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足球1v1：站位、角度与位似变换

足球1v1：站位、角度与位似变换
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2020-07-07 13:04
测试改名0角变换几何作图滑块动画
所属专题 Soccer & Geometry: Positions, Angles, & Dilations
本范例通过足球1v1攻防场景，直观演示了球员站位、射门角度与位似（相似）变换之间的几何关系。核心数学概念包括角度、相似三角形、位似变换（Dilation）、几何变换以及特殊点（如中点、交点）的性质。作图要点：使用GeoGebra命令Point、Midpoint、Line、Segment、Circle、Angle、Ray、Intersect、Distance等构造了射手、守门员、球门、影子等对象，并通过滑块或比例参数（如Ratio）控制位似缩放，动态展示不同站位下射门角度的变化。适合中学几何课程中讲解相似三角形、位似变换与角度测量，也可用于体育数学或跨学科项目，帮助学生理解几何在实际运动策略中的应用。

GeoGebra 命令及参数

  1. Point(Circle[Shooter_1, 2]) → K_1
  2. Midpoint(Shooter_1, K_1) → Shooter
  3. Point(yAxis) → A
  4. Line(A, B) → f
  5. Point(f) → Width_1
  6. Point(f) → Goal
  7. Midpoint(Goal, Width_1) → goal
  8. Segment(goal, Shooter) → m
  9. Point(f) → C
  10. Point(f) → D
  11. Circle(goal, Shooter_1) → c
  12. Segment(Shooter_1, K_1) → h
  13. Segment(Width_1, Shooter) → g
  14. Segment(Goal, Shooter) → i
  15. Angle(Width_1, Shooter, Goal) → α
  16. Point(Circle[Goalkeeper, 2]) → Width
  17. Segment(Goalkeeper, Width) → j
  18. Ray(Shooter, Goalkeeper) → k
  19. Ray(Shooter, Width) → l
  20. Intersect(f, k) → Shadow
  21. Intersect(f, l) → Width_2
  22. Segment(Goal, Width_1) → n
  23. Midpoint(Goalkeeper, Width) → K
  24. Distance(Shooter, goal) → distanceLGoal
  25. Distance(Shooter, K) → distanceLG
  26. Distance(Shooter, K) → LG
  27. Distance(Shooter, K) → LK
  28. Distance(Goalkeeper, Width) → distanceGoalkeeperN
  29. Distance(Goal, Width_1) → distanceEF
  30. Segment(Shooter, K) → p
  31. Point(p) → GoalKeeper_1
  32. Distance(goal, Shooter) → distancegoalShooter
  33. Distance(Shooter, GoalKeeper_1) → distanceShooterGoalKeeper1
  34. Distance(Shooter, goal) → distanceShootergoal
  35. Distance(Shadow, Width_2) → distanceShadowWidth2
  36. Distance(GoalKeeper_1, goal) → distanceGoalKeeper1goal
  37. Segment(Width, Goalkeeper) → t
  38. Segment(Shadow, Width_2) → d
  39. Point(p) → F
  40. Segment(Shooter, goal) → f_1