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GeoGebra几何与微积分示例

GeoGebra几何与微积分示例
几何画板及绘图内容加载中，请稍等……
2022-07-03 17:49
三角函数数列微积分几何作图
该示例展示了如何使用GeoGebra进行几何图形与微积分概念的结合演示。核心数学概念包括三角函数、连续性、序列与级数以及几何变换。作图要点涉及Textfield、Line、Intersect、Polygon、Function等GeoGebra命令，以及A1、A2、A3、A4等对象的使用。适合高中生或大学低年级学生用于学习几何与微积分的基础知识，以及掌握GeoGebra的作图技巧。

GeoGebra 命令及参数

  1. Textfield(ax) → InputBox1
  2. Textfield(bx) → InputBox2
  3. Textfield(ay) → InputBox3
  4. Textfield(by) → InputBox4
  5. Textfield(b) → InputBox5
  6. Line(A4, xAxis) → i
  7. Line(A3, xAxis) → j
  8. Line(A2, yAxis) → k
  9. Line(A1, yAxis) → l
  10. Intersect(i, l) → A
  11. Intersect(i, k) → B
  12. Intersect(k, j) → C
  13. Intersect(l, j) → D
  14. Polygon(A, B, C, D) → poly1, s, t, d, e
  15. Segment(D', D) → m
  16. Segment(C', C) → n1
  17. Segment(B, B') → q
  18. Segment(A', A) → r
  19. Function(b, ax, bx, ay, by) → o
  20. Surface(ax, s, (t * o(ax, s)), s, ay, by, t, 0, 1) → u1
  21. Surface(bx, s, (t * o(bx, s)), s, ay, by, t, 0, 1) → u2
  22. Surface(s, ay, (t * o(s, ay)), s, ax, bx, t, 0, 1) → u3
  23. Surface(s, by, (t * o(s, by)), s, ax, bx, t, 0, 1) → u4
  24. Integral(b, y) → u
  25. Sequence(ay + (i * (by - ay) / n), i, 0, n) → list1, {0, 0.004, 0.008, 0.012, 0.016, 0.02, 0.024, 0.028, 0.032, 0.036000000000000004, 0.04, 0.044, 0.048, 0.052000000000000005, 0.056, 0.06, 0.064, 0.068, 0.07200000000000001, 0.076, 0.08, 0.084, 0.088, 0.092, 0.096, 0.1, 0.10400000000000001, 0.108, 0.112, 0.116, 0.12, 0.124, 0.128, 0.132, 0.136, 0.14, 0.14400000000000002, 0.148, 0.152, 0.156, 0.16, 0.164, 0.168, 0.17200000000000001, 0.176, 0.18, 0.184, 0.188, 0.192, 0.196, 0.2, 0.20400000000000001, 0.20800000000000002, 0.212, 0.216, 0.22, 0.224, 0.228, 0.232, 0.23600000000000002, 0.24, 0.244, 0.248, 0.252, 0.256, 0.26, 0.264, 0.268, 0.272, 0.276, 0.28, 0.28400000000000003, 0.28800000000000003, 0.292, 0.296, 0.3, 0.304, 0.308, 0.312, 0.316, 0.32, 0.324, 0.328, 0.332, 0.336, 0.34, 0.34400000000000003, 0.34800000000000003, 0.352, 0.356, 0.36, 0.364, 0.368, 0.372, 0.376, 0.38, 0.384, 0.388, 0.392, 0.396, 0.4, 0.404, 0.40800000000000003, 0.41200000000000003, 0.41600000000000004, 0.42, 0.424, 0.428, 0.432, 0.436, 0.44, 0.444, 0.448, 0.452, 0.456, 0.46, 0.464, 0.468, 0.47200000000000003, 0.47600000000000003, 0.48, 0.484, 0.488, 0.492, 0.496, 0.5, 0.504, 0.508, 0.512, 0.516, 0.52, 0.524, 0.528, 0.532, 0.536, 0.54, 0.544, 0.548, 0.552, 0.556, 0.56, 0.5640000000000001, 0.5680000000000001, 0.5720000000000001, 0.5760000000000001, 0.58, 0.584, 0.588, 0.592, 0.596, 0.6, 0.604, 0.608, 0.612, 0.616, 0.62, 0.624, 0.628, 0.632, 0.636, 0.64, 0.644, 0.648, 0.652, 0.656, 0.66, 0.664, 0.668, 0.672, 0.676, 0.68, 0.684, 0.6880000000000001, 0.6920000000000001, 0.6960000000000001, 0.7000000000000001, 0.704, 0.708, 0.712, 0.716, 0.72, 0.724, 0.728, 0.732, 0.736, 0.74, 0.744, 0.748, 0.752, 0.756, 0.76, 0.764, 0.768, 0.772, 0.776, 0.78, 