立方体中的金字塔 by Nicolas ERDRICH
几何画板及绘图内容加载中,请稍等……
①本范例演示在立方体内部构建金字塔的几何关系;②涉及核心数学概念包括立体几何、中心点、正交线、角度计算等;③构造过程中运用了正交线、点、序列、元素、多边形、线段、点在对象内、角度等 GeoGebra 命令与对象;④适合高中立体几何教学与学习,可用于理解空间几何构造与性质。
GeoGebra 命令及参数
OrthogonalLine(I, xAxis) → l_1OrthogonalLine(I, l_1) → m_1Point(m_1) → KPoint(l_1) → PSequence(Mat * Element[cube, k], k, 1, 8) → cube'Element(Element[AE, 3], 1) → droiteSequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepointsPoint(listepoints) → APoint(listepoints) → EPoint(listepoints) → C_1Point(listepoints) → DPolygon(A, E, C_1, D) → poly1, a_1, b, c_1, dPoint(listepoints) → BPoint(listepoints) → FPoint(listepoints) → GPoint(listepoints) → HPolygon(B, F, G, H) → poly2, e, f, g, hPoint(listepoints) → CPolygon(F, C, A, B) → poly3, f_1, i, a_2, b_1Element(AB, 3, 1) → avantPolygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1Element(AC, 3, 1) → dessusPolygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2Segment(E, A) → cSegment(A, C) → jSegment(A, B) → kSegment(C, C_1) → lSegment(C_1, E) → mSegment(H, E) → nSegment(A, B) → pSegment(B, H) → qSegment(H, E) → rSegment(H, G) → sSegment(B, F) → tSegment(G, C_1) → d_1Segment(F, G) → i_1Segment(F, C) → j_1PointIn(poly5) → JSegment(J, E) → k_1Polygon(J, E, H) → poly7, h_3, j_2, e_3Polygon(J, H, B) → poly8, b_3, j_3, h_4Polygon(J, E, A) → poly9, a_4, j_4, e_4Polygon(J, A, B) → poly10, b_4, j_5, a_5Angle(Line[A, E], Line[A, J]) → ang1Angle(Line[E, H], Line[E, J]) → ang2Angle(Line[H, B], Line[H, J]) → ang3Angle(Line[B, A], Line[B, J]) → ang4Polygon(A, B, H, E) → poly11, a_6, b_5, h_5, e_5Angle(Line[B, H], Line[B, A]) → ang5
AI 绘图提示语参考
在一个立方体内部绘制一个金字塔,金字塔的顶点位于立方体的对角线上,底面与立方体的一个面重合。首先画出立方体的对角线,然后在对角线上找到中点,以此为基础绘制金字塔的侧面,确保侧面与底面垂直。金字塔的底面由立方体的四个顶点和一个中点构成,侧面由底面顶点和金字塔顶点连接而成。最后,标注出金字塔的各个边和顶点,以及侧面与底面的夹角。
以上提示语为根据原始绘图命令整理而来,仅供参考。