πι v. ταυ (geo-flashmob) Mystery Cache

This cache has been archived.

SageInThyme82: I really love the idea of this cache! But nobody seems to have even attempted it in the 4½ years since the group FTF. Now that the cache & host have been removed, it makes more sense to archive than to maintain. So sad...

More
Hidden : 2/27/2016
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size: micro (micro)

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Geocache Description:

This mystery cache is NOT at the published coordinates listed above.

This is a special type of inter-cache called a geo-mob! You need to gather more than π people and their smart-devices within proximity of the listed coordinates. Have everybody locate this webpage and enter mob #1662!
(Before pi-day 2016, the requirement was to exceed τ.)

Every year, nerds aplenty (including myself and many geocachers) celebrate something known as Pi-Day. They've taken the mathematical value of π (approximately 3.14) and decided that they should celebrate it on a day written in short notation as 3/14. But this doesn't make much sense...
  1. The method of writing the date is a convention that changes in different countries. Also the form of π is sometimes taught differently, such as 22⁄7. This leads to different geocachers celebrating Pi-day on March 14th in some countries and 22 July in others!
  2. Others have argued that relating a number arbitrarily written in base10 to a date that is in some ways (months, hours) more closely aligned to base12 is already ridiculous. They insist this constant should be re-written in base12 and celebrated on 3/18.
  3. Many have converted from faith in πι to ταυism. This new constant, τ, is defined as 2π, which most math students recognize is more common than π in a variety of math equations, anyway. This would suggest celebrating on 6/28, or Tau-day. (Some still disagree, insisting that π has always been better than τ.)
All of these reasons and more just emphasize the problem to me: the fundamental meaning of ταυ and πι are lost or ignored! So I'm creating this geocache to celebrate these constants properly.
What exactly is π? It's the ratio of a circle's circumference to its diameter. And, what is τ? Though the diameter makes more sense to engineers, mathematicians define circles by a radius. The ratio of a circumference to its radius (half the diameter) is known as τ.

So is there a sensible way to apply circle formulas to the calendar? Although our calendar is irregular (30 days hath September, April, June...), the path our planet takes around the sun is a nearly perfect circle! So if we treat it that way, then one radius from the centers of Earth and Sun could be measured also as a distance around the perimeter of our orbit. An average perimeter of 365.242 days means that one radian past January 1st brings us (365⁄τ) ≈ 58 days. That's February 27th, now celebrated as ㎭-day*.

You do have to gather a group of devices at the posted location that both can access internet and are GPS-enabled (smart-phones, tablets, etc.), and then finding the final will require a little bit of the math you may have just learned here.

*Note that the Feb. 28th date given on the linked webpage is not correct. Check the math yourself to verify.

Additional Hints (Decrypt)

cv nccebkvzngryl rdhnyf guerr cbvag bar sbhe bar svir avar gjb fvk svir guerr fvk gnh nccebkvzngryl rdhnyf fvk cbvag gjb rvtug guerr bar rvtug svir guerr mreb frira gjb

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)


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