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矩形、三角形、梯形、圆形、扇形面积计算与无限问题

矩形、三角形、梯形、圆形、扇形面积计算与无限问题
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2017-05-07 13:58
圆几何作图
①本范例演示了如何使用 GeoGebra 计算并可视化矩形、三角形、梯形、圆形和扇形的面积，并探讨无限问题。②涉及核心数学概念包括面积公式、几何作图、随机变量和三角函数。③作图要点：使用了 Random, Segment, Line, OrthogonalLine, Intersect, Circle, Point, Midpoint, Polygon, PointIn, Textfield, Cell, Distance, Vector, Rotate, CircleArc, Angle 等命令和对象。④适合高中及以上数学学习者，用于几何计算和概念理解。

GeoGebra 命令及参数

  1. Random(14, 22) → l
  2. Random(0, 20) → e
  3. Random(-2, 8) → d
  4. Random(8, 13) → c
  5. Random(0, 5) → b
  6. Random(0, 5) → a
  7. Segment(A, B) → f
  8. Line(D, f) → p
  9. OrthogonalLine(B, p) → s
  10. Intersect(p, s) → G
  11. OrthogonalLine(A, p) → r
  12. Intersect(p, r) → E
  13. Circle(E, G) → q
  14. Point(q) → secpoint1
  15. Midpoint(A, B) → C
  16. Polygon(A, D, B) → poly1, b_1, a_1, d_1
  17. OrthogonalLine(D, f) → g
  18. Line(A, B) → h
  19. OrthogonalLine(D, h) → i
  20. Intersect(h, i) → F
  21. Segment(D, F) → j
  22. Segment(A, F) → k
  23. PointIn(poly1) → Pointpoly1
  24. Textfield(area) → InputBox1
  25. Random(1, 14) → A16
  26. Cell(2, A16) → B16
  27. Polygon(A, E, G, B) → poly2, a_2, e_1, g_1, b_2
  28. PointIn(poly2) → Pointpoly2_1
  29. PointIn(poly2) → Pointpoly2
  30. Textfield(v) → InputBox2
  31. Distance(E, G) → w
  32. Vector(E, G) → u_1
  33. PointIn(q) → Pointq
  34. Segment(secpoint1, E) → leg1
  35. Rotate(secpoint1, randomangle, E) → secpoint2
  36. Segment(secpoint2, E) → leg2
  37. CircleArc(E, secpoint1, secpoint2) → sectorarc
  38. Angle(secpoint1, E, secpoint2) → sectoranglelabel
  39. Segment(TrapA, TrapB) → Trapbase
  40. Segment(TrapC, TrapB) → Trapright
  41. Line(TrapC, Trapbase) → Traptopparallel
  42. Segment(TrapD, TrapA) → Trapleft
  43. Segment(TrapD, TrapC) → traptop
  44. Midpoint(TrapA, TrapB) → trapbasemidpoint
  45. Distance(trapbasemidpoint, traptop) → distancetrapbasemidpointtraptop
  46. OrthogonalLine(trapbasemidpoint, Trapbase) → i_1
  47. Intersect(traptop, i_1) → traptopmidpoint
  48. Segment(traptopmidpoint, trapbasemidpoint) → trapperpendicularheightline
  49. Polygon(TrapA, TrapB, TrapC, TrapD) → poly3, trapa, trapb, trapc, trapd
  50. Line(G, E) → j_1
  51. Intersect(q, j_1) → H, I
  52. Segment(I, G) → diameter