a bell curve never reaches 0, so past d = r it's cut off by force. the cutoff always slices the hillside somewhere.
σ sets how wide the hill is.
σ=r/2.2 positions the cutoff at d=2.2σ
i(r)=e−2.42≈ 0.089 where d=r
0≤ i(r)≈ 0.089≤ 1⟹ [.]
by having r=2σ the cutoff lies on the gaussian tail