. Segment(C, C') → f
  10. Segment(A', C') → g
  11. Intersect(yAxis, g) → D
  12. Point(yAxis) → E
  13. Polygon((10.455803599971945, 4.428079038697364), (11.45154195318282, 4.426628459182624), (11.45154195318282, 4.926628459182623), (10.455803599971945, 4.928079038697364)) → poly2, i, j, k, m
  14. Segment(D, E) → h
  15. Polygon(F, G, H, I) → poly3, f_1, g_1, h_1, i_1
  16. Midpoint(J, M) → O
  17. Sequence(Polygon[(-4.5, B - 0.5 + t / 2), (-3.5, B - 0.5 + t / 2), (-3.5, B + t / 2), (-4.5, B + t / 2)], t, 1, L, 1) → list1
  18. Polygon((-11.445852088028492, 4.308916490437969), (-10.445852088028493, 4.308916490437969), (-10.445852088028493, 4.8089164904379675), (-11.445852088028492, 4.8089164904379675)) → poly4, n, p, q, s
  19. Polygon((-10.543680266275816, -2.544527077316755), (-10.543680266275816, -1.5445270773167552), 4) → poly1
  20. Polygon((11.557939744940192, -2.5558711836942214), (11.557939744940192, -1.5558711836942218), 4) → poly1_3
  21. Polygon((-10.806626137271166, 7.362992675821548), (-9.806626137271168, 7.362992675821548), (-9.806626137271168, 7.8629926758215465), (-10.806626137271166, 7.8629926758215465)) → poly4_1, n_1, p_1, q_1, s_1
  22. Polygon((-10.806626137271166, 7.362992675821548), (-9.806626137271168, 7.362992675821548), (-9.806626137271168, 7.8629926758215465), (-10.806626137271166, 7.8629926758215465)) → poly4_2, n_2, p_2, q_2, s_2
  23. Sequence(Polygon[(-6.5, B - 1 + t), (-5.5, B - 1 + t), 4], t, 1, UL, 1) → list3
  24. Sequence(Polygon[(3.5, (-B) - 1 + t), (4.5, (-B) - 1 + t), 4], t, 1, UR, 1) → list4
  25. Sequence(Polygon[(5.5, (-B) - 0.5 + t / 2), (6.5, (-B) - 0.5 + t / 2), (6.5, (-B) + t / 2), (5.5, (-B) + t / 2)], t, 1, R, 1) → list2
  26. Textfield(fml) → input_fml
  27. Textfield(fmr) → InputBox1
  28. Textfield(fmul) → InputBox2
  29. Textfield(fmur) → InputBox3
  30. Textfield(dl) → InputBox4
  31. Textfield(dr) → InputBox5