TWC - Pythagorean Musings

The cache is not at the posted coordinates. To obtain the coordinates, solve the puzzle below.

Numbers have been the focus of a love hate relationship with people since the earliest stages of what we would call civilisation. There are archaeological artefacts dating back 30,000 years showing scratches on bones which are thought to represent numbers.
The ancient Babylonians used numbers to record the movements of planets, and to predict eclipses and the like.
Early Egyptians used numbers to predict the flooding of the Nile, the outcome of which determined their future fate.
In ancient Greece there was a cult obsessed with numerical fact and fable, event to the extent of believing numbers determined magical outcomes. Numbers such a "666" took on special and widespread significance.
We could go on, but our interest here centres on the Greek cult know as Pythagoreans, founded by the man we immediately relate to right angled triangles (however there is much doubt whether he was actually involved at all in the mathematical rule which bears his name).

These people seemed to lead relatively comfortable lives, most likely drinking the brew of the day and speculating about the properties of numbers, which seemed to fascinate them. They related numbers to all sorts of objects, especially celestial bodies, and they they also investigated the representation of music in numerical notation. It's worth while researching their activities a little if you find yourself with time on your hands, like they probably did.

Anyway, where this is leading to is that they loved to classify numbers. In the included diagram, you can see four of these classifications depicted.

In the following puzzle, I've depicted the Triangular numbers 1, 3, 6 and 10, as T1, T2, T3 and T4, and I'm sure you can see where that leads with the others.

The final coordinates are determined by adding the following numbers to the minutes in the listed coordinates. Add A to the South minutes and add B to the East minutes.

A = (T1-S1).S2(S3-P1)(T4-T2+H1)
B = P1.(S3-P2)(H4-P4-T1-H1)(P3-T3-H1)
You can validate your puzzle solution with certitude.

We have chosen locations for caches where safe parking is available. Under NO circumstance should driveways and gates be blocked or used for parking. With nearby property owners in mind, these geocaches have been placed out of view, so as not to cause alarm. If you feel a location is causing concern to nearby homeowners, please let us know.