or

## Kendra's Cache-Triangulate This!-FTFC #27

A cache by ATMA
Hidden : 8/25/2006
In Texas, United States
Difficulty:
Terrain:

Size:  (micro)

#### Watch

How Geocaching Works

Please note Use of geocaching.com services is subject to the terms and conditions in our disclaimer.

### Geocache Description:

A micro cache for you. This one may be a difficult find.
Roll log up and place in top THEN screw it closed. This keeps the cache working for the next hunters.

This cache is dedicated to our third and youngest child, Kendra, of KandRS.

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent triangles. It was proven in 1925 that every surface has a triangulation, but it might require an infinite number of triangles and the proof is difficult. A surface with a finite number of triangles in its triangulation is called compact.
Wickham-Jones (1994) gives an algorithm for triangulation ("otectomy"), and O'Rourke (1998, p. 47) sketches a method for improving this too, as first done by Lennes (1911).
Garey et al. (1978) gave an algorithmically straightforward method for triangulation, which was for many years believed optimal. However, Tarjan and van Wyk (1988) produced an algorithm. This was followed by an unexpected result due to Chazelle (1991), who showed that an arbitrary simple polygon can be triangulated. However, according to Skiena (1997), "this algorithm is quite hopeless to implement."

In trigonometry and elementary geometry, triangulation is the process of finding coordinates and distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other known reference points, using the law of sines.
Some identities often used (valid only in flat or euclidean geometry): The sum of the angles of a triangle is p rad or 180 degrees.

1. The law of sines
2. The law of cosines
3. The Pythagorean theorem

Triangulation is used for many purposes, including surveying, geocaching, navigation, metrology, astrometry, binocular vision, finding FTF Trophies and gun direction of weapons.
Many of these surveying problems involve the solution of large meshes of triangles, with hundreds or even thousands of observations. Complex triangulation problems involving real-world observations with errors require the solution of large systems of simultaneous equations to generate solutions. If this were a hide that required triangulation, you would have to worry about the text above and below but in this case it doesnt so just go get it. We are thinking that this might be how this hide came by at least part of its name.
Given a set of points, the plane can be split in domains for which the first point is closest, the second point is closest, etc. Such a partition is called a Voronoi diagram. If one draws a line between any two points whose Voronoi domains touch, a set of triangles is obtained, known as the Delaunay triangulation. Generally, this triangulation is unique. One of its properties is that the outcircle of every triangle does not contain any other data point. It is used, for instance, when one wishes to construct an approximation to a function z(x,y) whose values are only known for a finite set of points (x,y) (e.g. these could be depth measurements in a canal and the approximation z(x,y) would be used to determine how much sediment has accumulated since an earlier measurement).
This cache is located in a really neat little park we found the other day. It is a nice short walk out with many different ways to get there. Love the green belts.

###### Please note that not all GPS Receivers will give the same level of accuracy. Dont post revised coordinates. It’s close enough to add excitement to the hunt.
Happy Caching!

Whfg Unat Va Gurer! Lbh jvyy svaq vg.

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)

### Inventory

There are no Trackables in this cache.

Find...

### 98 Logged Visits

77      10      4      1      1      3      1      1

**Warning! Spoilers may be included in the descriptions or links.