给定表面积创建长方体

给定表面积创建长方体
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2020-10-09 00:44
①本范例演示如何根据给定表面积创建长方体;②涉及的核心数学概念包括表面积计算、立体几何、几何构造;③作图要点:使用了Point, Ray, Prism, Net, Sequence, Translate, Vector, Mirror, RandomElement, Mode, IndexOf, Element, CountIf, If等GeoGebra命令和对象;④适合高中数学课堂,用于教学和探索长方体表面积与几何特性。

GeoGebra 命令及参数

  1. Point(Segment[(0, 0, 0), (0, 0, 9)]) → A_1
  2. Ray((0, 0, 0), (1, 0, 0)) → f
  3. Ray((0, 0, 0), (0, 1, 0)) → g
  4. Ray((0, 0, 0), (0, 0, 1)) → h
  5. Prism(E, A, D, B, C) → d, F, edgeAE, edgeAD, edgeBD, edgeBE, edgeCE, edgeAF, edgeDG, edgeBH, edgeCF, edgeFG, G, edgeGH, edgeCH, H, faceADBE, faceAECF, faceADGF, faceBDGH, faceBECH, faceCFGH
  6. Net(d, openclose) → i, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  7. Sequence(Segment[(i, 0, 0), (i, WIDTH, 0)], i, 1, LENGTH - 1, 1) → L_1
  8. Translate(L_1, Vector[A, F]) → L_2
  9. Sequence(Segment[(0, i + 1, 0), (LENGTH, i + 1, 0)], i, 0, WIDTH - 2) → L_3
  10. Translate(L_3, Vector[A, F]) → L_4
  11. Vector(M, V) → u
  12. Sequence((x(M) + i, y(M), z(M)), i, 1, LENGTH - 1, 1) → L_5
  13. Translate(L_5, u) → L_6
  14. Sequence(Segment[Element[L_5, i], Element[L_6, i]], i, 1, LENGTH - 1) → L_7
  15. Sequence((x(M), y(M) + (i * y(u) / WIDTH), z(M) + (i * z(u) / WIDTH)), i, 1, WIDTH - 1, 1) → L_8
  16. Vector(V, U) → v
  17. Translate(L_8, v) → L_9
  18. Sequence(Segment[Element[L_8, i], Element[L_9, i]], i, 1, WIDTH - 1) → L_{10}
  19. Vector(A, O) → w
  20. Sequence((x(A) + (i * x(w) / HEIGHT), y(A), z(A) + (i * z(w) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{11}
  21. Vector(O, P) → l
  22. Translate(L_{11}, l) → L_{12}
  23. Sequence(Segment[Element[L_{11}, i], Element[L_{12}, i]], i, 1, HEIGHT - 1) → L_{13}
  24. Sequence((x(O), y(O) + (i * y(l) / WIDTH), z(O) + (i * z(l) / WIDTH)), i, 1, WIDTH - 1, 1) → L_{14}
  25. Translate(L_{14}, Vector[(-w)]) → L_{15}
  26. Sequence(Segment[Element[L_{14}, i], Element[L_{15}, i]], i, 1, WIDTH - 1) → L_{16}
  27. Mirror(L_{13}, k) → L_{17}
  28. Mirror(L_{16}, k) → L_{18}
  29. Vector(D, Q) → m
  30. Sequence((x(B) + (i * x(v) / LENGTH), y(B), z(B)), i, 1, LENGTH - 1, 1) → L_{19}
  31. Translate(L_{19}, m) → L_{20}
  32. Sequence(Segment[Element[L_{19}, i], Element[L_{20}, i]], i, 1, LENGTH - 1) → L_{21}
  33. Sequence((x(B), y(B) + (i * y(m) / HEIGHT), z(B) + (i * z(M) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{22}
  34. Translate(L_{22}, v) → L_{23}
  35. Sequence(Segment[Element[L_{22}, i], Element[L_{23}, i]], i, 1, HEIGHT - 1) → L_{24}
  36. Mirror(L_{21}, n) → L_{25}
  37. Mirror(L_{24}, n) → L_{26}
  38. RandomElement(l2) → a
  39. Mode(l2) → l3
  40. IndexOf(a, l2) → e
  41. Element(l2, e + 1) → j
  42. Element(l2, e + 2) → o
  43. Element(l2, e + 3) → p
  44. CountIf(x ≟ a, l2) → q
  45. If(q ≟ 1, "There is 1 solution here.", q ≟ 2, "There are 2 solutions here.", q ≟ 3, "There are 3 solutions here.") → text2

AI 绘图提示语参考

绘制一个给定表面积的矩形棱柱,展示其三维实体、展开图及内部网格线。先建立三维坐标系,从原点出发沿三个轴方向作射线,确定棱柱的底面顶点和高度,构造出棱柱体及其六个面。随后生成棱柱的展开图,并沿棱柱的长、宽、高方向绘制等距网格线,覆盖所有面。最后随机选取一个网格交点,统计该点在整个网格中出现的次数,并显示对应的解的数量提示文本。整体图形包含棱柱、展开图、网格线及动态文本标注。
以上提示语为根据原始绘图命令整理而来,仅供参考。