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Date: 20-1-2020
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Date: 12-8-2020
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Date: 2-9-2020
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Nice approximations for the golden ratio are given by
(1) |
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(2) |
the last of which is due to W. van Doorn (pers. comm., Jul. 18, 2006) and which are accurate to and , respectively. An even more amazing approximation uses Catalan's constant and the Feigenbaum constant is given by
(3) |
which is accurate to within (D. Ross, cited in Pegg 2005).
A curious (although not particularly useful) approximation due to D. Barron is given by
(4) |
where is Catalan's constant and is the Euler-Mascheroni constant, which is good to two digits.
REFERENCES:
Pegg, E. Jr. "Math Games: Keen Approximations." Feb. 14, 2005. http://www.maa.org/editorial/mathgames/mathgames_02_14_05.html.
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