积极 AI Logo 积极 AI

用单位立方体构建体积模型

用单位立方体构建体积模型
几何画板及绘图内容加载中，请稍等……
2018-06-11 08:19
函数数列立体几何几何作图滑块动画
① 本范例通过堆积单位立方体来直观展示长方体体积的计算模型，用户可动态调整长、宽、高方向上的立方体数量，观察总体积的变化。② 核心数学概念是体积的定义与计算，即长方体体积等于长、宽、高三个维度上单位立方体个数的乘积，同时涉及空间计数与乘法原理。③ 作图要点：利用GeoGebra的SelectedIndex和Sequence命令生成三维网格，通过对象nx、ny、nz控制三个方向的单位立方体数量，并借助l_x、s_x等变量定义每个立方体的位置与尺寸，最终由L_s1、L_b等列表对象组合成完整的长方体模型，配合sp滑块和text1文本显示体积数值。④ 适合小学高年级至初中阶段学习体积概念，也可用于几何教学中的直观演示，帮助学生建立从一维长度到三维体积的认知桥梁。

GeoGebra 命令及参数

  1. SelectedIndex(nx) → l_x
  2. SelectedIndex(ny) → l_y
  3. SelectedIndex(nz) → l_z
  4. Sequence(Sequence[Sequence[Polygon[(x(A) + i - 1, y(A) + j - 1, z(A) + k - 1), (x(A) + i, y(A) + j - 1, z(A) + k - 1), (x(A) + i, y(A) + j - 1, z(A) + k), (x(A) + i - 1, y(A) + j - 1, z(A) + k)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{s1}
  5. Sequence(Sequence[Sequence[Polygon[(x(A) + i - 1, y(A) + j - 1, z(A) + k - 1), (x(A) + i, y(A) + j - 1, z(A) + k - 1), (x(A) + i, y(A) + j, z(A) + k - 1), (x(A) + i - 1, y(A) + j, z(A) + k - 1)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{b}
  6. Sequence(Sequence[Sequence[Polygon[(x(A) + i - 1, y(A) + j - 1, z(A) + k), (x(A) + i, y(A) + j - 1, z(A) + k), (x(A) + i, y(A) + j, z(A) + k), (x(A) + i - 1, y(A) + j, z(A) + k)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{t}
  7. Sequence(Sequence[Sequence[Polygon[(x(A) + i - 1, y(A) + j, z(A) + k - 1), (x(A) + i, y(A) + j, z(A) + k - 1), (x(A) + i, y(A) + j, z(A) + k), (x(A) + i - 1, y(A) + j, z(A) + k)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{s3}
  8. Sequence(Sequence[Sequence[Polygon[(x(A) + i, y(A) + j - 1, z(A) + k - 1), (x(A) + i, y(A) + j, z(A) + k - 1), (x(A) + i, y(A) + j, z(A) + k), (x(A) + i, y(A) + j - 1, z(A) + k)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{s2}
  9. Sequence(Sequence[Sequence[Polygon[(x(A) + i - 1, y(A) + j - 1, z(A) + k - 1), (x(A) + i - 1, y(A) + j, z(A) + k - 1), (x(A) + i - 1, y(A) + j, z(A) + k), (x(A) + i - 1, y(A) + j - 1, z(A) + k)], i, 1, (l_x * (1 + s_x)), 1 + s_x], j, 1, (l_y * (1 + s_y)), 1 + s_y], k, 1, (l_z * (1 + s_z)), 1 + s_z) → L_{s4}