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橙子切片几何演示

橙子切片几何演示
几何画板及绘图内容加载中，请稍等……
2020-01-14 23:10
三角函数解析几何立体几何微积分几何作图
①本范例通过动态演示橙子切片，直观展示球体与截面圆的关系；②涉及核心数学概念包括分数、球体、割线、乘法、等腰三角形、微分方程和中值定理；③构造过程中运用了Circle（圆）、Segment（线段）、Vector（向量）、Sequence（数列）、Surface（曲面）、CurveCartesian（笛卡尔曲线）、Translate（平移）、Join（连接）等GeoGebra命令；④适合高中数学教学，用于立体几何与解析几何的直观化教学。

GeoGebra 命令及参数

  1. Circle(O, R, xOyPlane) → d
  2. Segment(B, A) → j
  3. Vector(O, C) → z
  4. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * sin(i)) * cos(j)), z(C) + (R * sin(j)), i, 0, Angle], j, -1.5708, 1.5708, (2 * π / Part)) → liste1
  5. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * cos(i)) * sin(j)), z(C) + (R * sin(i)), i, -1.5708, 1.5708], j, 0, Angle, (2 * π / Part)) → liste2
  6. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * cos(i)) * sin(j)), z(C) + (R * sin(i)), i, -1.5708, 1.5708], j, 0, Angle, π / Part) → liste6
  7. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * sin(i)) * cos(j)), z(O) + (R * sin(j)), i, Angle, 6.28319, j, -1.5708, 1.5708) → a
  8. Surface(x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * sin(i)) * cos(j)), z(C) + (R * sin(j)), i, 0, Angle, j, -1.5708, 1.5708) → k
  9. CurveCartesian(x(O) + ((R * cos(i)) * cos(Angle)), y(O) + ((R * cos(i)) * sin(Angle)), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → o
  10. CurveCartesian(x(O) + (R * cos(i)), y(O) + ((R * cos(i)) * 0), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → p
  11. CurveCartesian(x(C) + ((R * cos(i)) * cos(Angle)), y(C) + ((R * cos(i)) * sin(Angle)), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → q
  12. CurveCartesian(x(C) + (R * cos(i)), y(C) + ((R * cos(i)) * 0), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → r
  13. CurveCartesian(x(C) + ((R * cos(i)) * cos(Angle)), y(C) + ((R * cos(i)) * sin(Angle)), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → e
  14. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * sin(i)) * cos(j)), z(O) + (R * sin(j)), i, Angle, 6.28319, j, -1.5708, 1.5708) → m
  15. CurveCartesian(x(C) + (R * cos(i)), y(C) + ((R * cos(i)) * 0), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → f
  16. CurveCartesian(x(O) + (R * cos(i)), y(O) + ((R * cos(i)) * 0), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → i
  17. Translate(B, Vector[(Extend * u)]) → B'
  18. Translate(A, Vector[(Extend * u)]) → A'
  19. Segment(B', A') → j'
  20. Join(Sequence[Sequence[(x(O) + ((R * cos(j)) * sin(i)), y(O) - ((R * sin(j)) * sin(i)), z(O) - (R * cos(i))), j, Angle, 6.28319, π / n], i, Angle, 6.28319, π / n]) → liste3
  21. Sequence(CurveCartesian[x(C) + ((k * cos(i)) * cos(Angle)), y(C) + ((k * cos(i)) * sin(Angle)), z(C) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste4
  22. Sequence(CurveCartesian[x(O) + ((k * cos(i)) * cos(Angle)), y(O) + ((k * cos(i)) * sin(Angle)), z(O) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste7
  23. Sequence(CurveCartesian[x(O) + (k * cos(i)), y(O) + ((k * cos(i)) * 0), z(O) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste8
  24. Sequence((x(C) + (((R - 0.26) * cos(i)) * cos(Angle)), y(C) + (((R - 0.26) * cos(i)) * sin(Angle)), z(C) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste9
  25. Sequence(CurveCartesian[x(C) + (k * cos(i)), y(C) + ((k * cos(i)) * 0), z(C) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.035, 0.025) → liste5
  26. Sequence(Polygon[Element[liste9, i], Element[liste9, i + 1], C], i, 1, Length[liste9]) → liste10
  27. Sequence((x(C) + ((R - 0.26) * cos(i)), y(C) + (((R - 0.26) * cos(i)) * 0), z(C) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste11
  28. Sequence(Polygon[Element[liste11, i], Element[liste11, i + 1], C], i, 1, Length[liste11]) → liste12
  29. Sequence((x(O) + (((R - 0.26) * cos(i)) * cos(Angle)), y(O) + (((R - 0.26) * cos(i)) * sin(Angle)), z(O) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste13
  30. Sequence((x(O) + ((R - 0.26) * cos(i)), y(O) + (((R - 0.26) * cos(i)) * 0), z(O) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste14
  31. Sequence(Polygon[Element[liste13, i], Element[liste13, i + 1], O], i, 1, Length[liste13]) → liste15
  32. Sequence(Polygon[Element[liste14, i], Element[liste14, i + 1], O], i, 1, Length[liste14]) → liste16
  33. Sequence(Segment[Element[liste9, i], C], i, 1, Length[liste9], 4) → liste17
  34. Sequence(Segment[Element[liste11, i], C], i, 1, Length[liste11], 4) → liste18
  35. Sequence(Segment[Element[liste13, i], O], i, 1, Length[liste13], 4) → liste19
  36. Sequence(Segment[Element[liste14, i], O], i, 1, Length[liste14], 4) → liste20