Year Zoom:几何与函数动态演示
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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
Segment(C, D) → cSegment(D, E) → dSegment(E, F) → eSegment(F, G) → fSegment(G, H) → gSegment(H, I) → hSegment(I, J) → iSegment(J, K) → jSegment(K, L) → kSegment(M, B) → mSegment(L, M) → lSequence(375 - ((375 - Element[rightmonthpoint, Element[list1, 6]] - 5) / 10 * i), i, 0, 10) → rightmonthSequence((Element[rightmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] + 0.2) * i), i, 0, 1, 0.1) → rightdaySegment(A, C) → bElement({b, c, d, e, f, g, h, i, j, k, l, m}, Element[list1, 6]) → monthlengthSequence(Point[{Element[leftmonthpoint, Element[list1, 6]] + i, 0}], i, 0, monthlength) → daypointsSequence(Point[{x(Element[daypoints, Element[list1, 5]]) + i, 0}], i, 0, 1.0416666666666667, 0.04167) → hourpointsSequence((Element[rightday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 2]) + 0.01) * i), i, 0, 1, 0.1) → righthourSequence((x(Element[hourpoints, Element[list1, 4] + 1]) + (1 / ((24 * 60)) * i), 0), i, 0, 60) → minutepointsJoin({{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]}) → rightminuteSequence(-10 + ((Element[leftmonthpoint, Element[list1, 6]] + 5) / 10 * i), i, 0, 10) → leftmonthSequence((Element[leftmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] - 1.2) * i), i, 0, 1, 0.1) → leftdaySequence((Element[leftday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 1]) - 0.01) * i), i, 0, 1, 0.1) → lefthourJoin({{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]}) → leftminuteJoin({{-10}, leftmonth, {Element[leftmonth, 11], Element[leftmonth, 11]}, leftday, {Element[leftday, 11], Element[leftday, 11], Element[leftday, 11], Element[leftday, 11]}, lefthour, leftminute}) → leftSegment(A, B) → aElement({"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"}, Element[list1, 6]) → monthnameJoin({{375}, rightmonth, {Element[rightmonth, 11], Element[rightmonth, 11]}, rightday, {Element[rightday, 11], Element[rightday, 11], Element[rightday, 11], Element[rightday, 11]}, righthour, rightminute}) → rightSequence(Segment[Element[daypoints, i], Element[daypoints, i + 1]], i, 1, monthlength) → list2Element(list2, Element[list1, 5]) → daysegmentElement(list1, 5) → daytextSegment(Element[hourpoints, 1], Element[hourpoints, 13]) → amsegmentSegment(Element[hourpoints, 13], Element[hourpoints, 25]) → pmsegmentSegment(Element[hourpoints, Element[list1, 4] + 1], Element[hourpoints, Element[list1, 4] + 2]) → hoursegmentIf(Mod[Element[list1, 4], 12] ≟ 0, 12, Mod[Element[list1, 4], 12]) → hourIf(Element[list1, 4] < 12, "AM", "PM") → amorpmSequence(If[i < 11, Text["0" + (i - 1), (x(Element[minutepoints, i]), 4)], Text[i - 1, (x(Element[minutepoints, i]), 4)]], i, 1, 60) → minutenumbersElement(left, step) → leftboundElement(right, step) → rightboundLength(left) → leftlengthLength(right) → rightlengthSegment(Element[minutepoints, Element[list1, 3] + 1], Element[minutepoints, Element[list1, 3] + 2]) → minutesegmentElement(minutenumbers, Element[list1, 3] + 1) → minuteSequence(Text[If[Mod[12 + i, 12] ≟ 0, 12, Mod[12 + i, 12]], (x(Element[hourpoints, 1 + i]) - 0.0005, 4)], i, 0, 24) → hournumbersSequence(Text[i, (x(Element[daypoints, 1]) - 0.5 + i, 5)], i, 1, monthlength) → list3Midpoint(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。