Abstract
THE problem of random fragmentation of a line into a finite number of N parts has received considerable attention, partly because of its application in assessing the randomness of radioactive disintegrations and cosmic ray events. For a line of length l the average number of fragments equal to or greater than x is1: 
This equation is readily applied to discuss2 an idealized case of random fragmentation of area. Consider a rectangle of sides l
1 and l
2 (area Σ = l
1
l
2) and imagine it to be divided into subrectangles by drawing at random N
1and N
2 lines respectively parallel to the two sides of the rectangle. If N(S) be the average number of elements of area equal to or exceeding S, we have, using equation (1): 
where K
1(z) is the usual Bessel function of imaginary argument, N
0= N
1
N
2 is the total number of elements and S
0 the average area of an element, 
For S≫S
0 we obtain the approximate relation: 
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References
Feller, W., Phys. Rev., 57, 906 (1940).
Goudsmit, S., Revs. Mod. Phys., 17, 321 (1945).
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AULUCK, F., KOTHARI, D. Random Fragmentation. Nature 174, 565–566 (1954). https://doi.org/10.1038/174565a0
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DOI: https://doi.org/10.1038/174565a0
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