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Collection of Some Machin-Type Formulas

 

 
One Term Formulas
 
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Three Terms Machin-Like Formulas
 
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Two Terms Machin-Like Formulas
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Four Terms Machin-Like Formulas
 
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More Than Four Terms Machin-Like Formulas
 
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  • For each positive n,
.

  •    .
(Chien-Lih Hwang [1])
 
  • For each positive n,

(Tue N. Vu)
 
 
Special Arctan Identity Involved 4 Nested Radical (Math Art)
 
  • For arbitrary x,

(Tue N. Vu)

 

References
 
[1] Chien-Lih Hwang, More Machin-Type Identities, The Mathematical Gazette, 1997, p. 120-121.