刘徽立方体分割

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2017-02-27 18:42

①本范例演示刘徽提出的立方体分割几何问题，通过动态演示分割过程；②涉及核心数学概念包括立体几何、勾股定理、三角函数及最值优化；③构造要点提炼自GeoGebra命令：Intersect（交点）、Point（点）、Cube（立方体）、Segment（线段）、Pyramid（金字塔）、Prism（棱柱）、LaTeX（公式）；④适合高中及以上学生及数学爱好者学习几何分割与优化问题。

GeoGebra 命令及参数

Intersect(xAxis, yAxis) → A
Point(xAxis) → B
Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
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_1, faceABFE, faceBCGF
Segment(H, F) → f
Segment(D, B) → g
Segment(B, E) → h
Segment(H, B) → j
Pyramid(D, A, E, H, B) → c, faceADHE, edgeBD_1, edgeAB, edgeBE_1, edgeBH_1, faceABD, faceABE, faceBEH_1, faceBDH, edgeAD, edgeAE, edgeEH_2, edgeDH_2
Pyramid(F, E, B, H) → d, faceBEF, edgeBH, faceEFH, faceBEH, faceBFH, edgeEF, edgeBE, edgeBF, edgeFH, edgeEH
Prism(D, C, B, H) → b, I, edgeBD, edgeDH, edgeCI, edgeBJ, edgeHI, edgeIJ, edgeHJ, J, faceBCD, faceCDHI, faceBCIJ, faceBDHJ, faceHIJ, edgeCD, edgeBC
LaTeX(B, true, true) → text1