H. Weyl 对称性数学范例
几何画板及绘图内容加载中,请稍等……
①本范例通过动态演示展示了H. Weyl理论中的对称性概念,结合了减法、散点图和三角函数等元素;②涉及的核心数学概念包括对称性、三角函数、圆锥和几何变换;③作图要点提炼自GeoGebra命令:使用了对象I, poly2, f, g, i, j, l, r, i_1, q_1, r_1, s_1, t_1, a_1, b_1, f_2, g_2, h_2, R, I_1, poly2_1, f_1, g_1, i_2, j_1, l_1, r_2, i_3, q_2, r_3, s_2, t_2, a_2, b_2, f_3, g_3, h_1, R_1, I_2, poly2_2等;④适合高中及以上数学学习者,用于理解抽象数学概念的可视化表示。
GeoGebra 命令及参数
IjonTicky2(I) → poly2, f, s_1, t_1, a_1, b_1, f_2, g_2, h_2, R, g, i, j, l, r, i_1, q_1, r_1IjonTicky2(I_1) → poly2_1, f_1, s_2, t_2, a_2, b_2, f_3, g_3, h_1, R_1, g_1, i_2, j_1, l_1, r_2, i_3, q_2, r_3IjonTicky2(I_2) → poly2_2, f_4, s_3, t_3, a_3, b_3, f_5, g_5, h_3, R_2, g_4, i_4, j_2, l_2, r_4, i_5, q_3, r_5IjonTicky2(I_3) → poly2_3, f_6, s_4, t_4, a_4, b_4, f_7, g_7, h_4, R_3, g_6, i_6, j_3, l_3, r_6, i_7, q_4, r_7IjonTicky2(I_4) → poly2_4, f_8, s_5, t_5, a_5, b_5, f_9, g_9, h_5, R_4, g_8, i_8, j_4, l_4, r_8, i_9, q_5, r_9IjonTicky2(I_5) → poly2_5, f_{10}, s_6, t_6, a_6, b_6, f_{11}, g_{11}, h_6, R_5, g_{10}, i_{10}, j_5, l_5, r_{10}, i_{11}, q_6, r_{11}IjonTicky2(I_6) → poly2_6, f_{12}, s_7, t_7, a_7, b_7, f_{13}, g_{13}, h_7, R_6, g_{12}, i_{12}, j_6, l_6, r_{12}, i_{13}, q_7, r_{13}IjonTicky2(I_7) → poly2_7, f_{14}, s_8, t_8, a_8, b_8, f_{15}, g_{15}, h_8, R_7, g_{14}, i_{14}, j_7, l_7, r_{14}, i_{15}, q_8, r_{15}IjonTicky2(I_8) → poly2_8, f_{16}, s_9, t_9, a_9, b_9, f_{17}, g_{17}, h_9, R_8, g_{16}, i_{16}, j_8, l_8, r_{16}, i_{17}, q_9, r_{17}IjonTicky2(I_9) → poly2_9, f_{18}, s_{10}, t_{10}, a_{10}, b_{10}, f_{19}, g_{19}, h_{10}, R_9, g_{18}, i_{18}, j_9, l_9, r_{18}, i_{19}, q_{10}, r_{19}IjonTicky2(I_{10}) → poly2_{10}, f_{20}, s_{11}, t_{11}, a_{11}, b_{11}, f_{21}, g_{21}, h_{11}, R_{10}, g_{20}, i_{20}, j_{10}, l_{10}, r_{20}, i_{21}, q_{11}, r_{21}IjonTicky2(I_{11}) → poly2_{11}, f_{22}, s_{12}, t_{12}, a_{12}, b_{12}, f_{23}, g_{23}, h_{12}, R_{11}, g_{22}, i_{22}, j_{11}, l_{11}, r_{22}, i_{23}, q_{12}, r_{23}IjonTicky2(I_{12}) → poly2_{12}, f_{24}, s_{13}, t_{13}, a_{13}, b_{13}, f_{25}, g_{25}, h_{13}, R_{12}, g_{24}, i_{24}, j_{12}, l_{12}, r_{24}, i_{25}, q_{13}, r_{25}IjonTicky2(I_{13}) → poly2_{13}, f_{26}, s_{14}, t_{14}, a_{14}, b