We prove that the projective triangle of
odd, defines via indicator sets a regular nearfield spread of
PG(3,q) , and conversely one of the indicator sets of such a spread is the projective triangle. Then we rephrase our results in the framework of the direction problem. Recall that if
U is a set of
s points in
AG(2,s) and
N is the number of the determined
... [Show full abstract] directions, when with p an odd prime, Gács, Lovász and Szőnyi have proved that for there is a unique example and U is affinely equivalent to the graph of the function . Here we prove a similar result for any odd prime power, assuming some extra hypotheses.