构造四分之三角的 GeoGebra 示例

构造四分之三角的 GeoGebra 示例
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2015-02-18 02:16
①本范例演示如何使用 GeoGebra 构造一个角,其度数是已知角 ∠S 的四分之三;②涉及的核心数学概念包括角度测量、几何作图、比例关系;③作图要点——从下方『构造摘要』提炼用到了 Polygon(多边形)、Segment(线段)、Ray(射线)、Circle(圆)、Intersect(交点)、Midpoint(中点)、Vector(向量)、Translate(平移)、CircumcircleArc(圆弧)、Mirror(镜像)等 GeoGebra 命令/对象;④适合高中学段学生学习和理解角度比例关系及几何作图技巧。

GeoGebra 命令及参数

  1. Polygon((22, y(Corner[1])), Corner[2], Corner[3], (22, y(Corner[4]))) → mask, a, b, c, d
  2. Segment(S, U) → FirstArcDistance
  3. Ray(S, U) → FirstAngleRay1
  4. Ray(S, FirstAngleRaypt) → FirstAngleRay2
  5. Circle(S, Segment[S, U]) → CircRad1
  6. Circle(S, (2 * Segment[S, U])) → CircRad2
  7. Intersect(CircRad2, FirstAngleRay1) → Udouble,
  8. Intersect(CircRad2, FirstAngleRay2) → Tdouble,
  9. Intersect(CircRad1, FirstAngleRay2) → T,
  10. Circle(U, Udouble) → CircCenU
  11. Circle(T, Tdouble) → CircCenT
  12. Midpoint(U, T) → F
  13. Ray(S, F) → MidRay
  14. Vector(S, S + (2 * (F - S))) → ShiftVec
  15. Translate(F, ShiftVec) → Ftranslated
  16. Intersect(CircCenT, Segment[F, Ftranslated]) → W,
  17. CircumcircleArc(Tdouble, W, S) → ArcT
  18. CircumcircleArc(Udouble, W, S) → ArcU
  19. Intersect(CircRad2, MidRay) → A,
  20. Intersect(CircRad1, MidRay) → X,
  21. Midpoint(X, U) → G
  22. Ray(S, G) → ThreeQuarterRay
  23. Translate(G, Vector[(2 * Vector[S, G])]) → Gtranslated
  24. Intersect(ArcU, Segment[G, Gtranslated]) → Z,
  25. CircumcircleArc(A, Z, S) → ArcX
  26. Mirror(X, FirstAngleRay1) → FirstArcA
  27. Mirror(X, FirstAngleRay2) → FirstArcB
  28. CircumcircleArc(FirstArcB, X, FirstArcA) → FirstArc
  29. Intersect(ArcX, Segment[U, Udouble]) → B,
  30. CircumcircleArc(A, Z, B) → ArcXShort
  31. Midpoint(T, X) → C
  32. Ray(S, C) → QuarterRay
  33. Intersect(ArcT, Segment[G, Gtranslated]) → I,
  34. CircumcircleArc(Tdouble, W, I) → ArcTShort
  35. Translate(C, Vector[(2 * Vector[S, C])]) → Ctranslated
  36. Intersect(ArcU, Segment[C, Ctranslated]) → E,
  37. CircumcircleArc(Udouble, W, E) → ArcUShort
  38. Ray(S, G) → EndRay1
  39. Ray(S, FirstAngleRaypt) → EndRay2

AI 绘图提示语参考

构造一个角,使其大小为给定角∠S的3/4。首先,画出角∠S的两条边,然后构造一个圆心在角顶点S,半径为角S边长两倍的圆,找到该圆与角两边的交点。接着,通过这些交点构造新的圆弧和射线,逐步调整角度直至达到3/4倍。最后,利用镜像和平移等操作,精确地确定出目标角的边。
以上提示语为根据原始绘图命令整理而来,仅供参考。