Approximations to Catalan's constant include
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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(M. Hudson, pers. comm., Nov. 19, 2004), where 
is the golden ratio, which
are good to 4, 5, 6, 6, 7, 7, and 9 digits, respectively.
Other approximations include
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(7)
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(8)
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(K. Hammond, pers. comm., Dec. 31, 2005), where 
is the golden ratio, which
are good to 5 and 9 digits, respectively.
