积极 AI Logo 积极 AI

混合任务 - deltoid

混合任务 - deltoid
几何画板及绘图内容加载中，请稍等……
2024-07-10 20:52
多边形角几何作图
所属专题 Deltoid - Flächeninhalt und Umkehraufgaben
这个范例演示了 deltoid 图形的构造与性质。涉及的核心数学概念包括多边形、角度计算和公式变形。构造过程中用到了 Join, Sequence, Element, Zip, If, Segment, Textfield, Polygon, Append, Remove, Intersect, Angle, NumberSeparationComma, Text 等 GeoGebra 命令和对象。适合 7-8 年级学生，用于练习解决四边形相关的逆向问题。

GeoGebra 命令及参数

  1. Join({Sequence[1, 15], {20, 30, 40, 50}}) → listPool
  2. Sequence(RandomElement[listPool], m, 1, 110) → randomNosForX, {1, 30, 11, 11, 8, 15, 20, 7, 14, 4, 30, 7, 3, 5, 3, 6, 13, 11, 9, 1, 50, 1, 30, 9, 5, 1, 8, 10, 11, 9, 30, 14, 8, 11, 8, 14, 15, 1, 13, 3, 14, 15, 13, 50, 12, 1, 40, 30, 2, 40, 50, 14, 10, 6, 7, 4, 4, 15, 12, 2, 30, 12, 6, 1, 15, 7, 1, 30, 8, 8, 40, 14, 6, 10, 11, 8, 6, 8, 1, 1, 7, 11, 10, 12, 50, 15, 11, 40, 2, 1, 15, 9, 8, 40, 15, 9, 12, 40, 2, 40, 20, 11, 8, 7, 14, 50, 5, 14, 10, 5}
  3. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  4. Zip(RandomElement[listPool \ Join[{{m}, Sequence[1, (floor(m) * (1 - percentage))], Sequence[(ceil(m) * (1 + percentage)), 50]}]], m, randomNosForX) → randomNosForY
  5. If(Defined[numYrandom], numYrandom, floor((numX * 1.5))) → numY
  6. If(numX ≥ numY, P1, P5) → A
  7. If(numX ≥ numY, P3, P7) → C
  8. Segment(A, C) → e1
  9. Sequence(RandomElement[Sequence[0.3, 0.5, 0.01]], m, 1, 110) → randomNosForProp, {0.38000000000000006, 0.31, 0.32, 0.32, 0.3, 0.35000000000000003, 0.47000000000000014, 0.48000000000000015, 0.31, 0.5000000000000001, 0.39000000000000007, 0.35000000000000003, 0.4100000000000001, 0.47000000000000014, 0.37000000000000005, 0.48000000000000015, 0.3, 0.35000000000000003, 0.3, 0.47000000000000014, 0.47000000000000014, 0.4500000000000001, 0.38000000000000006, 0.34, 0.33, 0.38000000000000006, 0.48000000000000015, 0.36000000000000004, 0.46000000000000013, 0.3, 0.4300000000000001, 0.4300000000000001, 0.46000000000000013, 0.4200000000000001, 0.32, 0.36000000000000004, 0.34, 0.36000000000000004, 0.3, 0.37000000000000005, 0.31, 0.32, 0.46000000000000013, 0.4100000000000001, 0.34, 0.34, 0.37000000000000005, 0.4200000000000001, 0.4100000000000001, 0.38000000000000006, 0.46000000000000013, 0.3, 0.4400000000000001, 0.4500000000000001, 0.4100000000000001, 0.4400000000000001, 0.38000000000000006, 0.33, 0.4000000000000001, 0.46000000000000013, 0.4400000000000001, 0.3, 0.46000000000000013, 0.4500000000000001, 0.38000000000000006, 0.4300000000000001, 0.5000000000000001, 0.4100000000000001, 0.31, 0.37000000000000005, 0.4000000000000001, 0.48000000000000015, 0.47000000000000014, 0.31, 0.4500000000000001, 0.35000000000000003, 0.4200000000000001, 0.36000000000000004, 0.36000000000000004, 0.49000000000000016, 0.4500000000000001, 0.4400000000000001, 0.39000000000000007, 0.47000000000000014, 0.4500000000000001, 0.4100000000000001, 0.5000000000000001, 0.36000000000000004, 0.47000000000000014, 0.47000000000000014, 0.48000000000000015, 0.49000000000000016, 0.35000000000000003, 0.32, 0.3, 0.49000000000000016, 0.33, 0.5000000000000001, 0.4100000000000001, 0.3, 0.34, 0.32, 0.4000000000000001, 0.48000000000000015, 0.37000000000000005, 0.35000000000000003, 0.36000000000000004, 0.4100000000000001, 0.4400000000000001, 0.49000000000000016}
  10. If(numX ≥ numY, P4, P8) → D
  11. If(numX ≥ numY, P2, P6) → B
  12. Segment(B, D) → f1
  13. Join(Sequence[Shuffle[{1, 2, 3}], k, 1, 34]) → CaseList
  14. If(Case ≟ 1, numX, Case ≟ 2, numY, numZ) → sol
  15. Textfield(input1) → InputBox1
  16. Textfield(input2) → InputBox2
  17. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  18. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  19. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  20. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  21. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  22. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  23. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  24. Intersect(e1, f1) → E
  25. Angle(A, E, D) → α
  26. NumberSeparationComma((numX * numY)) → numberSeparationZaehler
  27. Text("\scriptsize{\textsf{Skizze ist maßstabsgetreu}}", C + (0, -0.6), false, true, 0, -1) → txtSkizze

AI 绘图提示语参考

画一个 deltoid，首先画出四条线段 e1 和 f1，它们分别连接点 A 和 C，B 和 D。A、B、C、D 的坐标由随机数生成，确保它们满足 deltoid 的性质。接着画出线段 e1 和 f1 的交点 E，并计算角 α。最后，根据给定的 x 和 y 值生成一个矩形，确保矩形的尺寸与 deltoid 相匹配。
以上提示语为根据原始绘图命令整理而来，仅供参考。