.a2a7Z88XSX0r                              
                                :XrXi             ;Z2ar                         
                           :7W@@2ii22X.               .XZZ                      
                     ,SaX;MrS         ;X07Z               rS:                   
                  :SZ:   S              .  aaX              :Zr                 
                ZZ,    27               .     77               2r               
              Z;     ,Z                 ;      28MZS7SS0XXa     ia              
            S;      X7                     XZa    i:       raZS.  0             
          .B       i2                   a27        ;S          :aS Z            
         X7        Z                  SX             Z             rM           
        B         M                  @  i            Xi              M:         
       Xi        ,  i8XSXZ80XSX8X  .7   ,             W              :Z;        
       Z         M:7.            77M    ;             W               0 8       
      M       XZ M                i:;8  .             rX              0  Sr     
     a      XS   M                W   2.              ;Z               M  S;    
     B    :S     M                W    a7             a                M   W    
     W   a:      8                W     @        SX2Z7MS8Xa,           M    M   
    0   W         W               2;    M     ZSS    2     ;aa,        M    .r  
    W  Z.         M                Z.   M   rS      7;        :2;     S.     M  
    W 2            ai               a:  @  8.      0            .0    W      S  
    r M             X7     :XXSSSX7   XiW S     ;SX               7X  8       W 
     M               i; :X2:       XX  i;.M.Z7aZ                   .r2        B 
.    M  ,..  ....,,.  2M0            BZ   0       .  ....,,..  ...  Mr   .... M 
     M7              W   ,7ZX8Z88ZSX;  WM M;287XS.                 0 7;       B 
    8 8            rX                XX 8  S     ;2i              8   W       Z 
    W  8          .X               ia   M   8      :a           ai    B      M  
    W  .8         M                W    M    Sr      M       iZ2       M     M  
    Sr  .a        S               B     W      22XX   r  rSZSi         M    8   
     W    8      M                W     M         .;X:M:X,             M   7r   
     W     a2    M                W    Z              X                M  .8    
      M      2r  M                B  S7 i             :B               0  0     
      0        a:M                 Mr   .             Z               0 :a      
       W         BrXSS         SSSi7    ;             W               Zir       
        M         W   i08XSXZ0i     7r  ,             Z              W;,        
         8        r;                 ra .            B              82          
          Sr       Z.                  22           M             SW;           
           rX       W                   ;S22       8          72S.i:            
             ai      W                      SaariSX     rXX8S2   Z              
              :a7     7S                ;       S;;7SSXX        Z               
                 S2r    S,              .    rZi              22                
                   .S87  .;.             ,SS2               SS                  
                       rZS;@MX;i;7XSXS8XW:               X27                    
                              XSX                    ,ZaS                       
                                 .ZS20XaW8   S80XZZ22,                          
                                          i;;   


Parametric Cartesian equation: x = (a - b)cos(t) + ccos((a/b -1)t), y = (a - b)sin(t) - csin((a/b -1)t)

There are four curves which are closely related. These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point P on a circle of radius b which rolls round a fixed circle of radius a.

For the hypotrochoid, shown above in hit or miss ASCII, the circle of radius b rolls on the inside of the circle of radius a. The point P is at distance c from the centre of the circle of radius b. For this example a = 5, b = 7 and c = 2.2.

These curves were studied by Newton, la Hire, Desargues, and Leibniz amoung others.

Hy`po*tro"choid (?), n. [Pref. hypo- + trochoid.] Geom.

A curve, traced by a point in the radius, or radius produced, of a circle which rolls upon the concave side of a fixed circle. See Hypocycloid, Epicycloid, and Trochoid.

 

© Webster 1913.

Log in or registerto write something here or to contact authors.