2022/11/12 by Klazar, Martin · 1 citation
#60D05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #Probability (math.PR)
paper · doi:10.48550/arxiv.2211.06749
We investigate Bertrand's probabilistic paradox through the lens of discrete geometry and old-fashioned but reliable discrete probability. We approximate the plane unit circle with 1/n times 1/n boxes and count the pairs of boxes separated by distance more than √(3). For n→∞ the proportion of such pairs goes to (1+√(3))/(8)-(π(2-√(3)))/(96)=0.33273… .