风筝周长与旋转演示

风筝周长与旋转演示
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2015-11-12 23:05
① 本范例演示一个风筝(凸四边形)的几何构造、周长计算及其绕定点旋转的动态过程。② 涉及核心数学概念:四边形/风筝的性质、周长公式、向量表示、旋转变换、数列/滑块控制动画。③ 作图要点:使用 Circle、Point、Segment、Intersect 创建顶点与边;用 Vector 表示边向量;通过 Sequence 与 Slider(Slider1、Slider2)驱动旋转角度并生成动态轨迹;LaTeX 标注尺寸与公式;Progressbar、Hint 等 UI 对象辅助教学交互。④ 适用于初中几何(四边形、周长)、高中向量与变换章节,也可作为 GeoGebra 几何作图与滑块动画教学示例。

GeoGebra 命令及参数

  1. Circle(C, Slider1) → c
  2. Point(c) → D
  3. Segment((0, 0), (0, 1)) → i
  4. Segment(A_0, B_0) → Scaleline
  5. Sequence(Segment[A_0 + (i, 0), A_0 + (i, (-0.5))], i, 0, 10) → list1
  6. Sequence(Segment[A_0 + (i - 0.5, 0), A_0 + (i - 0.5, (-0.4))], i, 1, 10) → list2
  7. Sequence(Sequence[Segment[A_0 + ((0.5 * i) + (0.1 * j), 0), A_0 + ((0.5 * i) + (0.1 * j), (-0.3))], j, 1, 4], i, 0, 19) → list3
  8. Segment(D_0, (x(D_0), 0)) → j
  9. Vector(C_0, D_0) → u
  10. LaTeX("\text{Hank made a kite to fly in the local kite festival. The dimensions of his kite are shown in the following diagram.}") → text1
  11. LaTeX("\text{If Hank wants to put trim around the edges of his kite, how much trim does he need?}") → text2
  12. LaTeX("\text{Determine the length of each side.}") → text3
  13. LaTeX("\text{Find the perimeter.}") → text6
  14. LaTeX("\text{To find the perimeter, add the lengths of all the sides.}") → text7
  15. LaTeX("\text{Write an equation.}") → text9
  16. LaTeX("\text{Simplify.}") → text11
  17. Segment(C, D) → b
  18. Point(c) → E
  19. Segment(C, E) → d
  20. Circle(D, Slider2) → e
  21. Circle(E, Slider2) → f
  22. Intersect(e, f, 1) → F
  23. Segment(D, F) → g
  24. Segment(F, E) → l
  25. LaTeX("\text{0}") → Scalevalue0
  26. LaTeX("\text{10}") → Scalevalue1
  27. LaTeX("\text{20}") → Scalevalue2
  28. LaTeX("\text{30}") → Scalevalue3
  29. LaTeX("\text{40}") → Scalevalue4
  30. LaTeX("\text{50}") → Scalevalue5
  31. LaTeX("\text{60}") → Scalevalue6
  32. LaTeX("\text{70}") → Scalevalue7
  33. LaTeX("\text{80}") → Scalevalue8
  34. LaTeX("\text{90}") → Scalevalue9
  35. LaTeX("\text{100}") → Scalevalue10
  36. Segment(G, H) → h
  37. Vector(H, P1) → v
  38. Segment(P1, (x(P1), 0)) → k
  39. LaTeX((("\text{The sides marked with one tick mark are both \textcolor{#000099}{" * v1) * "} inches long.}")) → text4
  40. LaTeX((("\text{The sides marked with two tick marks are both \textcolor{#000099}{" * v2) * "} inches long.}")) → text5
  41. LaTeX((((((((("\text{\textcolor{#000099}{P = " * v1) * "+") * v1) * "+") * v2) * "+") * v2) * "}}")) → text8
  42. LaTeX((("\text{\textcolor{#000099}{P = " * sol) * "}}")) → text10
  43. LaTeX("\text{of trim.}") → text12_1
  44. LaTeX((((("\text{The perimeter of the kite is \textcolor{#000099}{" * sol) * "} inches; therefore, Hank will need \textcolor{#000099}{") * sol) * "} inches }")) → text12
  45. LaTeX("\text{\mathbf{Perimeter} the distance around a two-dimensional figure.}") → text13
  46. LaTeX("\text{\mathbf{Line\; segment} a part of a line that is noted by two endpoints,(x ,y ) and (x ,y ). }") → text14

AI 绘图提示语参考

请绘制一个风筝图形,风筝是凸四边形,具有两条等长的对称边。图形中包含一个固定的旋转中心,风筝的一个顶点围绕该中心旋转,旋转角度由滑块控制,旋转轨迹用线段表示。风筝的四个顶点和边通过线段连接,构造顺序为:先确定风筝的初始形状和旋转中心,然后添加滑块控制旋转角度,最后绘制旋转轨迹。图形应清晰展示风筝的几何结构、旋转变换和动态动画效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。