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Why is $22/7$ a better approximation for $\pi$ than $3.14$?
Approximating $\pi$ with least digits

do we know any representation/fraction other that $\frac{22}{7}$ which is a closer approximation of $\pi$

I have one representation $k$ which is not a fraction but a closer approximation of $\pi$, when compared to the fraction $\frac{22}{7}$

$k=(9.87654321)^{\frac{1}{2}}$

Here, $\pi \lt k \lt \frac{22}{7}$

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8  
Sure, 314159/100000. –  JSchlather Aug 20 '12 at 6:19
    
Also 3.141592653589793 is a pretty good representation –  Fabian Aug 20 '12 at 6:29
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Lu Chao might know a good approximation... –  Arthur Fischer Aug 20 '12 at 6:38
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:D The OP has a love in the approximation of $\pi$. Example of another 22/7. –  FrenzY DT. Aug 20 '12 at 6:47
    
Remember that a "decimal" is, properly speaking, a decimal fraction. The approximation \pi\approx 3.1416$ was known, in fractional form, in Hellenistic times. –  André Nicolas Aug 20 '12 at 7:05
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marked as duplicate by Zhen Lin, Arthur Fischer, t.b., mixedmath Aug 20 '12 at 7:02

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2 Answers

I guess 355/113 = 3.1415929203539825.

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Well, same here, 335/113 :) –  FrenzY DT. Aug 20 '12 at 6:34
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Check out the page http://en.wikipedia.org/wiki/Approximations_of_%CF%80 for all you want.... and more!

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"Jamshīd al-Kāshī (Kāshānī), a Persian astronomer and mathematician, correctly computed 2π to 9 sexagesimal digits in 1424" Sexagesimal... those crazy Persians.... –  Euler....IS_ALIVE Aug 20 '12 at 6:23
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