The cache is located at N xx xx.xxx, W yy yy.yyy.
You can find the string of digits representing the North coordinates embedded fairly close to (that is, within a couple hundred digits of) the 6,484,000th digit of the decimal expansion of pi.
Similarly, you can find the West coordinates in the vicinity of the 3,991,500th digit.
It is worth noting that the nature of pi (defined simply as the ratio of any circle's circumference to its diameter -- a ratio which turns out to be identical for all circles!) was the subject of considerable study in ancient times. Approximations range from the imprecise (e.g pi = 4) to the remarkably close, and the search for better and better rational approximations has occupied the minds of many great mathematicians over the millennia.
Johann Heinrich Lambert is credited with the first proof that pi is irrational (i.e., that it cannot be expressed as a ratio of two integers). His proof using an infinite series for tan(x) was published in his "Mémoires sur quelques propriétés remarquables des quantités transcendantes, circulaires et logarithmiques" in 1761.
This cache was inspired by the Slice of pi(e) cache (GC2EQKT) over near Wautoma. Thanks for the inspiration, pezmon!
You can check your answers for this puzzle on Geochecker.com. Happy hunting!
Congrats to the "ultra ninja" drhaas for a well-earned FTF! 