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立方体与内切球

立方体与内切球
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2019-04-12 18:25
解析几何立体几何几何作图
本范例展示了立方体与其内切球的比较。涉及的核心数学概念包括立体几何和解析几何。通过使用Surface, Rotate, Sphere, Translate, Line, Polygon, CurveCartesian, Mirror, Plane等GeoGebra命令，可以构造出立方体及其内切球。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Surface((t, (s * (1 - sin(acosd(t)))), 0), t, 0, 1, s, 0, 1) → sup
  2. Rotate(sup, (-(90°)), yAxis) → sup2
  3. Sphere((0, 1, 0), 1) → esf
  4. Translate(Rotate[sup, (-(90°)), xAxis], Vector[(0, 1, 1)]) → sup3
  5. Line(PCentro, PCentro + (0, 0, 1)) → r
  6. Polygon({(1, 0, 0), (0, 0, 0), (0, 0, 1), (1, 0, 1)}) → Cara1
  7. CurveCartesian(PCentro + (0, (-cos(t)), sin(t)), t, 0, π / 2) → c2
  8. Polygon({(1, 0, 0), (1, 1, 0), (1, 1, 1), (1, 0, 1)}) → Cara2
  9. Surface(c2, 90°, r) → s
  10. Mirror(capa1, PCentro) → capa2
  11. Polygon((1, 0, 1), (1, 1, 1), (1, 1, 1), (1, 0, 1)) → Cara3, f, g, h, i
  12. Mirror({Cara1, Cara2, Cara3}, PCentro) → capa2b
  13. Plane(x = 0) → Plano1
  14. Plane(z = 0) → Plano2
  15. Mirror(capa2b, Plano1) → capa2c
  16. Plane(y = 1) → Plano3
  17. Mirror(capa2b, Plano2) → capa2d
  18. Mirror(capa2b, Plano3) → capa2e
  19. CurveCartesian(PCentro + (cos(t), 0, sin(t)), t, 0, π / 2) → c21
  20. CurveCartesian(PCentro + (cos(t), (-sin(t)), 0), t, 0, π / 2) → c22