天秤遊戲

天秤遊戲
几何画板及绘图内容加载中,请稍等……
2018-02-08 15:18
①本范例通过动态演示天秤平衡的力学原理,直观展示杠杆原理与力矩平衡;②涉及核心数学概念包括向量、几何作图、解析几何、概率统计(如期望值);③构造中运用了Join, RandomElement, Random, Point, Polygon, Segment, If, Textfield等GeoGebra命令与对象,实现动态平衡点的计算与显示;④适合高中物理与数学教学,用于理解力矩、向量运算及概率模型。

GeoGebra 命令及参数

  1. Join({Sequence[Point[{i, 8}], i, -22, -10], Sequence[Point[{i, 8}], i, 6, 18]}) → startingPoint
  2. RandomElement(startingPoint) → K_1anchor
  3. Random(1, 40) → weight
  4. Point({(-14 * cos((-tipper))), (14 * sin((-tipper))) + 20}) → leftPoint
  5. Polygon(C_1 + (-2, 2), C_1 + (-2, -2), C_1 + (16, -2), C_1 + (16, 2)) → leftZone, t_1, a_1, b_1, c_1
  6. Polygon(A, B, 4) → poly1, f, g, h, i, K, L
  7. Polygon(C, D, 4) → poly2, j, k, l, m, M, N
  8. Polygon(E, F, 4) → poly3, n, p, q, r, O, P
  9. Polygon(G, H, 4) → poly4, s, t, a, b, Q, R
  10. Polygon(I, J, 4) → poly5, c, d, e, f_1, S, T
  11. Point(xAxis) → U
  12. Point(xAxis) → V
  13. Point(yAxis) → W
  14. Polygon(U, V, W) → poly6, w, u, v
  15. Segment(W, Z) → g_1
  16. Point(g_1) → A_1
  17. Point({(14 * cos(tipper)), (14 * sin(tipper)) + 20}) → rightPoint
  18. Segment(leftPoint, rightPoint) → h_1
  19. Segment(C_1, D_1) → i_1
  20. Segment(F_1, E_1) → j_1
  21. Segment(leftPoint, D_1) → k_1
  22. Segment(C_1, leftPoint) → l_1
  23. Segment(E_1, rightPoint) → n_1
  24. Segment(rightPoint, F_1) → m_1
  25. Polygon(F_1 + (-2, 2), F_1 + (-2, -2), F_1 + (16, -2), F_1 + (16, 2)) → rightZone, p_1, q_1, r_1, s_1
  26. If(abs(tipper) ≟ π / 6, true, false) → tipped
  27. Textfield(answerText) → InputBox1
  28. RandomElement({-1, 1}) → starter
  29. If(Max[rightTotal, leftTotal] ≟ Min[rightTotal, leftTotal], 0, (1 / 3 * (Max[rightTotal, leftTotal] - Min[rightTotal, leftTotal])) + 4 / 3) → speed

AI 绘图提示语参考

画一个动态平衡的天平,展示杠杆原理和力矩平衡。天平有左右两个支点,通过向量运算和几何构造,随机生成不同重量的物体放置在左右两侧区域,用线段连接支点和物体,根据重量计算平衡点,并用文字显示动态平衡状态和概率统计信息。
以上提示语为根据原始绘图命令整理而来,仅供参考。