立方体分割金字塔
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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
Point(Circle[B, Distance[A, B], Segment[A, B]]) → CCube(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, faceBCGFMidpoint(edgeFG_{1}) → IMidpoint(edgeEF_{1}) → JMidpoint(edgeCG_{1}) → KMidpoint(edgeCD_{1}) → LMidpoint(edgeAD_{1}) → MMidpoint(edgeAE_{1}) → NSegment(F, C) → fSegment(F, A) → gSegment(C, A) → hSegment(F, H) → iSegment(H, C) → jSegment(H, A) → kPyramid(C, H, A, D) → b, faceACH, edgeAD, faceCDH, faceADH, faceACD, edgeCH_{1}, edgeAH_{1}, edgeAC_{1}, edgeCD, edgeDHPyramid(H, F, A, E) → c, faceAFH, edgeAE, faceEFH, faceAEF, faceAEH, edgeFH_{1}, edgeAF_{1}, edgeAH, edgeEH, edgeEFPyramid(F, H, C, G) → d, faceCFH, edgeCG, faceFGH, faceCGH, faceCFG, edgeFH, edgeCH, edgeCF_{1}, edgeFG, edgeGHPyramid(A, C, F, B) → e, faceACF, edgeBF, faceABC, faceBCF, faceABF, edgeAC, edgeCF, edgeAF, edgeAB, edgeBCCircle(A, l, xOyPlane) → qIntersect(p, q) → O, PVector(A, O) → uVector(A, P) → vTranslate(c, u) → c'Translate(d, v) → d'Intersect(q, yAxis, 2) → QVector(A, Q) → wTranslate(b, w) → b'Intersect(r, q) → R, SVector(A, S) → mTranslate(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。