I guess I should clarify "triangulate"...
If one has a GPS, one can use a feature called "project waypoint" to find the
intersection of two or more flight vectors, and then use the GPS to find
that location, which certainly may not locate the exact tree, but gets you
close enough to where you can start looking around for bees doing their
thing near the hive entrance.
But you need not depend upon only a few vectors. You could keep
releasing bees, and use all the vectors, thereby locating multiple hives.
It is not at all unusual to find that some bees released fly away in
an unexpected direction, which may indicate that one has multiple
hives in the area being surveyed.
Fair warning, the following gets a bit "technical"...
If you use any GPS, you have a very accurate waypoint from which you
released each bee, and you have a fair-to-good estimate of the point at
which you lost sight of the bee, which you can walk to and mark as another
So, for each bee, you have a Longitude/Latitude where you released the
bee (x1, y1), and a Longitude/Latitude pretty near where you lost sight
of the bee (x2, y2). If you have another bee that appeared to be flying
in the same general direction, you can do some math to extend the vectors
to their intersection, as follows:
Do the following or each bee flight vector:
A = y2 - y1
B = x1 - x2
C = A*x1 + B*y1
To find the intersection of any two bee vectors,
you take the A, B, and C for each and find "D":
D = A1*B2 - A2*B1
And the intersection of the two flight vectors
(a possible hive location) is:
x intersection scalar = (B2 * C1 - B1 * C2) / D
y intersection scalar = (A1 * C2 - A2 * C1) / D
In all of the above:
"x" is always a longitude
and "y" is always a latitude
And you can map all the data on any mapping
system. If you don't have a mapping system,
you can plug your longitudes and latitudes intohttp://www.gpsvisualizer.com/map?form=google
and make a Google map.
So, all you really need to do is capture bees
with a beelining box and release them from
a reasonable spread of locations. Finding the
hives (or counting them) is a matter of simply
mapping enough data from enough bees.
When you have 3 bees all flying from a
bee-lining box from different locations
to the same general area, that area's
nearly certain to contain a hive.