_{14}, f_{27}, g_{27}, h_{14}, R_{13}, g_{26}, i_{26}, j_{13}, l_{13}, r_{26}, i_{27}, q_{14}, r_{27}IjonTicky2(I_{14}) → poly2_{14}, f_{28}, s_{15}, t_{15}, a_{15}, b_{15}, f_{29}, g_{29}, h_{15}, R_{14}, g_{28}, i_{28}, j_{14}, l_{14}, r_{28}, i_{29}, q_{15}, r_{29}IjonTicky2(I_{15}) → poly2_{15}, f_{30}, s_{16}, t_{16}, a_{16}, b_{16}, f_{31}, g_{31}, h_{16}, R_{15}, g_{30}, i_{30}, j_{15}, l_{15}, r_{30}, i_{31}, q_{16}, r_{31}IjonTicky2(I_{16}) → poly2_{16}, f_{32}, s_{17}, t_{17}, a_{17}, b_{17}, f_{33}, g_{33}, h_{17}, R_{16}, g_{32}, i_{32}, j_{16}, l_{16}, r_{32}, i_{33}, q_{17}, r_{33}IjonTicky2(I_{17}) → poly2_{17}, f_{34}, s_{18}, t_{18}, a_{18}, b_{18}, f_{35}, g_{35}, h_{18}, R_{17}, g_{34}, i_{34}, j_{17}, l_{17}, r_{34}, i_{35}, q_{18}, r_{35}IjonTicky2(I_{18}) → poly2_{18}, f_{36}, s_{19}, t_{19}, a_{19}, b_{19}, f_{37}, g_{37}, h_{19}, R_{18}, g_{36}, i_{36}, j_{18}, l_{18}, r_{36}, i_{37}, q_{19}, r_{37}IjonTicky2(I_{19}) → poly2_{19}, f_{38}, s_{20}, t_{20}, a_{20}, b_{20}, f_{39}, g_{39}, h_{20}, R_{19}, g_{38}, i_{38}, j_{19}, l_{19}, r_{38}, i_{39}, q_{20}, r_{39}IjonTicky2(I_{20}) → poly2_{20}, f_{40}, s_{21}, t_{21}, a_{21}, b_{21}, f_{41}, g_{41}, h_{21}, R_{20}, g_{40}, i_{40}, j_{20}, l_{20}, r_{40}, i_{41}, q_{21}, r_{41}IjonTicky2(I_{21}) → poly2_{21}, f_{42}, s_{22}, t_{22}, a_{22}, b_{22}, f_{43}, g_{43}, h_{22}, R_{21}, g_{42}, i_{42}, j_{21}, l_{21}, r_{42}, i_{43}, q_{22}, r_{43}IjonTicky2(I_{22}) → poly2_{22}, f_{44}, s_{23}, t_{23}, a_{23}, b_{23}, f_{45}, g_{45}, h_{23}, R_{22}, g_{44}, i_{44}, j_{22}, l_{22}, r_{44}, i_{45}, q_{23}, r_{45}IjonTicky2(I_{23}) → poly2_{23}, f_{46}, s_{24}, t_{24}, a_{24}, b_{24}, f_{47}, g_{47}, h_{24}, R_{23}, g_{46}, i_{46}, j_{23}, l_{23}, r_{46}, i_{47}, q_{24}, r_{47}IjonTicky2(I_{24}) → poly2_{24}, f_{48}, s_{25}, t_{25}, a_{25}, b_{25}, f_{49}, g_{49}, h_{25}, R_{24}, g_{48}, i_{48}, j_{24}, l_{24}, r_{48}, i_{49}, q_{25}, r_{49}IjonTicky2(I_{25}) → poly2_{25}, f_{50}, s_{26}, t_{26}, a_{26}, b_{26}, f_{51}, g_{51}, h_{26}, R_{25}, g_{50}, i_{50}, j_{25}, l_{25}, r_{50}, i_{51}, q_{26}, r_{51}IjonTicky2(I_{26}) → poly2_{26}, f_{52}, s_{27}, t_{27}, a_