矩形和菱形对角线长度

矩形和菱形对角线长度
几何画板及绘图内容加载中,请稍等……
2019-04-27 03:32
本范例演示矩形和菱形对角线长度的计算。核心数学概念包括几何作图、向量和最值优化。通过使用GeoGebra命令如Flatten、Circle、Polygon等,可以动态调整矩形和菱形的尺寸,观察对角线长度的变化。适合初中及以上学生学习几何和优化问题。

GeoGebra 命令及参数

  1. Flatten(Sequence[Sequence[(i, j), i, left, right, 0.5], j, bottom, top, 1]) → gridSpace
  2. Circle(Rcenter, 2) → RcenterCirc
  3. Polygon({(left, bottom), (left, top), (-1, top), (-1, bottom)}) → R1Region
  4. PointIn(R1Region) → R1
  5. UnitVector(Vector[R1, Rcenter]) → u1
  6. Polygon({(left, top), (left, bottom), (right, bottom), (right, top)}) → viewbox
  7. Segment(R1, R2) → diag1
  8. UnitOrthogonalVector(u1) → u2
  9. Min(Distance[Element[EndPoints, 1], Rcenter], Distance[Element[EndPoints, 2], Rcenter]) → maxLengthR
  10. LaTeX((((("\text{\textbf{Question: }" * QUESTION) * "\\\textbf{Instructions: }") * INSTRUCTIONS) * "}")) → allInstruc
  11. PointIn(viewbox) → A12
  12. PointIn(viewbox) → A13
  13. Intersect(Line[A13, v], Line[A12, u]) → A15
  14. Intersect(Line[A13, u], Line[A12, v]) → A14
  15. Segment(A12, A14) → B12
  16. Segment(A12, A15) → B14
  17. Segment(A13, A14) → B13
  18. Segment(A13, A15) → B15
  19. Segment(A12, A13) → D12
  20. Segment(A14, A15) → D13
  21. If(Angle[A14, A12, A15] ≟ 90°, Angle[A14, A12, A15], Angle[A15, A12, A14]) → C12
  22. If(Angle[A15, A13, A14] ≟ 90°, Angle[A15, A13, A14], Angle[A14, A13, A15]) → C13
  23. If(Angle[A13, A14, A12] ≟ 90°, Angle[A13, A14, A12], Angle[A12, A14, A13]) → C14
  24. If(Angle[A12, A15, A13] ≟ 90°, Angle[A12, A15, A13], Angle[A13, A15, A12]) → C15
  25. Element(radioButtonLocations, RECTANGLE) → rbRectangle
  26. Element(radioButtonLocations, RHOMBUS) → rbRhombus
  27. Element(radioButtonLocations, showObject) → highlightButton
  28. Sequence(Rcenter + (i * u2), i, 2, maxLengthR, 0.5) → R3Region
  29. Point(R3Region) → R3
  30. Mirror(R3, diag1) → R4
  31. Segment(R1, R3) → Rside1
  32. Segment(R3, R2) → Rside2
  33. Segment(R2, R4) → Rside3
  34. Segment(R4, R1) → Rside4
  35. Segment(R3, R4) → diag2
  36. Ray(Rcenter, u2) → rayRcenter