On Wed, 29 Mar 2000, Vernon Jenkins wrote:
> This statement is supported by a comprehensive body of evidence,
> recently-assembled under the heading, "The Lamp: a role for numerical
> coincidence in the pursuit of truth." The page address is
>
> http://homepage.virgin.net/vernon.jenkins/Symb.htm
Vernon,
Your claims for certain properties of the number 37 being special are very
much overblown. An analysis of why these properties hold shows that many
of them hold for other numbers as well.
Many of them hold simply because 37 is a divisor of 999 and would also
hold for any other divisor of 999. (999 has eight divisors in all.) For
example, one gets a cyclic permutation of the digits of a 3-digit number
by multiplying it by 10 and then subtracting 999 times the first digit. So
the resulting number is divisible by whatever factor of 999 divides the
original number. Adding clusters of three digits is something like
"casting out nines" except it is casting out 999's (hence casting out any
divisor of 999). Likewise, your observations on sums of cubes would hold
for any divisor of 999, not just 37.
Many of your observations about repeating decimals are valid because you
are computing the reciprocal of a factor of 999,999. If ab=999,999, then
the repeated sequence in the decimal expansion of 1/a will be b. If a is
not divisible by 37, then b will be.
Any odd number not divisible by 5 will divide some number all of whose
digits are 9's. Thus you can get the same sort of properties for these
numbers but with clusters of some other number of digits and cubes
replaced by some other powers. As for numbers divisible by 2 or 5, you can
get the same sort of properties if you are willing to replace base 10 by
some base that is relatively prime to the number in question.
One should not assume that just because he sees some fascinating
mathematical property associated with a particular number, it must be a
special property of that number only. A more general analysis of the
situation using algebra may reveal other numbers with the same property.
Gordon Brown
Department of Mathematics
University of Colorado
Boulder, CO 80309-0395
This archive was generated by hypermail 2b29 : Fri Mar 31 2000 - 17:01:50 EST