{27}, b_{27}, f_{53}, g_{53}, h_{27}, R_{26}, g_{52}, i_{52}, j_{26}, l_{26}, r_{52}, i_{53}, q_{27}, r_{53}IjonTicky2(I_{27}) → poly2_{27}, f_{54}, s_{28}, t_{28}, a_{28}, b_{28}, f_{55}, g_{55}, h_{28}, R_{27}, g_{54}, i_{54}, j_{27}, l_{27}, r_{54}, i_{55}, q_{28}, r_{55}IjonTicky2(I_{28}) → poly2_{28}, f_{56}, s_{29}, t_{29}, a_{29}, b_{29}, f_{57}, g_{57}, h_{29}, R_{28}, g_{56}, i_{56}, j_{28}, l_{28}, r_{56}, i_{57}, q_{29}, r_{57}IjonTicky2(I_{29}) → poly2_{29}, f_{58}, s_{30}, t_{30}, a_{30}, b_{30}, f_{59}, g_{59}, h_{30}, R_{29}, g_{58}, i_{58}, j_{29}, l_{29}, r_{58}, i_{59}, q_{30}, r_{59}IjonTicky2(I_{30}) → poly2_{30}, f_{60}, s_{31}, t_{31}, a_{31}, b_{31}, f_{61}, g_{61}, h_{31}, R_{30}, g_{60}, i_{60}, j_{30}, l_{30}, r_{60}, i_{61}, q_{31}, r_{61}IjonTicky2(I_{31}) → poly2_{31}, f_{62}, s_{32}, t_{32}, a_{32}, b_{32}, f_{63}, g_{63}, h_{32}, R_{31}, g_{62}, i_{62}, j_{31}, l_{31}, r_{62}, i_{63}, q_{32}, r_{63}IjonTicky2(I_{32}) → poly2_{32}, f_{64}, s_{33}, t_{33}, a_{33}, b_{33}, f_{65}, g_{65}, h_{33}, R_{32}, g_{64}, i_{64}, j_{32}, l_{32}, r_{64}, i_{65}, q_{33}, r_{65}IjonTicky2(I_{33}) → poly2_{33}, f_{66}, s_{34}, t_{34}, a_{34}, b_{34}, f_{67}, g_{67}, h_{34}, R_{33}, g_{66}, i_{66}, j_{33}, l_{33}, r_{66}, i_{67}, q_{34}, r_{67}IjonTicky2(I_{34}) → poly2_{34}, f_{68}, s_{35}, t_{35}, a_{35}, b_{35}, f_{69}, g_{69}, h_{35}, R_{34}, g_{68}, i_{68}, j_{34}, l_{34}, r_{68}, i_{69}, q_{35}, r_{69}IjonTicky2(I_{35}) → poly2_{35}, f_{70}, s_{36}, t_{36}, a_{36}, b_{36}, f_{71}, g_{71}, h_{36}, R_{35}, g_{70}, i_{70}, j_{35}, l_{35}, r_{70}, i_{71}, q_{36}, r_{71}IjonTicky2(I_{36}) → poly2_{36}, f_{72}, s_{37}, t_{37}, a_{37}, b_{37}, f_{73}, g_{73}, h_{37}, R_{36}, g_{72}, i_{72}, j_{36}, l_{36}, r_{72}, i_{73}, q_{37}, r_{73}IjonTicky2(I_{37}) → poly2_{37}, f_{74}, s_{38}, t_{38}, a_{38}, b_{38}, f_{75}, g_{75}, h_{38}, R_{37}, g_{74}, i_{74}, j_{37}, l_{37}, r_{74}, i_{75}, q_{38}, r_{75}IjonTicky2(I_{38}) → poly2_{38}, f_{76}, s_{39}, t_{39}, a_{39}, b_{39}, f_{77}, g_{77}, h_{39}, R_{38}, g_{76}, i_{76}, j_{38}, l_{38}, r_{76}, i_{77}, q_{39}, r_{77}IjonTicky2(I_{39}) → poly2_{39}, f_{78}, s_{40}, t_{40