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观察抛物线内部结构

观察抛物线内部结构
几何画板及绘图内容加载中，请稍等……
2018-12-26 18:07
函数解析几何变换
这个范例通过一个窗口展示了抛物线的内部结构。它涉及抛物线的几何性质和函数图像。通过使用Surface, CurveCartesian, Sequence, Vector, Translate等GeoGebra命令，可以动态展示抛物线的切线、向量和平移变换。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, 0, c2) → b
  2. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, c2 + k2, π) → c
  3. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, 0, π) → e
  4. CurveCartesian(e(t, c2), t, c1, c1 + k1) → f
  5. CurveCartesian(e(t, c2 + k2), t, c1, c1 + k1) → g
  6. CurveCartesian(e(c1, t), t, c2, c2 + k2) → h
  7. CurveCartesian(e(c1 + k1, t), t, c2, c2 + k2) → i
  8. Surface((k * h(t)), t, c2, c2 + k2, k, 0, 1) → j
  9. Surface((k * f(t)), t, c1, c1 + k1, k, 0, 1) → k
  10. Surface((k * i(t)), t, c2, c2 + k2, k, 0, 1) → l
  11. Surface((k * g(t)), t, c1, c1 + k1, k, 0, 1) → m
  12. Surface(e((k * c1) + ((1 - k) * (c1 + k1)), t), t, c2, c2 + k2, k, 0, 1) → p
  13. Sequence(CurveCartesian[e(k, t), t, c2 + k2, π], k, c1, c1 + k1, k2 / 8) → l5
  14. Sequence(CurveCartesian[e(k, t), t, 0, c2], k, c1, c1 + k1, k2 / 8) → l6
  15. Sequence(CurveCartesian[e(t, k), t, 0, (2 * π)], k, 0, c2, k1 / 15) → l2
  16. Sequence(CurveCartesian[e(t, k), t, 0, (2 * π)], k, c2 + k2, π, k1 / 15) → l3
  17. Sequence(CurveCartesian[e(t, k), t, c1, c1 + k1], k, c2, c2 + k2, k2 / 8) → l7
  18. Sequence(CurveCartesian[e(k, t), t, c2, c2 + k2], k, c1, c1 + k1, k2 / 8) → l8
  19. Vector((0, 0), (10 * CG)) → u
  20. Translate(ls, Vector[(tr * u)]) → ls'
  21. Translate(ll, Vector[(tr * u)]) → ll'
  22. Translate(lc, Vector[(tr * u)]) → lc'
  23. Sequence(CurveCartesian[e(t, k), t, c1 + k1 - (2 * π), c1], k, c2, c2 + k2, k2 / 8) → l4
  24. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, c1 + k1 - (2 * π), c1, v, c2, c2 + k2) → a
  25. Sequence(CurveCartesian[e(k, t), t, 0, π], k, c1 + k1 - (2 * π), c1, k2 / 8) → l1

AI 绘图提示语参考

绘制一个抛物线的内部结构，包括其切线、向量和变换。首先绘制抛物线的表面，然后通过变换和序列命令动态展示切线和向量，最后通过平移和旋转展示抛物线的平移变换。
以上提示语为根据原始绘图命令整理而来，仅供参考。