动物园中的混沌现象

几何画板及绘图内容加载中，请稍等……

2023-03-14 18:44

所属专题 Wiederholung: absolute, relative & prozentuelle Häufigkeit

这个范例演示了如何通过 GeoGebra 构造和模拟动物园中动物的随机移动和分布，形成混沌现象。涉及的核心数学概念包括概率统计和数据分析。作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Join, Sequence, If, Remove, Textfield, Max, Polygon, Shuffle, Element, Append, Translate, IndexOf, Sum, Point, OrthogonalLine, Midpoint；对象：PosCorrectIndex5, PosCorrectIndex4, PosCorrectIndex3, PosCorrectIndex2, PosCorrectIndex1, listPosCorrectText, questionCount, A4GeringstenHäufigsten, LPD5, A5WenigerMehr, LPD4, AAufgabenText, LPD3, A5Vielfaches, LPD2, LPD1, IndexA12, IndexList, Index, StartA, StartListe, ZwischenFolge, ElefantenA2, RowEis, AAufgaben, IndexA11, A3AufgabenText, Dropdown4, A3Aufgaben, correct04, A4Aufgabe3, A4RightSide, sol4, b, a, aInput, InputBox1, IndexA1TrueFalse, erlaubteZeichen, inputCorrect01。适合的学段或用途：本范例适合小学5-6年级学生，用于学习和实践概率统计的基本概念，如绝对频率的计算。