}, a_{40}, b_{40}, f_{79}, g_{79}, h_{40}, R_{39}, g_{78}, i_{78}, j_{39}, l_{39}, r_{78}, i_{79}, q_{40}, r_{79}IjonTicky2(I_{40}) → poly2_{40}, f_{80}, s_{41}, t_{41}, a_{41}, b_{41}, f_{81}, g_{81}, h_{41}, R_{40}, g_{80}, i_{80}, j_{40}, l_{40}, r_{80}, i_{81}, q_{41}, r_{81}IjonTicky2(I_{41}) → poly2_{41}, f_{82}, s_{42}, t_{42}, a_{42}, b_{42}, f_{83}, g_{83}, h_{42}, R_{41}, g_{82}, i_{82}, j_{41}, l_{41}, r_{82}, i_{83}, q_{42}, r_{83}IjonTicky2(I_{42}) → poly2_{42}, f_{84}, s_{43}, t_{43}, a_{43}, b_{43}, f_{85}, g_{85}, h_{43}, R_{42}, g_{84}, i_{84}, j_{42}, l_{42}, r_{84}, i_{85}, q_{43}, r_{85}IjonTicky2(I_{43}) → poly2_{43}, f_{86}, s_{44}, t_{44}, a_{44}, b_{44}, f_{87}, g_{87}, h_{44}, R_{43}, g_{86}, i_{86}, j_{43}, l_{43}, r_{86}, i_{87}, q_{44}, r_{87}IjonTicky2(I_{44}) → poly2_{44}, f_{88}, s_{45}, t_{45}, a_{45}, b_{45}, f_{89}, g_{89}, h_{45}, R_{44}, g_{88}, i_{88}, j_{44}, l_{44}, r_{88}, i_{89}, q_{45}, r_{89}IjonTicky2(I_{45}) → poly2_{45}, f_{90}, s_{46}, t_{46}, a_{46}, b_{46}, f_{91}, g_{91}, h_{46}, R_{45}, g_{90}, i_{90}, j_{45}, l_{45}, r_{90}, i_{91}, q_{46}, r_{91}IjonTicky2(I_{46}) → poly2_{46}, f_{92}, s_{47}, t_{47}, a_{47}, b_{47}, f_{93}, g_{93}, h_{47}, R_{46}, g_{92}, i_{92}, j_{46}, l_{46}, r_{92}, i_{93}, q_{47}, r_{93}IjonTicky2(I_{47}) → poly2_{47}, f_{94}, s_{48}, t_{48}, a_{48}, b_{48}, f_{95}, g_{95}, h_{48}, R_{47}, g_{94}, i_{94}, j_{47}, l_{47}, r_{94}, i_{95}, q_{48}, r_{95}IjonTicky2(I_{48}) → poly2_{48}, f_{96}, s_{49}, t_{49}, a_{49}, b_{49}, f_{97}, g_{97}, h_{49}, R_{48}, g_{96}, i_{96}, j_{48}, l_{48}, r_{96}, i_{97}, q_{49}, r_{97}IjonTicky2(I_{49}) → poly2_{49}, f_{98}, s_{50}, t_{50}, a_{50}, b_{50}, f_{99}, g_{99}, h_{50}, R_{49}, g_{98}, i_{98}, j_{49}, l_{49}, r_{98}, i_{99}, q_{50}, r_{99}IjonTicky2(I_{50}) → poly2_{50}, f_{100}, s_{51}, t_{51}, a_{51}, b_{51}, f_{101}, g_{101}, h_{51}, R_{50}, g_{100}, i_{100}, j_{50}, l_{50}, r_{100}, i_{101}, q_{51}, r_{101}
AI 绘图提示语参考
绘制一个动态演示H. Weyl对称理论的图形,包含多个子图形,每个子图形由多个三角函数曲线和几何变换构成,整体呈现出对称性和几何美感。首先绘制一个基础图形,然后通过旋转、缩放等变换生成多个子图形,每个子图形的曲线都经过精心设计,展现出三角函数的周期性和几何变换的复杂性。所有子图形共同构成一个完整的对称图案,适合用于教学演示和数学探索。
以上提示语为根据原始绘图命令整理而来,仅供参考。