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The book "Mathematical Constants" by Steven R. Finch contains 136 sections on constants or classes of constants. The table of numerical values at the back of the book is 23 pages long and about 13 pages of this table are taken up by values between 0 and 1, about 5 pages of values between 1 and 2, 2 pages between 2 and 3, 1 page between 3 and 4, slightly more than half a page for 4-5, less than half a page for 5-6 and about a page for all values above 6.

13, 5, 2, 1, .75, .25 ...

What reasons are there for numerical constants to be following this distribution ?

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Benford's law? –  Robin Chapman May 18 '10 at 17:11
    
Benford's law. Thanks. –  Roy Maclean May 18 '10 at 17:28
    
There is no accept button for comments, it seems. Only answers. –  Roy Maclean May 18 '10 at 17:31
    
Benford's law doesn't seem relevant, or at least couldn't explain the distribution you've noted: constants between 0 and 1 start with all digits 0-9. –  Scott Morrison May 18 '10 at 19:14
    
@Scott Morrison: It's similar to Benford's law. Instead of taking "first digit" you take "integer part" and instead of digits 1-n you take integers 0-infinity. Another part of the question is why they are clustered around zero, but then I suppose they couldn't be clustered around anything else really. –  Roy Maclean May 18 '10 at 19:33
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