or

Equilateral Triangle - South

A cache by SlideRule
Hidden : 9/2/2006
In Chile
Difficulty:
Terrain:

Size:  (micro)

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Geocache Description:

THE POSTED COORDINATES ARE NOT THAT OF THE CACHE

With a name like SlideRule, you know sooner or later there would be a problem of mathematical nature.

So here is today's problem:

In plane geometry, from any given two points, you can construct a line segment.  From that line segment, it is easy to construct an Equilateral Triangle.

 Point 1 S 13.556243643131 W 116.730255858190 Point 2 N 07.464291909245 W 075.221183660873

Using  those two points as one of the sides, construct an Equilateral Triangle using points on the surface of the Earth.  At the vertex of the triangle produced, there is the cache location.

Assumptions: (For the calculations)

• Perfectly Spherical Earth (NOT Ellipsoidal)

• This is a pure Euclidian geometry problem.

• The accuracy that I give you is excessive.  Close to a millimeter.

• Notice that the coords are in Decimal Degrees, Not in DD MM.MMM fromat.

• The resultant triangle is the results of equal secants drawn from point to point.

Some of you may suggest:

1. The Earth is not a perfect Sphere: That is true.  For this problem, assume that the Earth is a perfect sphere, Therefore, You can safely make the assumption that the Lat/Lon that you get as the solution to this problem  There will be a non-spherical problem in the future.  I will post the link [Here] after I position the caches.

2. That given the two points, there are two solutions:  Well, guess what boys and girls?  There are two caches.  One generally North of the line between the two points and another South of the line drawn between the two points.

 For You Information:  There are two Caches...  Equilateral Triangle - South [GCY3H2] Solve, or better yet, Find them both for the big EGO trip.

Now for a few hints:

• The Checksum for the North Cache is: N 16 and W 26 in DD MM.MMM format

• The Checksum for the South Cache is: S  28 and W 41 in DD MM.MMM format

• The LSD for the North Cache is 0 and 6,  For the South Cache is 8 and 7.

• The caches are both large Ammo sized boxes painted International orange with UV and Light reflectors, cleverly camoed to look like a small black magnetic Hide-A-Key.  Bring your own writing utensil.

• Owner requests that finders not inform others of the location of this Cache.  This is to maintain the difficulty of the Cache.

• All feedback about the coords and the cache hide will be appreciated.

Email owner the coords before going out to find this cache

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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