Efficient measurement of the percolation threshold for fully penetrable discs

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Anomalous transport in the crowded world of biological cells (2013, background): “323 652 5(6) for discs [125, 126]; numbers in parentheses indicate the uncertainty in the last digit.”
Sampling-based algorithms for optimal motion planning (2011, background): “The exact value of λc is not known; Meester and Roy provide 0.696 < λc < 3.372 for d = 2 (Meester and Roy 1996), and simulations suggest that λc ≈ 1.44 (Quintanilla et al. 2000).”
Connectivity of random k-nearest-neighbour graphs (2005, background): “Simulations [1], [15] suggest that πr2 crit ≈ 4.”
Spatial Networks (2010, methodology): “There is an extensive mathematical literature on geometric graph and the random case was studied by physicists in the context of continuum percolation (see for example [24, 261]).”