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给定截面的立体图形

给定截面的立体图形
几何画板及绘图内容加载中，请稍等……
2020-03-14 18:39
解析几何立体几何几何作图
这个范例展示了给定截面的立体图形。涉及的核心数学概念包括立体几何和解析几何。通过使用GeoGebra命令如Polygon, CurveCartesian, Surface等，可以构造出具有特定截面的立体图形。适合高中及以上学生学习立体几何和解析几何。

GeoGebra 命令及参数

  1. SelectedIndex(lifu) → selidxfu
  2. If(selidxfu ≟ 1, pa, selidxfu ≟ 2, ci, selidxfu ≟ 3, pb) → p
  3. Polygon(A1, A2, A3, A4) → squ, a1, a2, a3, a4
  4. Polygon(A1, A2, V3) → trieq, v3, f, g
  5. Polygon((mxk, 0, 0), (mxk, p(mxk), 0), (mxk, (1 / 2 * p(mxk)), (sqrt(3) / 2 * p(mxk)))) → trieqf, h, i, j
  6. CurveCartesian(x_0, (p(x_0) / 2 * (1 + cos(j))), (p(x_0) / 2 * sin(j)), j, 0, π) → cicu
  7. CurveCartesian(mxk, (p(mxk) / 2 * (1 + cos(j))), (p(mxk) / 2 * sin(j)), j, 0, π) → cicuf
  8. SelectedIndex(lishape) → selidxsha
  9. Polygon((mxk, 0, 0), (mxk, p(mxk), 0), (mxk, p(mxk), p(mxk)), (mxk, 0, p(mxk))) → skuf, k, l, m, n
  10. Polygon((x_0, 0, 0), (x_0, p(x_0), 0), (x_0, p(x_0), p(x_0)), (x_0, 0, p(x_0))) → squu, q, r_1, s, d
  11. CurveCartesian(k, (1 / 2 * p(k)), (sqrt(3) / 2 * p(k)), k, 0, mxk) → cuV
  12. CurveCartesian(k, 0, p(k), k, 0, mxk) → cu1
  13. CurveCartesian(k, p(k), p(k), k, 0, mxk) → cu2
  14. Segment(A1f, A2f) → bas
  15. Segment(A1, A2) → basx
  16. Surface(k, 0, (p(k) * j), k, mik, mxk, j, 0, 1) → su1
  17. Surface(k, p(k), (p(k) * j), k, mik, mxk, j, 0, 1) → su2
  18. Surface(k, (p(k) * j), p(k), k, mik, mxk, j, 0, 1) → su3
  19. Surface(k, ((1 / 2 * p(k)) * j), ((sqrt(3) / 2 * p(k)) * j), k, mik, mxk, j, 0, 1) → sut1
  20. Surface(k, p(k) / 2 + ((1 / 2 * p(k)) * j), (sqrt(3) / 2 * p(k)) - ((sqrt(3) / 2 * p(k)) * j), k, mik, mxk, j, 0, 1) → sut2
  21. Surface(k, (p(k) / 2 * (1 + cos(j))), (p(k) / 2 * sin(j)), k, mik, mxk, j, 0, π) → susc
  22. Sequence(CurveCartesian[k, j, 0, k, 0, mxk], j, 0, mxk) → gridx
  23. Sequence(CurveCartesian[j, k, 0, k, 0, mxk], j, 0, mxk) → gridy