铺纸条约分找公倍数与最小公倍数

几何画板及绘图内容加载中，请稍等……

2021-10-26 15:21

① 本范例通过动态铺设彩色纸条的方式，直观展示两个或多个整数的最小公倍数（LCM）的几何意义。② 核心数学概念包括公倍数、最小公倍数、因数与倍数关系，以及数轴上的等距排列。③ 作图要点：使用GeoGebra的Polygon命令绘制纸条，Sequence命令生成连续排列的纸条序列，If命令控制纸条的显示与颜色，通过滑块m调节数值，并利用多个对象（如A1、q1、a1等）构建不同长度的纸条组，实现视觉对比。④ 适合小学高年级至初中阶段学习因数与倍数、最小公倍数的直观教学，也可用于教师演示或学生自主探索，帮助理解LCM的求法及数论基础。

GeoGebra 命令及参数

Polygon(A_{1}, A_{1} + (m, 0), A_{1} + (m, 1), A_{1} + (0, 1)) → q_{1}, a_{1}, f_{1}, g_{1}, h_{1}
Polygon(A_{2}, A_{2} + (m, 0), A_{2} + (m, 1), A_{2} + (0, 1)) → q_{2}, a_{2}, f_{2}, g_{2}, h_{2}
Polygon(A_{3}, A_{3} + (m, 0), A_{3} + (m, 1), A_{3} + (0, 1)) → q_{3}, a_{3}, f_{3}, g_{3}, h_{3}
Polygon(A_{4}, A_{4} + (m, 0), A_{4} + (m, 1), A_{4} + (0, 1)) → q_{4}, a_{4}, f_{4}, g_{4}, h_{4}
Polygon(A_{5}, A_{5} + (m, 0), A_{5} + (m, 1), A_{5} + (0, 1)) → q_{5}, a_{5}, f_{5}, g_{5}, h_{5}
Polygon(A_{6}, A_{6} + (m, 0), A_{6} + (m, 1), A_{6} + (0, 1)) → q_{6}, a_{6}, f_{6}, g_{6}, h_{6}
Polygon(A_{7}, A_{7} + (m, 0), A_{7} + (m, 1), A_{7} + (0, 1)) → q_{7}, a_{7}, f_{7}, g_{7}, h_{7}
Polygon(A_{8}, A_{8} + (m, 0), A_{8} + (m, 1), A_{8} + (0, 1)) → q_{8}, a_{8}, f_{8}, g_{8}, h_{8}
Polygon(A_{9}, A_{9} + (m, 0), A_{9} + (m, 1), A_{9} + (0, 1)) → q_{9}, a_{9}, f_{9}, g_{9}, h_{9}
Polygon(A_{10}, A_{10} + (m, 0), A_{10} + (m, 1), A_{10} + (0, 1)) → q_{10}, a_{10}, f_{10}, g_{10}, h_{10}
Polygon(A_{11}, A_{11} + (m, 0), A_{11} + (m, 1), A_{11} + (0, 1)) → q_{11}, a_{11}, f_{11}, g_{11}, h_{11}
Polygon(A_{12}, A_{12} + (m, 0), A_{12} + (m, 1), A_{12} + (0, 1)) → q_{12}, a_{12}, f_{12}, g_{12}, h_{12}
Polygon(A_{13}, A_{13} + (m, 0), A_{13} + (m, 1), A_{13} + (0, 1)) → q_{13}, a_{13}, f_{13}, g_{13}, h_{13}
Polygon(A_{14}, A_{14} + (m, 0), A_{14} + (m, 1), A_{14} + (0, 1)) → q_{14}, a_{14}, f_{14}, g_{14}, h_{14}
Polygon(A_{15}, A_{15} + (m, 0), A_{15} + (m, 1), A_{15} + (0, 1)) → q_{15}, a_{15}, f_{15}, g_{15}, h_{15}
Polygon(A_{16}, A_{16} + (m, 0), A_{16} + (m, 1), A_{16} + (0, 1)) → q_{16}, a_{16}, f_{16}, g_{16}, h_{16}
Polygon(A_{17}, A_{17} + (m, 0), A_{17} + (m, 1), A_{17} + (0, 1)) → q_{17}, a_{17}, f_{17}, g_{17}, h_{17}
Polygon(A_{18}, A_{18} + (m, 0), A_{18} + (m, 1), A_{18} + (0, 1)) → q_{18}, a_{18}, f_{18}, g_{18}, h_{18}
Polygon(A_{19}, A_{19} + (m, 0), A_{19} + (m, 1), A_{19} + (0, 1)) → q_{19}, a_{19}, f_{19}, g_{19}, h_{19}
Polygon(A_{20}, A_{20} + (m, 0), A_{20} + (m, 1), A_{20} + (0, 1)) → q_{20}, a_{20}, f_{20}, g_{20}, h_{20}
