Tuesday, 20 August 2019

math history - Approximation for pi



I just stumbled upon




π95+95=3.141640786



which is δ=0.0000481330 different from π. Although this is a rather crude approximation I wonder if it has been every used in past times (historically). Note that the above might also be related to the golden ratio Φ=5+12 somehow (the 5 is common in both).



Φ=56(95+95)1



or



Φ56π1




I would like to know if someone (known) has used this, or something similar, in their work. Is it at all familiar to any of you?



Related Question (link).


Answer



Ramanujan found this approximation, among many others, according to Wolfram MathWorld equation 21 in linked page.


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