Mediane eines Tetraeders
 mit Schwerpunkt S
  
    
      
        
          
            
              
              
                
                  
                    
                      
                        |
                      
                      A
                      S
                      
                        |
                      
                    
                    
                      
                        |
                      
                      S
                      
                        S
                        
                          B
                          C
                          D
                        
                      
                      
                        |
                      
                    
                  
                
                =
                
                  
                    
                      
                        |
                      
                      B
                      S
                      
                        |
                      
                    
                    
                      
                        |
                      
                      S
                      
                        S
                        
                          A
                          C
                          D
                        
                      
                      
                        |
                      
                    
                  
                
                =
                
                  
                    
                      
                        |
                      
                      C
                      S
                      
                        |
                      
                    
                    
                      
                        |
                      
                      S
                      
                        S
                        
                          A
                          B
                          D
                        
                      
                      
                        |
                      
                    
                  
                
              
            
            
              
                =
              
              
                
                  
                    
                      
                        |
                      
                      D
                      S
                      
                        |
                      
                    
                    
                      
                        |
                      
                      S
                      
                        S
                        
                          A
                          B
                          C
                        
                      
                      
                        |
                      
                    
                  
                
                =
                
                  
                    3
                    1
                  
                
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}&{\frac {|AS|}{|SS_{BCD}|}}={\frac {|BS|}{|SS_{ACD}|}}={\frac {|CS|}{|SS_{ABD}|}}\\=&{\frac {|DS|}{|SS_{ABC}|}}={\frac {3}{1}}\end{aligned}}}
English: medians of a tetrahedron