We present new results for the 3-point correlation function, zeta, measured as a function of scale, luminosity and colour from the final version of the two-degree field galaxy redshift survey (2dFGRS). The reduced three point correlation function, Q_3 is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q_3 is consistent with the expectations for the Lambda-cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q_3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9-sigma level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, b_1 = 0.93^{+0.10}_{-0.08} and a quadratic bias c_2 = b_2 /b_1 = -0.34^{+0.11}_{-0.08}. This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three point function. Our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius 8Mpc/h is sigma_8 = 0.88^{+0.12}_{-0.10}, providing an independent confirmation of values derived from other techniques. On non-linear scales, where xi>1, we find that Q_3 has a strong dependence on scale, colour and luminosity.
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