Pythagoras' Theorem
Pythagoras' Theorem is a fundamental relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The theorem can be written as an equation relating the lengths of the sides a,b and c:
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.
The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it. In any event, the proof attributed to him is very simple, and is called a proof by rearrangement.
The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem, Q.E.D.
That Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus. Several other proofs of this theorem are known, but this is known as the Pythagorean one.
(Source: Wikipedia)
The Cache
To find the cache you'll need to employ some measurement and geometric techniques. You can do this in the field, or you can use your favourite on-line tools to determine the final location.
For the purposes of this cache we'll use a fictional unit of measure - the 'geo', written as 1geo, 10.5geo, etc.
The posted coordinates will take you to WP1, a geodetic marker bearing the code D5MQ
From WP1 find WP2. You'll find it on a roughly south-easterly bearing at a distance of exactly 12geo. It bears the code DQ04
Using the line WP1-WP2 construct a Pythagorean triangle WP1-WP2-WP3 such that the length of each side of the triangle is an integral number of geos. WP3 should have a bearing between 90º and 120º true from WP1.
From WP3 project a new waypoint on a bearing of 122º true, a distance of 11.357geo. This is the location of the cache.
You're looking for a camouflaged 200ml Sistema container. At placement it contained only a logbook - bring your own writing implement.
You can check your answers for this puzzle on GeoChecker.com.
Take care at GZ - you can be seen clearly from many directions. There may be times of the day when it is just not possible to be stealthy.
Ensure everyone who logs a find has signed the log, or that their team name is clearly identified in their log entry. Log entries that do not match the physical log may be deleted. Photo logs will not be accepted. If you can't sign the log because of a problem with the cache please log a maintenance request.
Ensure that the cache is replaced exactly where and how you found it. We don't want it to be muggled.
Kudos to huhugrub who managed to find the cache even with an error in the final bearing!