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

waypoint.

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 into

http://www.gpsvisualizer.com/map?form=googleand 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.