It’s just a number!
π is the ratio of a circle’s circumference to its diameter. However, that’s not all!
π also crops up in a plethora of other places in physics, mathematics and even (my favorite!) engineering.
(Not that I know anything about that of course...)
The first 100 digits of π are
3.14159265358979323846264338327950288419716939937510582097494
4592307816406286208998628034825342117067.
The Guinness Book of World Records recognizes a 24-year-old graduate student from China as having recited from memory 64,890 digits of π. It took him more than 24 hours.
And then the M.I.T. boys have at least one cheer that includes "3.14159!"
Guess that they have to have SOMETHING to cheer about....
Since π is an irrational number (cannot be represented as the ratio of two integers), there is no fixed pattern or repetition in its decimal expansion. Various rational approximations exist. The first is the most well known, but also the least accurate. Surprisingly though, good enough for many purposes.
| tolerance |
ratio |
value |
| 0.01 |
22 / 7 |
3.14285714285714 |
| 0.000001 |
355 / 113 |
3.14159292035398 |
| 0.000000001 |
104348 / 33215 |
3.14159265392142 |
| 0.0000000001 |
312689 / 99532 |
3.14159265361894 |
| 0.00000000001 |
1146408 / 364913 |
3.14159265359140 |
| 0.0000000000001 |
5419351 / 1725033 |
3.14159265358982 |
| 0.00000000000001 |
80143857 / 25510582 |
3.14159265358979 |
But not good enough to find this cache... You are going to have to find many digits in the precise value of π.
The cache is actually hidden at
| N |
33° 5A.BCD' |
| W |
84° 2E.FGH' |
where the letters are found from the following clues:
- A is the sixteenth digit in π.
- the rational approximation to π which is accurate to 0.00000000000001 is 80143857 / 255B0582.
- C occurs three-in-a-row at position 601.
- D is (the most frequent number in the first 100 digits of π) MINUS (the number that occurs exactly 10 times in the first 100 digits of π).
- E is the number of times 1 appears in the first 100 digits of π
- F first occurs at the thirty-second position after the decimal point.
- G is at position 31415927.
- H is the repeating digit at 307 & 308.
The area around GZ can be a bit Muggly, so practice "good stealth."
GOOD LUCK!
You can check your answers for this puzzle on Geochecker.com.
And thanks to haggishound for allowing me to "borrow" from his cache page GC16CA4 to implement this idea!