MX                                    .X                                      0
  7M;                                  .a                                    MM 
    WM                                 .a                                  ZM   
      MM                               .a                                .Ma    
       .Mr                             .a                               MM      
         WM                            .a                             MM        
           M0                          .a                           SMi         
            XM                         .a                          M8           
              MM                       .a                        MM             
                MX                     .a                      0M               
                 BM                    .a                    ,MX                
                   Mr                  .a                   MM                  
                    BM                 .a                 MM                    
                      M                .a                M;                     
                       M                X               M                       
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                 MM                    .a                 M                     
               WM                      .a                  MW                   
             7M,                       .a                   7M                  
            M8                         .a                     M@                
          MM                           .a                      rM.              
        0M                             .a                        MM             
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     MW                                .a                           8M          
   MM                                  .a                             MM        
 SM                                    .a                              .MS      
Ma                                     .a                                0M     
                                       .a                                  MM   
                                       .X                                    MS                     


Cartesian equation: y4 - x4 + ay2 + bx2 = 0
Parametric Cartesian equation: x = cost( (a2sin2t - b2cos2t)/(sin2t - cos2t) )1/2, y = sint( (a2sin2t - b2cos2t)/(sin2t - cos2t) )1/2
Polar equation: r2(sin2Θ - cos2Θ) = a2sin2Θ - b2cos2Θ

The Devil's Curve was studied by Cramer, a Swiss mathematician in 1750 and Lacroix in 1810. It also appears in Nouvelles Annales, a mathematics journal, in 1858.

The curve illustrated above corresponds to parameters a2 = 1 and b2 = 2.


A special case of the Devil's curve is the so-called "electric motor curve", where y2(y2 - 96) = x2(x2 - 100)


 a                                      i                                      :
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    Sr                                  ;                                  ,S   
     ,0                                 .                                 M,    
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                 W:       SZ            ,            7S:      ,Z                
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                 rr       2.            :             @i       a                
                :8         a2           :           .M         r2               
                M           .8,         ;          WS           X.              
               8              ZX        ,        72              M              
               S                87      ;      ,W,                S             
              M                  ;Z     ,     MX                  W            .
              W                    a8   ;   28                    M             
              W                      Z:   ,W,                      B            
             X                         r ;.                        W            
 .....,..  . M  ..,.  ...,.... ......  ,Ma  .,....,.  ...,.... ... W .,..  .,,..
              S                       M   87                       B            
              W                     87  i  :W                     X;            
              M                   aZ    .    88                   M             
              a.                :W      ;      W7                 B             
               B               87       .       .2               W              
               iZ            X2         ;         ra             8              
                Z           W,          .           W:          B               
                 M        72            ;            ,0        @                
                  M      M              ,              @      @                 
                   Z    8               i               W    ,r                 
                  ,2    a               i               W    :r                 
                  B      Xa             ,             r2      0i                
                rZ         20X          ;          ;20         XS               
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           Xa                                                       80          
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        aa                              .                              ;@       
      i2                                ;                                X7     
     Z.                                 :                                  Z,   
   S7                                   ,                                   ,B  
 Z0                                     ;                                     7r

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