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Text File  |  1996-03-01  |  1.5 KB  |  44 lines
  1. window(-1,1,-1,1);
  2. /*
  3. The Pythagoras.
  4.  
  5.  
  6. This construction can be used to proof the Pythagoras theorem.
  7. From the figure, we get by comparing the areas
  8.  
  9.     (a+b)^2=2ab+c^2,
  10.  
  11. which transforms to
  12.  
  13.     a^2+b^2=c^2.
  14.  
  15.  
  16. Move X to see the correctness of this reasoning.
  17. */
  18. Point_141()=point(-0.509537,-0.356948);
  19. Point_142()=point(0.362398,-0.356948);
  20. Segment_47()=segment(Point_141,Point_142);
  21. Point_143(hidden),Line_79(hidden)=rectangular(Point_141,Segment_47);
  22. Point_144(hidden),Line_80(hidden)=rectangular(Point_142,Segment_47);
  23. Circle_57(hidden)=circle(Point_142,Point_141);
  24. Cut_78(hidden),Cut_79()=intersection(Line_80,Circle_57);
  25. Point_147(hidden),Line_81(hidden)=parallel(Cut_79,Segment_47);
  26. Cut_80()=intersection(Line_79,Line_81);
  27. Segment_48()=segment(Point_141,Cut_80);
  28. Segment_49()=segment(Cut_80,Cut_79);
  29. Segment_50()=segment(Cut_79,Point_142);
  30. X(showname)=pointon(Segment_47,0.0344828,-0.356948);
  31. Point_150(hidden),Circle_58(hidden)=circle3(Cut_79,Point_142,X);
  32. Point_151(hidden),Circle_59(hidden)=circle3(Cut_80,Point_142,X);
  33. Cut_81(),Cut_82(hidden)=intersection(Circle_59,Segment_49);
  34. Cut_83(),Cut_84(hidden)=intersection(Circle_58,Segment_50);
  35. Segment_51()=segment(X,Cut_83);
  36. Segment_52()=segment(Cut_83,Cut_81);
  37. Point_156(hidden),Line_87(hidden)=parallel(Cut_81,Segment_51);
  38. Cut_85()=intersection(Segment_48,Line_87);
  39. Segment_53()=segment(Cut_81,Cut_85);
  40. Segment_54()=segment(Cut_85,X);
  41. a(color:green,showname)=segment(Point_141,X);
  42. b(color:green,showname)=segment(Point_141,Cut_85);
  43. c(color:green,showname)=segment(Cut_85,X);
  44.