  We introduce the concepts of participant triangularity and triangular flow in
heavy-ion collisions, analogous to the definitions of participant eccentricity
and elliptic flow. The participant triangularity characterizes the triangular
anisotropy of the initial nuclear overlap geometry and arises from
event-by-event fluctuations in the participant-nucleon collision points. In
studies using a multi-phase transport model (AMPT), a triangular flow signal is
observed that is proportional to the participant triangularity and corresponds
to a large third Fourier coefficient in two-particle azimuthal correlation
functions. Using two-particle azimuthal correlations at large pseudorapidity
separations measured by the PHOBOS and STAR experiments, we show that this
Fourier component is also present in data. Ratios of the second and third
Fourier coefficients in data exhibit similar trends as a function of centrality
and transverse momentum as in AMPT calculations. These findings suggest a
significant contribution of triangular flow to the ridge and broad away-side
features observed in data. Triangular flow provides a new handle on the initial
collision geometry and collective expansion dynamics in heavy-ion collisions.
