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AP 2006AB_1c 微积分几何问题演示

AP 2006AB_1c 微积分几何问题演示
几何画板及绘图内容加载中，请稍等……
2016-06-26 23:47
解析几何立体几何微积分积分复数
所属专题 Volumes in AP Calculus Volumes in AP Calculus
①本范例演示了利用 GeoGebra 构建复杂几何图形与微积分问题的交互式解决方案；②涉及核心数学概念包括复数、不定积分、角度、直线、平移、旋转、积分、矩形求和、曲面、数列等；③作图要点提炼自构造摘要，使用了 Intersect（相交）、Polygon（多边形）、Rotate（旋转）、Integral（积分）、RectangleSum（矩形求和）、Surface（曲面）、Sequence（数列）等 GeoGebra 命令与对象；④适合高中及以上学段，用于微积分与几何的综合应用教学与探索。

GeoGebra 命令及参数

  1. Intersect(f, g, 2, 4) → Right
  2. Intersect(f, g, 0.1, 1) → Left
  3. Polygon((fI(ay + ((DK + p) * h)), ay + (DK * h)), (fI(ay + ((DK + p) * h)), ay + ((DK + 1) * h)), (gI(ay + ((DK + p) * h)), ay + ((DK + 1) * h)), (gI(ay + ((DK + p) * h)), ay + (DK * h))) → Rectangle1, b, c, d, e
  4. Rotate(Rectangle1, (-α), yAxis) → Rectangle1'
  5. Integral((π * (fI(x)^(2) - gI(x)^(2))), ay, by) → VolInteg
  6. RectangleSum(A, ay, ay + (m * h), m, p) → WS
  7. Surface((gI(ay + ((DK + p) * h)) * cos(β)), u, (gI(ay + ((DK + p) * h)) * sin(β)), u, ay + (DK * h), ay + ((DK + 1) * h), β, 0, α) → Inner1
  8. Surface((fI(ay + ((DK + p) * h)) * cos(β)), u, (fI(ay + ((DK + p) * h)) * sin(β)), u, ay + (DK * h), ay + ((DK + 1) * h), β, 0, α) → Outer1
  9. Surface((((v * gI(ay + ((DK + p) * h))) + ((1 - v) * fI(ay + ((DK + p) * h)))) * cos(β)), ay + (DK * h), (((v * gI(ay + ((DK + p) * h))) + ((1 - v) * fI(ay + ((DK + p) * h)))) * sin(β)), v, 0, 1, β, 0, α) → SideFront1
  10. Surface((((v * gI(ay + ((DK + p) * h))) + ((1 - v) * fI(ay + ((DK + p) * h)))) * cos(β)), ay + ((DK + 1) * h), (((v * gI(ay + ((DK + p) * h))) + ((1 - v) * fI(ay + ((DK + p) * h)))) * sin(β)), v, 0, 1, β, 0, α) → SideBack1
  11. Surface((gI(u) * cos(β)), u, (gI(u) * sin(β)), u, ay, by, β, 0, (2 * π)) → Inner
  12. Sequence(Polygon[(fI(ay + ((k + p) * h)), ay + (k * h)), (fI(ay + ((k + p) * h)), ay + ((k + 1) * h)), (gI(ay + ((k + p) * h)), ay + ((k + 1) * h)), (gI(ay + ((k + p) * h)), ay + (k * h))], k, 0, m - 1) → Rectangles
  13. Rotate(Rectangles, (-α), yAxis) → Rectangles'
  14. Sequence(Surface[(gI(ay + ((k + p) * h)) * cos(β)), u, (gI(ay + ((k + p) * h)) * sin(β)), u, ay + (k * h), ay + ((k + 1) * h), β, 0, α], k, 0, m - 1) → Inners
  15. Sequence(Surface[(fI(ay + ((k + p) * h)) * cos(β)), u, (fI(ay + ((k + p) * h)) * sin(β)), u, ay + (k * h), ay + ((k + 1) * h), β, 0, α], k, 0, m - 1) → Outers
  16. Sequence(Surface[(((v * gI(ay + ((k + p) * h))) + ((1 - v) * fI(ay + ((k + p) * h)))) * cos(β)), ay + (k * h), (((v * gI(ay + ((k + p) * h))) + ((1 - v) * fI(ay + ((k + p) * h)))) * sin(β)), v, 0, 1, β, 0, α], k, 0, m - 1) → SidesFront
  17. Sequence(Surface[(((v * gI(ay + ((k + p) * h))) + ((1 - v) * fI(ay + ((k + p) * h)))) * cos(β)), ay + ((k + 1) * h), (((v * gI(ay + ((k + p) * h))) + ((1 - v) * fI(ay + ((k + p) * h)))) * sin(β)), v, 0, 1, β, 0, α], k, 0, m - 1) → SidesBack
  18. Rotate(g_1, (-α), yAxis) → a
  19. Rotate(f_1, (-α), yAxis) → i
  20. Surface((fI(u) * cos(β)), u, (fI(u) * sin(β)), u, ay, by, β, 0, (2 * π)) → Outer

AI 绘图提示语参考

绘制一个复杂的几何与微积分问题交互式解决方案，包含复数、不定积分、角度、直线、平移、旋转、积分、矩形和、曲面和序列等核心数学概念。首先交点确定左右边界，接着绘制矩形并旋转，计算体积积分和矩形和，构建曲面和序列，最后旋转图形并展示前后侧面，整体呈现立体几何与微积分的结合。
以上提示语为根据原始绘图命令整理而来，仅供参考。