立方体旋转轴
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①本范例演示立方体旋转轴的几何构造与性质;②涉及核心数学概念包括立体几何、向量、旋转变换;③构造要点:使用GeoGebra命令如Cube(立方体)、PointIn(点在路径上)、Line(线)、Rotate(旋转)、Midpoint(中点);④适合高中立体几何教学与学习,用于理解空间几何变换。
GeoGebra 命令及参数
Cube(A, B, xOyPlane) → a, C, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, D, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH, E, F, G, H, faceABCD, faceADHE, faceABFEPointIn(faceABCD) → JPointIn(faceEFGH) → ILine(I, J) → bRotate(a, (-α), b) → a'Rotate(faceABCD, (-α), b) → faceABCD'Rotate(faceABFE, (-α), b) → faceABFE'Rotate(faceADHE, (-α), b) → faceADHE'Rotate(faceBCGF, (-α), b) → faceBCGF'Rotate(faceCDHG, (-α), b) → faceCDHG'Rotate(faceEFGH, (-α), b) → faceEFGH'Midpoint(F, H) → KMidpoint(A, C) → LMidpoint(F, C) → MMidpoint(E, D) → NMidpoint(H, C) → OMidpoint(E, B) → PMidpoint(edgeFG) → QMidpoint(edgeGH) → RMidpoint(edgeEH) → SMidpoint(edgeEF) → TMidpoint(edgeBF) → UMidpoint(edgeCG) → VMidpoint(edgeBC) → WMidpoint(edgeDH) → ZMidpoint(edgeAE) → A_1Midpoint(edgeAD) → B_1Midpoint(edgeAB) → C_1Midpoint(edgeCD) → D_1
AI 绘图提示语参考
画一个立方体,并标示出其旋转轴。在立方体的底面和顶面上分别取一点,连接这两点得到一条直线,这条直线即为旋转轴。围绕旋转轴旋转立方体,观察旋转后的立方体形态。同时,计算并标示出立方体各边的中点,以便更清晰地展示旋转效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。