0.784, 0.788, 0.792, 0.796, 0.8, 0.804, 0.808, 0.812, 0.8160000000000001, 0.8200000000000001, 0.8240000000000001, 0.8280000000000001, 0.8320000000000001, 0.836, 0.84, 0.844, 0.848, 0.852, 0.856, 0.86, 0.864, 0.868, 0.872, 0.876, 0.88, 0.884, 0.888, 0.892, 0.896, 0.9, 0.904, 0.908, 0.912, 0.916, 0.92, 0.924, 0.928, 0.932, 0.936, 0.9400000000000001, 0.9440000000000001, 0.9480000000000001, 0.9520000000000001, 0.9560000000000001, 0.96, 0.964, 0.968, 0.972, 0.976, 0.98, 0.984, 0.988, 0.992, 0.996, 1, 1.004, 1.008, 1.012, 1.016, 1.02, 1.024, 1.028, 1.032, 1.036, 1.04, 1.044, 1.048, 1.052, 1.056, 1.06, 1.064, 1.068, 1.072, 1.076, 1.08, 1.084, 1.088, 1.092, 1.096, 1.1, 1.104, 1.108, 1.112, 1.116, 1.12, 1.124, 1.1280000000000001, 1.1320000000000001, 1.1360000000000001, 1.1400000000000001, 1.1440000000000001, 1.1480000000000001, 1.1520000000000001, 1.156, 1.16, 1.164, 1.168, 1.172, 1.176, 1.18, 1.184, 1.188, 1.192, 1.196, 1.2, 1.204, 1.208, 1.212, 1.216, 1.22, 1.224, 1.228, 1.232, 1.236, 1.24, 1.244, 1.248, 1.252, 1.256, 1.26, 1.264, 1.268, 1.272, 1.276, 1.28, 1.284, 1.288, 1.292, 1.296, 1.3, 1.304, 1.308, 1.312, 1.316, 1.32, 1.324, 1.328, 1.332, 1.336, 1.34, 1.344, 1.348, 1.352, 1.356, 1.36, 1.364, 1.368, 1.372, 1.3760000000000001, 1.3800000000000001, 1.3840000000000001, 1.3880000000000001, 1.3920000000000001, 1.3960000000000001, 1.4000000000000001, 1.4040000000000001, 1.408, 1.412, 1.416, 1.42, 1.424, 1.428, 1.432, 1.436, 1.44, 1.444, 1.448, 1.452, 1.456, 1.46, 1.464, 1.468, 1.472, 1.476, 1.48, 1.484, 1.488, 1.492, 1.496, 1.5, 1.504, 1.508, 1.512, 1.516, 1.52, 1.524, 1.528, 1.532, 1.536, 1.54, 1.544, 1.548, 1.552, 1.556, 1.56, 1.564, 1.568, 1.572, 1.576, 1.58, 1.584, 1.588, 1.592, 1.596, 1.6, 1.604, 1.608, 1.612, 1.616, 1.62, 1.624, 1.6280000000000001, 1.6320000000000001, 1.6360000000000001, 1.6400000000000001, 1.6440000000000001, 1.6480000000000001, 1.6520000000000001, 1.6560000000000001, 1.6600000000000001, 1.6640000000000001, 1.668, 1.672, 1.676, 1.68, 1.684, 1.688, 1.692, 1.696, 1.7, 1.704, 1.708, 1.712, 1.716, 1.72, 1.724, 1.728, 1.732, 1.736, 1.74, 1.744, 1.748, 1.752, 1.756, 1.76, 1.764, 1.768, 1.772, 1.776, 1.78, 1.784, 1.788, 1.792, 1.796, 1.8, 1.804, 1.808, 1.812, 1.816, 1.82, 1.824, 1.828, 1.832, 1.836, 1.84, 1.844, 1.848, 1.852, 1.856, 1.86, 1.864, 1.868, 1.872, 1.8760000000000001, 1.8800000000000001, 1.8840000000000001, 1.8880000000000001, 1.8920000000000001, 1.8960000000000001, 1.9000000000000001, 1.9040000000000001, 1.9080000000000001, 1.9120000000000001, 1.9160000000000001, 1.92, 1.924, 1.928, 1.932, 1.936, 1.94, 1.944, 1.948, 1.952, 1.956, 1.96, 1.964, 1.968, 1.972, 1.976, 1.98, 1.984, 1.988, 1.992, 1.996, 2}
  26. Element(list3, faces) → Selectedvector

AI 绘图提示语参考

请绘制一个由四个点A、B、C、D构成的四边形，并将其投影到坐标系中。通过函数o和参数b、a、x、y构造四个曲面u1、u2、u3、u4，形成一个三维曲面结构。同时计算积分u以得到体积，并生成一个从0到1的等差数列序列。图形应体现几何与微积分的结合，展示曲面与序列的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。