Eulers identity, 
  
    
      
        
          e
          
            i
            π
          
        
      
    
    {\displaystyle e^{i\pi }}
  + 
  
    
      
        1
      
    
    {\displaystyle 1}
   = 
  
    
      
        0
      
    
    {\displaystyle 0}
  , contains five essential numbers used widely in mathematics: Archimedes constant 
  
    
      
        π
      
    
    {\displaystyle \pi }
  , Eulers number 
  
    
      
        e
      
    
    {\displaystyle e}
  , the imaginary number 
  
    
      
        i
      
    
    {\displaystyle i}
  , unity 
  
    
      
        1
      
    
    {\displaystyle 1}
  , and zero 
  
    
      
        0
      
    
    {\displaystyle 0}
  , which makes this formula a renown example of beauty in mathematics.
Hearing loss has been reported and may be related to ear canal atresia or stenosis. Umbilical and inguinal hernias have been reported in a small number of people with ring 18. Unilateral renal hypoplasia and aplasia have both been reported in individuals with ring 18. Hydronephrosis as well as pyelonephritis have also been reported in a few individuals. Cryptorchidism, hypospadias, and micropenis have been seen in males with ring 18, while females have been reported with hypoplastic labia. Foot abnormalities are common within the ring 18 population. Scoliosis as well as pectus excavatum have also been frequently reported. Several people with ring 18 have growth hormone deficiency. Hypothyroidism has also been reported in a minority of people. Cognitive ability varies; according to a literature review, the degree of impairment may fall anywhere between the mild and severe ends of the spectrum. Facial features of ring 18 include low-set, dysplastic ears, epicanthic folds, and hypertelorism. Micrognathia has also been reported. Genetic
Individuals with ring 18 have one of their two copies of chromosome 18 that has formed the shape of a ring. The ring is formed when the caps on  both the long arm (q) and the short arm (p) of one copy of chromosome 18 are lost and the new ends re-join to form the ring. Because the ring involves deletions of both the long arm (18q-) and the short arm (18p-) of chromosome 18, individuals with ring 18 can have features of both 18p- as well as distal 18q-.