GeoGebra 命令及参数

Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * A4GeringstenHäufigsten(i)) * ".}$"), i, 1, CountIf[x ≠ "", A4GeringstenHäufigsten]]}) → LPD5
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * A5WenigerMehr(i)) * "}$"), i, 1, CountIf[x ≠ "", A5WenigerMehr]]}) → LPD4
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AAufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "", AAufgabenText]]}) → LPD3
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * A5Vielfaches(i)) * "}$"), i, 1, CountIf[x ≠ "", A5Vielfaches]]}) → LPD2
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AAufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "", AAufgabenText]]}) → LPD1
Sequence(Random[5, 7], i, 1, 100) → IndexA12, {5, 5, 6, 6, 5, 5, 6, 6, 5, 6, 6, 5, 5, 5, 5, 6, 5, 7, 7, 7, 7, 7, 6, 5, 6, 5, 7, 5, 7, 7, 6, 5, 6, 6, 6, 5, 7, 6, 6, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 5, 5, 7, 5, 6, 5, 6, 6, 7, 6, 7, 7, 6, 6, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 5, 6, 7, 5, 5, 6, 7, 6, 7, 5, 6, 6, 7, 7, 7, 7, 6, 5, 6, 5, 6, 6, 5, 7, 6, 5}
Sequence(Random[1, 4], i, 1, 100) → IndexList, {1, 4, 2, 3, 2, 4, 1, 2, 2, 4, 4, 1, 2, 3, 4, 1, 1, 1, 4, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 2, 4, 1, 3, 3, 1, 1, 3, 4, 2, 2, 1, 2, 3, 1, 1, 4, 2, 4, 1, 2, 4, 2, 3, 3, 2, 4, 3, 2, 2, 2, 1, 4, 2, 2, 2, 4, 3, 4, 4, 2, 1, 1, 3, 1, 4, 3, 3, 3, 3, 2, 4, 3, 4, 4, 2, 4, 4, 3, 1, 2, 3, 3, 2, 1, 4, 3, 3, 1, 1}
If(StartA, StartListe, Shuffle[Shuffle[Sequence[i, i, 8, 15]]]) → ZwischenFolge
Remove(Sequence[If[Mod[ZwischenFolge(Index + 1 + i), 2] ≟ 0, ZwischenFolge(Index + 1 + i) / 2, 0], i, 0, 10], Sequence[0, i, 1, 10]) → ElefantenA2
If(StartA, StartListe, Join[{{ElefantenA2(1)}, ZwischenFolge \ {ZwischenFolge(1)}}]) → RowEis
Sequence(RowEis(i), i, 1, 7) → AAufgaben, {5, 13, 12, 3, 4, 15, 26}
Sequence(Random[1, 4], i, 1, 100) → IndexA11, {2, 4, 4, 1, 2, 4, 4, 3, 2, 2, 1, 3, 1, 4, 2, 4, 3, 3, 1, 4, 3, 3, 4, 2, 3, 2, 1, 2, 4, 4, 3, 4, 1, 3, 2, 3, 4, 1, 4, 3, 3, 4, 2, 3, 3, 4, 1, 2, 3, 4, 3, 1, 3, 1, 3, 4, 3, 1, 1, 4, 1, 4, 3, 1, 1, 1, 1, 1, 3, 1, 2, 2, 2, 4, 2, 1, 1, 4, 4, 3, 3, 1, 1, 3, 4, 1, 3, 1, 2, 3, 3, 3, 1, 2, 2, 3, 4, 1, 1, 3}
Remove(AAufgabenText, {AAufgabenText(IndexA11(questionCount)), AAufgabenText(IndexA12(questionCount))}) → A3AufgabenText
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * A3AufgabenText(i)) * ".}$"), i, 1, CountIf[x ≠ "", A3AufgabenText]]}) → Dropdown4
Remove(AAufgaben, {AAufgaben(IndexA11(questionCount)), AAufgaben(IndexA12(questionCount))}) → A3Aufgaben
Textfield(aInput) → InputBox1
Sequence(RandomElement[{true, true, false, false, false}], i, 1, 100) → IndexA1TrueFalse, {false, false, false, true, false, false, false, true, false, true, false, false, false, false, true, false, true, false, false, false, false, false, false, false, false, false, true, true, true, false, false, true, true, false, false, true, true, false, false, true, true, false, false, true, false, true, true, false, false, false, true, true, false, false, false, true, true, true, false, false, true, false, false, true, false, false, true, true, false, true, false, false, false, false, false, false, true, false, false, true, false, true, false, false, false, false, true, false, false, false, true, false, true, false, true, true, false, true, true, true}
If(IndexA1TrueFalse(questionCount), AAufgaben(IndexA11(questionCount)) + AAufgaben(IndexA12(questionCount)), AAufgaben(IndexA11(questionCount))) → A1Angabe
Textfield(bInput) → InputBox2
Textfield(cInput) → InputBox3
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AAufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "", AAufgabenText]]}) → Dropdown2
Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AAufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "", AAufgabenText]]}) → Dropdown5
If(StartA, false, AAufgaben(IndexA11(questionCount)) > AAufgaben(IndexA12(questionCount))) → sol2
Join({{"$\textsf{Wähle aus!}$"}, ListeEis}) → SelectIce
Max(AAufgaben) → H1
Max(Remove[AAufgaben, {H1}]) → H2
Max(Remove[AAufgaben, {H1, H2}]) → H3
Max(Remove[AAufgaben, {H1, H2, H3}]) → H4
Max(Remove[AAufgaben, {H1, H2, H3, H4}]) → H5
If(Index ≟ 1, H1, Index ≟ 2, H2, Index ≟ 3, H3, Index ≟ 4, H5) → Sol1
If(a, FBPos1, FBPos2) → PtopLeftCornerFeedback
Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → Feedback5, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 9, 1, 1, 8, 10, 3, 4, 3, 3, 2, 10, 7, 5, 5, 2, 2, 4, 1, 8, 7, 2, 3, 0, 9, 8, 10, 6, 8, 2, 10, 8, 5, 5, 10, 5, 1, 0, 3, 5, 5, 6, 1, 1, 4, 6, 9, 2, 9, 10, 4, 7, 10, 3, 5, 0, 5, 2, 6, 4, 7, 7, 2, 7, 4, 2, 8, 5, 5, 10, 1, 2, 10, 9, 9, 5, 2, 6, 8, 8, 9, 7, 10, 6, 9, 10, 9, 5, 4, 0, 3, 2, 3, 1, 6, 10, 2, 9, 4, 9}
Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {7, 8, 4, 10, 1, 7, 7, 4, 1, 1, 1, 3, 6, 10, 7, 3, 9, 6, 4, 4, 8, 4, 7, 9, 4, 6, 5, 0, 6, 7, 3, 6, 2, 9, 9, 10, 9, 5, 7, 10, 7, 3, 9, 9, 0, 4, 2, 1, 1, 10, 6, 5, 1, 3, 10, 6, 8, 0, 8, 5, 3, 10, 1, 9, 3, 1, 4, 6, 0, 10, 6, 0, 0, 10, 8, 1, 2, 9, 7, 1, 7, 5, 10, 3, 5, 6, 2, 8, 9, 0, 4, 5, 6, 8, 6, 6, 0, 1, 5, 9}
Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
Sequence(Random[30, 45], i, 1, 30) → l1, {42, 42, 37, 42, 36, 34, 37, 34, 41, 30, 37, 35, 30, 31, 42, 37, 44, 35, 36, 39, 35, 43, 39, 42, 35, 35, 43, 31, 41, 31}
Polygon(A, B, C, D) → v1, a_{1}, b_{1}, c, d
Textfield(dInput) → InputBox4
Textfield(eInput) → InputBox5
Sequence(Pos1 + (i * (dx, 0)), i, 0, 3) → InputPos
Polygon(CornerFeedback, CornerFeedback + (length, 0), CornerFeedback + (length, height), CornerFeedback + (0, height)) → Feedback1, cornerfeedback, g, h, i
Translate(Feedback1, (dx, 0)) → Feedback2
Translate(Feedback2, (dx, 0)) → Feedback3
Translate(Feedback3, (dx, 0)) → Feedback4
Max(Remove[AAufgaben, {H1, H2, H3, H4, H5}]) → H6
Max(Remove[AAufgaben, {H1, H2, H3, H4, H5, H6}]) → H7
IndexOf(A5Aufgabe(1), AAufgaben) → Index5
If(AAufgaben(IndexA11(questionCount)) < AAufgaben(IndexA12(questionCount)), 1, false) → ZZZ
Polygon(Corner[InputBox1, 1] - (dx00, dy00), (x(Corner[InputBox1, 3] + (dx00, dy00 + dy01)), y(Corner[InputBox1, 1] - (dx00, dy00))), Corner[InputBox1, 3] + (dx00, dy00 + dy01), (x(Corner[InputBox1, 1] - (dx00, dy00)), y(Corner[InputBox1, 3] + (dx00, dy00 + dy01)))) → v2, f, j, k, l
Polygon(Corner[InputBox2, 1] - (dx00, dy00), (x(Corner[InputBox2, 3] + (dx00, dy00 + dy01)), y(Corner[InputBox2, 1] - (dx00, dy00))), Corner[InputBox2, 3] + (dx00, dy00 + dy01), (x(Corner[InputBox2, 1] - (dx00, dy00)), y(Corner[InputBox2, 3] + (dx00, dy00 + dy01)))) → v3, m, n, p, q
Polygon(Corner[InputBox3, 1] - (dx00, dy00), (x(Corner[InputBox3, 3] + (dx00, dy00 + dy01)), y(Corner[InputBox3, 1] - (dx00, dy00))), Corner[InputBox3, 3] + (dx00, dy00 + dy01), (x(Corner[InputBox3, 1] - (dx00, dy00)), y(Corner[InputBox3, 3] + (dx00, dy00 + dy01)))) → v4, r, s, t, e
Sum(AAufgaben) → SummeTiere
If(questionCount ∈ {1, 2, 4, 5} ∧ b, CPos2, questionCount ≟ 3, CPos3, CPos1) → CPos
Point(xAxis) → H
OrthogonalLine(H, xAxis) → f_1
Point(yAxis) → I
OrthogonalLine(I, yAxis) → g_1
Midpoint(J, K) → L
OrthogonalLine(L, g_1) → h_1
Midpoint(M, K) → N
OrthogonalLine(N, f_1) → i_1

AI 绘图提示语参考

绘制一个“动物在动物园里的混乱运动”概率练习版面：用一个多边形矩形作为反馈区域，并在其中显示基于数值比较得到的高亮角（通过计算五个候选最大值并按索引选择对应结果），同时提供上下文文字区与下拉选择区。画面中还要有用于输入的三个文本框，配合一个选择下拉菜单和一个结果区域。最后布置若干几何标记表示随机移动序列的选取与去重逻辑所对应的站位变化，让视图呈现从随机数生成到反馈框定位的连贯过程。

以上提示语为根据原始绘图命令整理而来，仅供参考。