长方体展开图探索
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所属专题
Cuboids & their Nets
①本范例演示长方体的展开图及其结构关系;②涉及核心数学概念包括多边形、立体几何、空间想象能力;③构造要点:使用Sequence、Element、Polygon、Segment等GeoGebra命令绘制展开图各面,并通过R_x, R_y, R_z等变换命令实现三维到二维的展开;④适合初中及以上学生用于理解立体几何与多边形关系,增强空间感知能力。
GeoGebra 命令及参数
Sequence(Mat * Element[cube, k], k, 1, 8) → cube'Element(Element[AE, 3], 1) → droiteSequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepointsElement(listepoints, 2) → AElement(listepoints, 1) → EElement(listepoints, 4) → C_1Element(listepoints, 3) → DPolygon(A, E, C_1, D) → poly1, a_1, b, c_1, dElement(listepoints, 6) → BElement(listepoints, 7) → FElement(listepoints, 8) → GElement(listepoints, 5) → HPolygon(B, F, G, H) → poly2, e, f, g, hElement(listepoints, 3) → 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(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_1Polygon(A, B, F', D') → poly7, a_4, b_3, f', d'Polygon(E, A, D'', C') → poly8, e_3, a_5, d'', c'Polygon(B, F'', G', H) → poly9, b_4, f'', g', h_3Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4Polygon(A_2, B_2, G'', C''') → poly11, a_6, b_5, g''_1, c'''_1
AI 绘图提示语参考
画一个长方体的展开图,包含六个矩形面,每个面用线条连接,展示长方体的三维结构。先画出三个矩形面,再连接剩余三个面,使展开图清晰可见,体现长方体的空间关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。