立方体分割金字塔

立方体分割金字塔
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2021-12-16 08:40
①本范例演示将立方体分割成多个金字塔的过程;②涉及的核心数学概念包括立体几何、全等、方程、特殊点、中位线、向量等;③作图要点提炼自构造摘要,使用了点、立方体、中点、线段、金字塔、圆、交点、向量、平移等GeoGebra命令与对象;④适合高中阶段学习立体几何、空间想象能力及几何作图的学生。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD_{1}, edgeAB_{1}, edgeBC_{1}, edgeCD_{1}, edgeAE_{1}, edgeDH_{1}, edgeEH_{1}, edgeEF_{1}, E, edgeBF_{1}, edgeFG_{1}, edgeCG_{1}, edgeGH_{1}, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Midpoint(edgeFG_{1}) → I
  4. Midpoint(edgeEF_{1}) → J
  5. Midpoint(edgeCG_{1}) → K
  6. Midpoint(edgeCD_{1}) → L
  7. Midpoint(edgeAD_{1}) → M
  8. Midpoint(edgeAE_{1}) → N
  9. Segment(F, C) → f
  10. Segment(F, A) → g
  11. Segment(C, A) → h
  12. Segment(F, H) → i
  13. Segment(H, C) → j
  14. Segment(H, A) → k
  15. Pyramid(C, H, A, D) → b, faceACH, edgeAD, faceCDH, faceADH, faceACD, edgeCH_{1}, edgeAH_{1}, edgeAC_{1}, edgeCD, edgeDH
  16. Pyramid(H, F, A, E) → c, faceAFH, edgeAE, faceEFH, faceAEF, faceAEH, edgeFH_{1}, edgeAF_{1}, edgeAH, edgeEH, edgeEF
  17. Pyramid(F, H, C, G) → d, faceCFH, edgeCG, faceFGH, faceCGH, faceCFG, edgeFH, edgeCH, edgeCF_{1}, edgeFG, edgeGH
  18. Pyramid(A, C, F, B) → e, faceACF, edgeBF, faceABC, faceBCF, faceABF, edgeAC, edgeCF, edgeAF, edgeAB, edgeBC
  19. Circle(A, l, xOyPlane) → q
  20. Intersect(p, q) → O, P
  21. Vector(A, O) → u
  22. Vector(A, P) → v
  23. Translate(c, u) → c'
  24. Translate(d, v) → d'
  25. Intersect(q, yAxis, 2) → Q
  26. Vector(A, Q) → w
  27. Translate(b, w) → b'
  28. Intersect(r, q) → R, S
  29. Vector(A, S) → m
  30. Translate(e, m) → e'

AI 绘图提示语参考

在三维空间中先构造一个立方体,并标出其顶点与若干面。取与立方体相关的多条棱:先求若干特定棱的中点,再连接给定的顶点组合,形成三棱锥的公共切割关系。随后用这些顶点与立方体内部点(由中点与连线引出)分别作四个三棱锥:以立方体的相应顶点为底边端点,另一个顶点作为顶点,得到拼合成“立方体到金字塔”的分割外形。沿用对称位置的圆与其与坐标轴的交点,确定平移所需的方向,并将两个相应三棱锥做对应的平移复制。
以上提示语为根据原始绘图命令整理而来,仅供参考。