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Text File  |  1996-03-21  |  1.7 KB  |  44 lines
  1. window(-1,1,-2,-1.56125e-17);
  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.