动态可调的开口长方体打包项目
几何画板及绘图内容加载中,请稍等……
①本范例演示了如何动态构建和修改开口长方体的形状与体积;②涉及的核心数学概念包括优化问题、体积计算、单位圆、函数图像、几何变换、阶跃函数和相关性;③作图要点:利用了Intersect(相交)、Segment(线段)、Point(点)、Mirror(镜像)、Circle(圆)、Polygon(多边形)、Rotate(旋转)等GeoGebra命令;④适合高中及以上学生学习和理解立体几何、优化问题及动态几何变换。
GeoGebra 命令及参数
Intersect(l, xAxis) → EIntersect(j, l) → FSegment(A, F) → mPoint(m) → GMirror(G, j) → G'Mirror(G, k) → G'_1Mirror(G', k) → G''Segment(A, G) → nCircle(A, G) → cIntersect(c, r, 1) → HIntersect(p, s) → IMirror(H, k) → H'Mirror(I, k) → I'Mirror(I, j) → I'_1Mirror(H, j) → H'_1Mirror(I'_1, k) → JMirror(H'_1, k) → KSegment(I', J) → tSegment(J, I'_1) → aSegment(I'_1, I) → bSegment(I, I') → dSegment(A, B) → eSegment(A, H) → n_1Polygon(G, G', I'_1, I) → poly2, g_1, g', i'_1, i_1Polygon(I, H, H', I') → poly3, i_2, h_1, h', i'Polygon(I', G'_1, G'', J) → poly4, i'_2, g'_1, g'', j_1Polygon(J, K, H'_1, I'_1) → poly5, j_2, k_1, h'_1, i'_3Polygon(I, I'_1, J, I') → poly6, i_3, i'_4, j_3, i'_5Segment(I, I'_1) → p_1Segment(I'_1, J) → q_1Segment(J, I') → r_1Segment(I', I) → s_1Rotate(G, α, b) → G'_2Rotate(G', α, b) → G''_1Rotate(I'_1, α, b) → LRotate(I, α, b) → I'_2Polygon(G'_2, G''_1, L, I'_2) → poly2', g'_2, g''_1, l_2, i'_6Rotate(J, α, x = x(J)) → J'Rotate(K, α, x = x(J)) → K'Rotate(I'_1, α, x = x(J)) → NRotate(J, (-α), x = x(J)) → J'_1Rotate(K, (-α), x = x(J)) → K'_1Rotate(H'_1, (-α), x = x(J)) → ORotate(I'_1, (-α), x = x(J)) → PPolygon(J'_1, K'_1, O, P) → poly5'_1, j'_1, k'_1, o, p_2Rotate(I', (-α), y = y(H')) → I''_1Rotate(G'_1, (-α), y = y(H')) → QRotate(G'', (-α), y = y(H')) → G'''_1Rotate(J, (-α), y = y(H')) → J'_3Polygon(I''_1, Q, G'''_1, J'_3) → poly4'_1, i''_1, q_2, g'''_1, j'_3Rotate(I, α, x = x(G)) → I'_3Rotate(H, α, x = x(G)) → H'_2Rotate(H', α, x = x(G)) → H''Rotate(I', α, x = x(G)) → I''Polygon(I'_3, H'_2, H'', I'') → poly3', i'_7, h'_2, h'', i''Rotate(A, ((-π)) / 2, B) → A'Rotate(B, ((-π)) / 2, B) → B'Segment(A', B') → e'Rotate(A', ((-π)) / 2, A') → A''Rotate(B', ((-π)) / 2, A') → B''Segment(A'', B'') → e''Rotate(A'', ((-π)) / 2, B'') → A'''Rotate(B'', ((-π)) / 2, B'') → B'''Segment(A''', B''') → e'''
AI 绘图提示语参考
画一个开口向上的长方体,动态展示其体积优化和几何变换。首先绘制长方体的底面和侧面,然后通过镜像和旋转操作创建顶部的几何形状,最后将所有部分组合成一个完整的开口长方体。展示过程中注意几何变换和体积变化的关系,以及如何通过函数图和单位圆来辅助理解和优化。
以上提示语为根据原始绘图命令整理而来,仅供参考。