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Q3数学范例 by Anthony OR 柯志明

Q3数学范例 by Anthony OR 柯志明
几何画板及绘图内容加载中，请稍等……
2018-03-20 09:50
向量三角函数复数不等式几何作图
所属专题 Exploring the Conditions for Congruence of 2 Triangles Exploring Congruence of Triangles
①本范例通过动态演示展示几何图形与向量的关系；②涉及核心数学概念包括向量、复数、二项分布、不等式、梯形等；③作图要点运用了Vector, Sequence, DynamicCoordinates, Point, Rotate, Segment, Polygon, If, Angle等GeoGebra命令与对象；④适合高中及以上数学学习者和教师用于教学演示与探索。

GeoGebra 命令及参数

  1. Vector(A, C1) → u
  2. Sequence((x(A) + (round(Length[u]) * cos(t°)), y(A) + (round(Length[u]) * sin(t°))), t, 0, 355, 5) → VPoints
  3. DynamicCoordinates(C1, x(ClosestPoint[VPoints, C1]), y(ClosestPoint[VPoints, C1])) → C
  4. Point(Sequence[A + (i, 0), i, 1, 20, 1]) → B
  5. Vector(B, C2) → v
  6. Rotate(D + (4, 0), 100°, D) → F
  7. Segment(F, D) → k
  8. Segment(E, F) → j
  9. Segment(A, C) → f
  10. Segment(A, B) → g
  11. DynamicCoordinates(C2, If[Distance[C2, C] < d, x(C), x(C2)], If[Distance[C2, C] < d, y(C), y(C2)]) → C'
  12. Sequence(B + (i * UnitVector[Segment[B, C2]]), i, 1, 20, 1) → UPoints
  13. Segment(C', B) → h
  14. Polygon({A, B, C}) → t1
  15. If(Distance[C', C] < d, true, false) → closed1
  16. Segment(D, E) → i
  17. Polygon(D, E, F) → t3, l, m, n
  18. Angle(E, D, F) → α
  19. Angle(B, A, C) → β