Polygon(B_{1}, B_{1} + (n, 0), B_{1} + (n, 1), B_{1} + (0, 1)) → r_{1}, b_{1}, k_{1}, j_{1}, i_{1}
Polygon(B_{2}, B_{2} + (n, 0), B_{2} + (n, 1), B_{2} + (0, 1)) → r_{2}, b_{2}, k_{2}, j_{2}, i_{2}
Polygon(B_{3}, B_{3} + (n, 0), B_{3} + (n, 1), B_{3} + (0, 1)) → r_{3}, b_{3}, k_{3}, j_{3}, i_{3}
Polygon(B_{4}, B_{4} + (n, 0), B_{4} + (n, 1), B_{4} + (0, 1)) → r_{4}, b_{4}, k_{4}, j_{4}, i_{4}
Polygon(B_{5}, B_{5} + (n, 0), B_{5} + (n, 1), B_{5} + (0, 1)) → r_{5}, b_{5}, k_{5}, j_{5}, i_{5}
Polygon(B_{6}, B_{6} + (n, 0), B_{6} + (n, 1), B_{6} + (0, 1)) → r_{6}, b_{6}, k_{6}, j_{6}, i_{6}
Polygon(B_{7}, B_{7} + (n, 0), B_{7} + (n, 1), B_{7} + (0, 1)) → r_{7}, b_{7}, k_{7}, j_{7}, i_{7}
Polygon(B_{8}, B_{8} + (n, 0), B_{8} + (n, 1), B_{8} + (0, 1)) → r_{8}, b_{8}, k_{8}, j_{8}, i_{8}
Polygon(B_{9}, B_{9} + (n, 0), B_{9} + (n, 1), B_{9} + (0, 1)) → r_{9}, b_{9}, k_{9}, j_{9}, i_{9}
Polygon(B_{10}, B_{10} + (n, 0), B_{10} + (n, 1), B_{10} + (0, 1)) → r_{10}, b_{10}, k_{10}, j_{10}, i_{10}
Polygon(B_{11}, B_{11} + (n, 0), B_{11} + (n, 1), B_{11} + (0, 1)) → r_{11}, b_{11}, k_{11}, j_{11}, i_{11}
Polygon(B_{12}, B_{12} + (n, 0), B_{12} + (n, 1), B_{12} + (0, 1)) → r_{12}, b_{12}, k_{12}, j_{12}, i_{12}
Polygon(B_{13}, B_{13} + (n, 0), B_{13} + (n, 1), B_{13} + (0, 1)) → r_{13}, b_{13}, k_{13}, j_{13}, i_{13}
Polygon(B_{14}, B_{14} + (n, 0), B_{14} + (n, 1), B_{14} + (0, 1)) → r_{14}, b_{14}, k_{14}, j_{14}, i_{14}
Polygon(B_{15}, B_{15} + (n, 0), B_{15} + (n, 1), B_{15} + (0, 1)) → r_{15}, b_{15}, k_{15}, j_{15}, i_{15}
Polygon(B_{16}, B_{16} + (n, 0), B_{16} + (n, 1), B_{16} + (0, 1)) → r_{16}, b_{16}, k_{16}, j_{16}, i_{16}
Polygon(B_{17}, B_{17} + (n, 0), B_{17} + (n, 1), B_{17} + (0, 1)) → r_{17}, b_{17}, k_{17}, j_{17}, i_{17}
Polygon(B_{18}, B_{18} + (n, 0), B_{18} + (n, 1), B_{18} + (0, 1)) → r_{18}, b_{18}, k_{18}, j_{18}, i_{18}
Polygon(B_{19}, B_{19} + (n, 0), B_{19} + (n, 1), B_{19} + (0, 1)) → r_{19}, b_{19}, k_{19}, j_{19}, i_{19}
Polygon(B_{20}, B_{20} + (n, 0), B_{20} + (n, 1), B_{20} + (0, 1)) → r_{20}, b_{20}, k_{20}, j_{20}, i_{20}
Sequence(Segment[((i * LCM[m, n]), 0), ((i * LCM[m, n]), 4)], i, 1, floor(Min[length1, length2] / LCM[m, n])) → l1, {}
If(B_{2} ≟ B_{1} + (n, 0), true, false) → o1
If(B_{3} ≟ B_{2}, true, false) → o2

AI 绘图提示语参考

绘制一个用于展示最小公倍数的数学教学图形：画面中有两排平行的彩色纸条水平排列，第一排每条宽度为m（可通过滑块调整），第二排每条宽度为n，两排纸条左端对齐从0开始依次排列。纸条用不同颜色区分，在数轴上方显示公倍数的位置，当两排纸条在某一点对齐时，该点即为m和n的最小公倍数位置，用垂直线段标识并标注LCM值。整体呈现数轴结构，帮助学生直观理解公倍数和最小公倍数的概念。

以上提示语为根据原始绘图命令整理而来，仅供参考。