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Resource: Pi

Pi \pi is a constant of nature with infinitely many decimals (an irrational number). It is defined as the ratio between circumference and diameter of any circle.

The first 500 decimals are:[1]

\begin{aligned}
\pi=3.&1415926535\;8979323846\; 2643383279 \; 5028841971 \;6939937510\\
~& 5820974944 \; 5923078164 \; 0628620899  \; 8628034825   \; 3421170679\\ 
~& 8214808651  \; 3282306647  \; 0938446095  \; 5058223172  \; 5359408128\\
 ~& 4811174502  \; 8410270193  \; 8521105559  \; 6446229489  \; 5493038196\\
 ~& 4428810975  \; 6659334461  \; 2847564823  \; 3786783165  \; 2712019091\\
 ~& 4564856692  \; 3460348610  \; 4543266482  \; 1339360726  \; 0249141273\\
 ~& 7245870066  \; 0631558817  \; 4881520920  \; 9628292540  \; 9171536436\\
 ~& 7892590360  \; 0113305305  \; 4882046652  \; 1384146951  \; 9415116094\\
 ~& 3305727036  \; 5759591953  \; 0921861173  \; 8193261179  \; 3105118548\\
 ~& 0744623799  \; 6274956735  \; 1885752724  \; 8912279381  \; 8301194912\\
 ~& \ldots
\end{aligned} 

\pi has no pattern (never starts repeating itself) and never ends – and this is not just something people think; it can be proven.[2] Pi has become an international phenomenon and there even is a pi day: March 14th (3/14). See the website www.piday.org.


References:

  1. The first 10 digits of pi (π) are 3.1415926535’ (web page), Pi Day2, 2018, www.piday.org/million (accessed May 10th, 2019)
  2. Q: How do we know that π never repeats? If we find enough digits, isn’t it possible that it will eventually start repeating?’ (web page), Ask a Mathematician / Ask a Physicist, 2013, www.askamathematician.com/2013/12/q-how-do-we-know-that-π-never-repeats-if-we-find-enough-digits-isnt-it-possible-that-it-will-eventually-start-repeating (accessed May 10th, 2019)

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