Toroidal coordinates

<p>Toroidal coordinates are a three-dimensional <a href="/facts/Orthogonal_coordinates/LLoa2lAJ">orthogonal</a> <a href="/facts/Coordinate_system/Mtd0q4SP">coordinate system</a> that results from rotating the two-dimensional <a href="/facts/Bipolar_coordinates/fyChoDRu">bipolar coordinate system</a> about the axis that separates its two foci.  Thus, the two <a href="/facts/Focus_(geometry)/WFtFnqoa">foci</a> 
  
    
      
        
          F
          
            1
          
        
      
    
    {\displaystyle F_{1}}
  
 and 
  
    
      
        
          F
          
            2
          
        
      
    
    {\displaystyle F_{2}}
  
 in <a href="/facts/Bipolar_coordinates/fyChoDRu">bipolar coordinates</a> become a ring of radius 
  
    
      
        a
      
    
    {\displaystyle a}
  
 in the 
  
    
      
        x
        y
      
    
    {\displaystyle xy}
  
 plane of the toroidal coordinate system; the 
  
    
      
        z
      
    
    {\displaystyle z}
  
-axis is the axis of rotation. The focal ring is also known as the reference circle.
</p>

Toroidal coordinates open-in-new

Toroidal coordinates