High-intensity exercises may cause lower treatment adherence. Meditative
A 2021 meta-analysis found that meditative exercise programs (tai chi, yoga, qigong) were superior to other forms of exercise (aerobic, flexibility, resistance) in improving sleep quality. Other meta-analyses also found positive effects of tai chi for sleep, fibromyalgia symptoms, and pain, fatigue, depression and quality of life. These tai chi interventions frequently included 1-hour sessions practiced 1-3 times a week for 12 weeks. Meditative exercises, as a whole, may achieve desired outcomes through biological mechanisms such as antioxidation, anti-inflammation, reduction in sympathetic activity and modulation of glucocorticoid receptor sensitivity. Aquatic
Several reviews and meta-analyses suggest that aquatic training can improve symptoms and wellness in people with fibromyalgia. Other
Limited evidence suggests vibration training in combination with exercise may improve pain, fatigue, and stiffness. Medications
A few countries have published guidelines for the management and treatment of fibromyalgia. As of 2018, all of them emphasize that medications are not required, only optional. The German guidelines outlined parameters for drug therapy termination and recommended considering drug holidays after six months. Approved medications
Health Canada and the US Food and Drug Administration (FDA) have approved pregabalin and duloxetine for the management of fibromyalgia. The FDA also approved milnacipran, but the European Medicines Agency refused marketing authority. Antidepressants
Antidepressants are one of the common drugs for fibromyalgia. A 2021 meta-analysis concluded that antidepressants can improve the quality of life for fibromyalgia patients in the medium-term.
Further extensions of the real numbers under Hurwitzs theorem states that there are four normed division algebras: the real numbers 
  
    
      
        
          R
        
      
    
    {\displaystyle \mathbb {R} }
  , the complex numbers 
  
    
      
        
          C
        
      
    
    {\displaystyle \mathbb {C} }
  , the quaternions 
  
    
      
        
          H
        
      
    
    {\displaystyle \mathbb {H} }
  , and the octonions 
  
    
      
        
          O
        
      
    
    {\displaystyle \mathbb {O} }
  .