Year Zoom:几何与函数动态演示

Year Zoom:几何与函数动态演示
几何画板及绘图内容加载中,请稍等……
2015-03-04 01:57
Year Zoom 范例展示了几何图形与函数图像的动态交互现象。核心数学概念包括几何作图、函数图像和序列与系列。作图要点涉及使用 GeoGebra 命令如 Segment、Sequence、Element、Join、If、Length、Midpoint 等对象进行构造。该范例适合高中或大学数学课程,用于理解几何与函数的结合应用。

GeoGebra 命令及参数

  1. Segment(C, D) → c
  2. Segment(D, E) → d
  3. Segment(E, F) → e
  4. Segment(F, G) → f
  5. Segment(G, H) → g
  6. Segment(H, I) → h
  7. Segment(I, J) → i
  8. Segment(J, K) → j
  9. Segment(K, L) → k
  10. Segment(M, B) → m
  11. Segment(L, M) → l
  12. Sequence(375 - ((375 - Element[rightmonthpoint, Element[list1, 6]] - 5) / 10 * i), i, 0, 10) → rightmonth
  13. Sequence((Element[rightmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] + 0.2) * i), i, 0, 1, 0.1) → rightday
  14. Segment(A, C) → b
  15. Element({b, c, d, e, f, g, h, i, j, k, l, m}, Element[list1, 6]) → monthlength
  16. Sequence(Point[{Element[leftmonthpoint, Element[list1, 6]] + i, 0}], i, 0, monthlength) → daypoints
  17. Sequence(Point[{x(Element[daypoints, Element[list1, 5]]) + i, 0}], i, 0, 1.0416666666666667, 0.04167) → hourpoints
  18. Sequence((Element[rightday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 2]) + 0.01) * i), i, 0, 1, 0.1) → righthour
  19. Sequence((x(Element[hourpoints, Element[list1, 4] + 1]) + (1 / ((24 * 60)) * i), 0), i, 0, 60) → minutepoints
  20. Join({{Element[righthour, 11], Element[righthour, 11], Element[righthour, 11]}, Sequence[(Element[righthour, 11] * (1 - i)) + ((x(Element[minutepoints, Element[list1, 3] + 2]) + 0.0001) * i), i, 0, 1, 0.1]}) → rightminute
  21. Sequence(-10 + ((Element[leftmonthpoint, Element[list1, 6]] + 5) / 10 * i), i, 0, 10) → leftmonth
  22. Sequence((Element[leftmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] - 1.2) * i), i, 0, 1, 0.1) → leftday
  23. Sequence((Element[leftday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 1]) - 0.01) * i), i, 0, 1, 0.1) → lefthour
  24. Join({{Element[lefthour, 11], Element[lefthour, 11], Element[lefthour, 11]}, Sequence[(Element[lefthour, 11] * (1 - i)) + ((x(Element[minutepoints, Element[list1, 3] + 1]) - 0.0001) * i), i, 0, 1, 0.1]}) → leftminute
  25. Join({{-10}, leftmonth, {Element[leftmonth, 11], Element[leftmonth, 11]}, leftday, {Element[leftday, 11], Element[leftday, 11], Element[leftday, 11], Element[leftday, 11]}, lefthour, leftminute}) → left
  26. Segment(A, B) → a
  27. Element({"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"}, Element[list1, 6]) → monthname
  28. Join({{375}, rightmonth, {Element[rightmonth, 11], Element[rightmonth, 11]}, rightday, {Element[rightday, 11], Element[rightday, 11], Element[rightday, 11], Element[rightday, 11]}, righthour, rightminute}) → right
  29. Sequence(Segment[Element[daypoints, i], Element[daypoints, i + 1]], i, 1, monthlength) → list2
  30. Element(list2, Element[list1, 5]) → daysegment
  31. Element(list1, 5) → daytext
  32. Segment(Element[hourpoints, 1], Element[hourpoints, 13]) → amsegment
  33. Segment(Element[hourpoints, 13], Element[hourpoints, 25]) → pmsegment
  34. Segment(Element[hourpoints, Element[list1, 4] + 1], Element[hourpoints, Element[list1, 4] + 2]) → hoursegment
  35. If(Mod[Element[list1, 4], 12] ≟ 0, 12, Mod[Element[list1, 4], 12]) → hour
  36. If(Element[list1, 4] < 12, "AM", "PM") → amorpm
  37. Sequence(If[i < 11, Text["0" + (i - 1), (x(Element[minutepoints, i]), 4)], Text[i - 1, (x(Element[minutepoints, i]), 4)]], i, 1, 60) → minutenumbers
  38. Element(left, step) → leftbound
  39. Element(right, step) → rightbound
  40. Length(left) → leftlength
  41. Length(right) → rightlength
  42. Segment(Element[minutepoints, Element[list1, 3] + 1], Element[minutepoints, Element[list1, 3] + 2]) → minutesegment
  43. Element(minutenumbers, Element[list1, 3] + 1) → minute
  44. Sequence(Text[If[Mod[12 + i, 12] ≟ 0, 12, Mod[12 + i, 12]], (x(Element[hourpoints, 1 + i]) - 0.0005, 4)], i, 0, 24) → hournumbers
  45. Sequence(Text[i, (x(Element[daypoints, 1]) - 0.5 + i, 5)], i, 1, monthlength) → list3
  46. Midpoint(minutesegment) → X

AI 绘图提示语参考

绘制一个动态的日历时间可视化图形,展示月份、日期、小时和分钟的几何关系。左侧显示过去月份的日期和时间刻度,右侧显示当前月份的日期和时间刻度,中间通过函数图形连接。使用不同颜色和线条粗细区分月份、日期、小时和分钟,并标注数字。整体呈现为一个完整的年份时间周期,强调几何构造与函数图形的动态交互。
以上提示语为根据原始绘图命令整理而来,仅供参考。