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使用GeoGebra计算立方体和长方体的表面积

使用GeoGebra计算立方体和长方体的表面积
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2022-11-30 14:29
所属专题 Wiederholung: Quader und Würfel
本范例演示如何利用GeoGebra工具计算立方体和长方体的表面积。核心数学概念包括表面积公式、几何体表面积计算及长方体与立方体的区别。作图要点包括使用GeoGebra命令如Remove、Shuffle、Sequence、Flatten、Element、Polygon、Prism等构建几何对象，并通过调整参数观察表面积变化。适合小学五年级至六年级学生，用于理解立体几何表面积计算及公式应用。

GeoGebra 命令及参数

  1. Remove(Join[Join[Sequence[Sequence[Sequence[{i, j, k}, k, j, 6], j, i, 6], i, 2, 6]]], Sequence[{a, a, a}, a, 1, 6]) → randomTripelUnique
  2. Shuffle(Zip[Shuffle[a], a, randomTripelUnique]) → randomTripleUniqueShuffle, {{4, 5, 3}, {2, 4, 2}, {3, 5, 6}, {4, 2, 6}, {3, 4, 6}, {4, 3, 4}, {4, 4, 6}, {4, 5, 4}, {6, 6, 3}, {3, 4, 3}, {5, 5, 3}, {2, 2, 5}, {5, 6, 6}, {6, 5, 2}, {2, 4, 4}, {2, 3, 4}, {5, 2, 5}, {4, 6, 5}, {6, 6, 4}, {2, 2, 3}, {5, 5, 6}, {6, 3, 3}, {4, 2, 5}, {3, 3, 2}, {3, 2, 5}, {6, 2, 3}, {5, 3, 3}, {2, 6, 6}, {5, 5, 4}, {6, 2, 2}}
  3. Sequence(Element[randomTripleUniqueShuffle(i), 3], i, 1, Length[randomTripleUniqueShuffle]) → randomc
  4. Sequence(Element[randomTripleUniqueShuffle(i), 2], i, 1, Length[randomTripleUniqueShuffle]) → randomb
  5. Flatten(Sequence[Shuffle[{"Quader", "Quader", "Quader", "Würfel"}], i, 1, 30]) → randomNosForX
  6. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  7. Sequence(Element[randomTripleUniqueShuffle(i), 1], i, 1, Length[randomTripleUniqueShuffle]) → randoma
  8. Element(randoma, Mod[questionCount, Length[randoma]] + 1) → numa
  9. If(numX ≟ "Würfel", numa, Element[randomc, Mod[questionCount, Length[randomc]] + 1]) → numc
  10. If(numX ≟ "Würfel", numa, Element[randomb, Mod[questionCount, Length[randomb]] + 1]) → numb
  11. Textfield(aInput) → InputBox1
  12. Textfield(bInput) → InputBox2
  13. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  14. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {5, 6, 2, 0, 5, 4, 6, 2, 1, 0, 8, 1, 0, 4, 7, 4, 7, 9, 7, 0, 0, 2, 6, 6, 3, 0, 7, 8, 7, 10, 10, 3, 5, 1, 1, 5, 2, 0, 6, 4, 6, 3, 1, 1, 3, 8, 2, 3, 9, 3, 1, 8, 7, 9, 0, 6, 10, 10, 0, 8, 9, 7, 6, 5, 7, 3, 0, 6, 7, 7, 0, 0, 8, 1, 9, 5, 2, 5, 4, 0, 3, 4, 0, 1, 5, 9, 1, 7, 9, 8, 6, 5, 0, 5, 2, 6, 4, 7, 1, 3}
  15. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  16. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  17. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  18. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  19. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  20. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  21. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  22. Point(Circle[A, numa]) → B
  23. Segment(A, B) → g
  24. Segment(B, C) → h
  25. Segment(C, D) → i
  26. Segment(D, E) → j
  27. Polygon(D, C, B, A) → v1, m, n, p, q
  28. Prism(v1, numc) → a, F, KanteDF, KanteCG, KanteBH, KanteEI, KanteFG, KanteGH, KanteHI, KanteFI, G, H, I, FlächeCDFG, FlächeBCGH, FlächeBEIH, FlächeDEIF, FlächeFGHI
  29. Net(a, k) → l, J, S, T, U, V, W, FlächeJKLM, FlächeJKON, FlächeKLQP, FlächeLMSR, FlächeJMTU, K, FlächeNOVW, KanteJK, KanteKL, KanteLM, KanteJM, KanteJN, KanteNO, KanteKO, KanteKP, KantePQ, L, KanteLQ, KanteLR, KanteRS, KanteMS, KanteMT, KanteTU, KanteJU, KanteOV, KanteVW, KanteNW, M, N, O, P, Q, R