Euclidean planes in three-dimensional space

<p>In <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a>, a plane is a <a href="/facts/Flat_space/vDkfkQJn">flat</a> two-<a href="/facts/Dimension/0ktmUyac">dimensional</a> <a href="/facts/Surface_(geometry)/whF08jvy">surface</a> that extends indefinitely. 
<a href="/facts/Euclidean_plane/tAUtRFcn">Euclidean planes</a> often arise as <a href="/facts/Euclidean_subspace/IlMjx7RK">subspaces</a> of <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a> 
  
    
      
        
          
            R
          
          
            3
          
        
      
    
    {\displaystyle \mathbb {R} ^{3}}
  
.
A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.
While a pair of real numbers 
  
    
      
        
          
            R
          
          
            2
          
        
      
    
    {\displaystyle \mathbb {R} ^{2}}
  
 suffices to describe points on a plane, the relationship with out-of-plane points requires special consideration for their <a href="/facts/Embedding/HKeVKc42">embedding</a> in the <a href="/facts/Ambient_space/umgCRklf">ambient space</a> 
  
    
      
        
          
            R
          
          
            3
          
        
      
    
    {\displaystyle \mathbb {R} ^{3}}
  
.
</p>

Euclidean planes in three-dimensional space open-in-new

Euclidean planes in three-dimensional space