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H. Weyl Symmetry Example

H. Weyl Symmetry Example
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2017-08-16 00:28
FunctionTrigonometryGeometric Construction
This example dynamically demonstrates H. Weyl's theory of symmetry, incorporating elements like subtraction, scatter plots, and trigonometric functions. Core math concepts include symmetry, trigonometric functions, cones, and geometric transformations. Construction highlights GeoGebra commands like objects 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. Suitable for high school and above learners to visualize abstract mathematical concepts.

GeoGebra Commands & Parameters

  1. 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_1
  2. IjonTicky2(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_3
  3. IjonTicky2(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_5
  4. IjonTicky2(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_7
  5. IjonTicky2(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_9
  6. IjonTicky2(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}
  7. 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}
  8. 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}
  9. 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}
  10. 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}
  11. 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}
  12. 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}
  13. 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}
  14. 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}
  15. 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}
  16. 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}
  17. 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}
  18. 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}
  19. 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}
  20. 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}
  21. 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}
  22. 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}
  23. 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}
  24. 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}
  25. 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}
  26. 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}
  27. 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}
  28. 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}
  29. 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}
  30. 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}
  31. 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}
  32. 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}
  33. 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}
  34. 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}
  35. 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}
  36. 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}
  37. 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}
  38. 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}
  39. 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}
  40. 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}
  41. 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}
  42. 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}
  43. 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}
  44. 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}
  45. 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}
  46. 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}
  47. 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}
  48. 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}
  49. 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}
  50. 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}
  51. 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 Drawing Prompt Reference

Create a dynamic illustration demonstrating H. Weyl's theory of symmetry, featuring multiple subgraphs, each composed of trigonometric functions and geometric transformations. The overall design should exhibit symmetry and geometric beauty. Begin by drawing a base graph, then generate several subgraphs through rotations and scalings, with each curve carefully designed to showcase the periodicity of trigonometric functions and the complexity of geometric transformations. All subgraphs together form a complete symmetric pattern, ideal for educational demonstrations and mathematical exploration.
The prompt above was compiled from the original drawing commands and is for reference only.