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平衡方程

平衡方程
几何画板及绘图内容加载中，请稍等……
2016-08-22 23:25
函数解析几何
①本范例演示通过动态交互演示方程平衡的原理；②涉及核心数学概念包括方程平衡、解析几何、函数图像与动态几何变换；③构造要点：使用Sequence、Segment、Point等命令创建几何对象，通过animate_d、balance_x等对象实现动态平衡演示，并利用滑块动画Slider Animation调整参数；④适合高中数学教学，用于理解方程平衡与函数性质。

GeoGebra 命令及参数

  1. Sequence(Segment[Element[balanceCorners, k], Element[balanceCorners, k] + (0, (-3))], k, 1, 2) → balanceChains
  2. Segment(Element[balanceCorners, 1], Element[balanceCorners, 2]) → balancePost_1
  3. Segment((-5, -10), (5, -10)) → balancePost_2
  4. Segment((0, 0), (0, -10)) → balancePost_3
  5. Point(e) → A
  6. Point(e) → B
  7. Point(e) → C
  8. Sequence(Polygon[Element[balanceCorners, k] + (0, (-3)), Element[balanceCorners, k] + (3, (-5.5)), Element[balanceCorners, k] + (3, (-7)), Element[balanceCorners, k] + ((-3), (-7)), Element[balanceCorners, k] + ((-3), (-5.5))], k, 1, 2) → balanceTrays
  9. Sequence(Circle[(x(Element[balanceCorners, 1]) - 0.4 - (0.7 * Mod[k, 4]), (0.7 * floor(k / 4)) + y(Element[balanceCorners, 1]) - 6.6), 0.3], k, 0, abs(a) - 1) → LeftXBeads
  10. Sequence(Circle[(x(Element[balanceCorners, 1]) + 0.4 + (0.4 * Mod[k, 6]), (0.4 * floor(k / 6)) + y(Element[balanceCorners, 1]) - 6.7), 0.175], k, 0, abs(b) - 1) → LeftNumberBeads
  11. Sequence(Circle[(x(Element[balanceCorners, 2]) + 0.4 + (0.4 * Mod[k, 6]), (0.4 * floor(k / 6)) + y(Element[balanceCorners, 2]) - 6.7), 0.175], k, 0, abs(d) - 1) → RightNumberBeads
  12. Sequence(Circle[(x(Element[balanceCorners, 2]) - 0.4 - (0.7 * Mod[k, 4]), (0.7 * floor(k / 4)) + y(Element[balanceCorners, 2]) - 6.6), 0.3], k, 0, abs(c) - 1) → RightXBeads