Hope you saved your compass and straight edge from 9th grade
geometry, because you're going to need them. I got the inspiration
for this cache from Euclid's Revenge: a cache which gives three
vertices of a triangle and asks you to search at its circumcenter.
I seemed to recall that there were at least three or four different
ways to define the center of a triangle and did a little research
to verify. It turns out that mathemeticians have thought of at
least 13 ways to define the center of a triangle, though most of
them are pretty esoteric. (see reference
page) Anyhow, I thought I would incorporate this little
geometry lesson into a cache.
Below are three sets of coordinates:
N 42 36.528, W 070 47.101
N 42 36.376, W 070 46.488
N 42 35.072, W 070 48.072
This set defines a triangle. At each of the following three
centers you will find a micro containing a part of the clue to the
final cache:
The Centroid
The Circumcenter
The Incenter
The centroid represents the effective center of mass of the
triangle. The circumcenter is the point that is equidistant from
the three corners of a triangle. The incenter is the center of a
circle inscribed in the triangle, tangent to the three sides. You
could find these centers using a compass and straight edge on a
map, or using a drafting or mapping program on a computer. (check
the
reference page to find out how) Use Caution! Only one of the
above centers is insensitive to a stretching transformation, so do
not assume the coordinates represent a regular grid or you will not
find the other two! My best efforts on paper have resulted in an
accuracy of 20-30 feet, which I believe is adequate. When you get
coordinates, feel free to email them to me for verification before
striking out.
The coordinates listed for this cache are the recommended
parking spot. If you're not familiar with the area, I suggest you
have a look at the map before you start. You can warm up by
visiting the boardwalk cache which is nearby. Be prepared to copy
down the clues as you find them. There will be at least 4 miles of
hiking over difficult terrain, so expect to spend at least 2-3
hours. Heavy snow could make this tricky, but not impossible. Once
you get all the clues, stop and think about it for a minute. You
should be able to find the cache on the spot without doing any
complicated calculations.
Hope you enjoy the hike in what I think is a beautiful piece of
woods.