长方体展开图 by Daryl Cox

几何画板及绘图内容加载中，请稍等……

2018-04-25 00:46

所属专题 Surface Area Discovery

①本范例演示长方体的展开图及其相关属性；②涉及核心数学概念包括立体几何、多边形构造、向量运算；③作图要点运用了GeoGebra命令Sequence（序列）、Element（元素）、Polygon（多边形）、Segment（线段）等，以及对象z, R_z, a, echelle, P, β, sinβ, cosβ, R_y, α, sinα, cosα, R_x, I, u, v, w, Mat, cube, cube', alpha, texte1, texte2, AE, droite, listepoints, A, E, C_1, D, poly1, a_1, b, c_1, d, B, F, G, H, poly2；④适合高中阶段学生用于理解空间几何与几何作图，也可用于教学演示。

GeoGebra 命令及参数

Sequence((Mat * Element[cube, k]), k, 1, 8) → cube'
Element(Element[AE, 3], 1) → droite
Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
Element(listepoints, 2) → A
Element(listepoints, 1) → E
Element(listepoints, 4) → C_1
Element(listepoints, 3) → D
Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
Element(listepoints, 6) → B
Element(listepoints, 7) → F
Element(listepoints, 8) → G
Element(listepoints, 5) → H
Polygon(B, F, G, H) → poly2, e, f, g, h
Element(listepoints, 3) → C
Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
Element(AB, 3, 1) → avant
Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
Element(AC, 3, 1) → dessus
Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
Segment(E, A) → c
Segment(A, C) → j
Segment(A, B) → k
Segment(C, C_1) → l
Segment(C_1, E) → m
Segment(A, B) → p
Segment(B, H) → q
Segment(H, E) → r
Segment(H, G) → s
Segment(B, F) → t
Segment(G, C_1) → d_1
Segment(F, G) → i_1
Segment(F, C) → j_1
Polygon(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_3
Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4
Polygon(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，按顺序连接形成十字形，并标注各边的长度和角度，展示其三维空间结构。先画出基础的长方体，再将其展开成平面图形，依次连接各顶点形成展开图的各个面，最后标注关键点和边的名称以及角度信息，使图形清晰易懂。

以上提示语为根据原始绘图命令整理而来，仅供参考。