积极 AI Logo 积极 AI

棱柱演示

棱柱演示
几何画板及绘图内容加载中，请稍等……
2020-01-23 16:58
向量立体几何概率统计复数几何作图
①本范例演示棱柱的几何构造与相关属性；②涉及核心数学概念包括立体几何、向量运算、条件概率及复数；③作图要点运用了Point, Intersect, Segment, Slope, CircleSector, PointIn, Vector, Angle, Rotate, Ray, LaTeX, Polygon等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于理解几何体构造与概率统计应用。

GeoGebra 命令及参数

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → A
  3. Segment(C, A) → c
  4. Slope(c) → m_c
  5. Point(c) → D
  6. CircleSector(D, D - (Length[c] * (1, -1 / m_c)), A) → k
  7. Segment(C, B) → b
  8. PointIn(k) → E
  9. Vector(E, D) → u
  10. Slope(b) → m_b
  11. Segment(D_{plus}, D_{minus}) → a
  12. Angle(E, D, D_{minus}) → da
  13. Rotate(D_{plus}, (db / 180 * π), D) → F
  14. Ray(D, F) → d
  15. Intersect(d, b) → G
  16. Segment(D, G) → e
  17. Segment(G_{minus}, G_{plus}) → f
  18. Angle(D, G, G_{minus}) → ga
  19. Rotate(G_{plus}, (((-gb)) / 180 * π), G) → H
  20. Vector(G, G + (Vector[G, H] / Length[Vector[G, H]] * Length[u])) → g
  21. Rotate(D_{plus}, (db2 / 180 * π), D) → I
  22. Ray(D, I) → h
  23. Intersect(h, b) → J
  24. Segment(J_{minus}, J_{plus}) → i
  25. Angle(D, J, J_{minus}) → ja
  26. Rotate(J_{plus}, (((-jb)) / 180 * π), J) → K
  27. Vector(J, J + (Vector[J, K] / Length[Vector[J, K]] * Length[u])) → w
  28. Segment(D, J) → j
  29. LaTeX("\text{Typically, longer wavelengths (redder) have lower indices of refraction.}") → text1
  30. Polygon(A, C, B) → t1, b_1, a_1, c_1
  31. Angle(A, C, B) → α