Many animals regularly return to particular locations such as hives, n
ests, wintering grounds or cache sites. This ability clearly implies t
hat animals possess information that allows them to find a route from
their current location to their goal. However, the nature of this info
rmation is, in many cases, unknown. One particularly important issue i
s whether this information encodes at least some of the geometric rela
tionships among real-world objects, which would meet a strict definiti
on of a cognitive map(1,2). Are animals sensitive to such geometric re
lationships? Although there is dear evidence that animals can learn ve
ctors that represent a goal location in terms of absolute distance and
direction to a landmark, there is little evidence of any ability to e
xtract abstract geometric rules(3-8). Here we report data demonstratin
g that the corvid Clark's nutcracker (Nucifraga columbiana) can learn
to find the point halfway between two landmarks that vary in the dista
nce that separates them. This learning is based on a general principle
, as the birds correctly find the halfway point when the landmarks are
presented with new distances between them. This demonstrates the abil
ity to find a point defined not by the relationship between a goal and
a landmark but by the relationship between landmarks. Further experim
ents demonstrate that there were two distinct processes involved in lo
cating the halfway point, the use of directional bearings to find the
(hypothetical) line connecting the landmarks and finding the correct p
lace along that line.