[ July 22, 2002 ]
An irrational palindromic number
John Prophet (email)

If you take phi, the square root of 5, plus 1, the sum divided by 2,
or 1.618033989..., and if you raise this to the 25^th power,
you get a very close approximation of 167761. 

This number, factored, yields 11, 101, and 151 as prime factors.
The products of pairs of these factors are
1111, 1661, and 15251. All palindromes !

If you divide 167761 by 53400,
you get a very close approximation of pi.

53400 comes from the Book of Numbers, among the census
figures for the children of Israel, in Numbers 1:43 and 26:47.
Of the 24 numbers for the 12 tribes generated by the
two censuses, 53400 is one of two that appears twice.

This is summed up by the equation, "Phi to the 25^th, divided
by 53400, equals approximately pi." Aside from this equation,
it is a rare artifact that incorporates both pi and phi.
Only the Great Pyramid of Cheops comes to mind. I would be
interested in hearing of other such artifacts.

Please note that all this has been published in
“The Geometry of God - A Glimpse”, by John Prophet,
(copyright 1999, 157 pages) available from Esansa Corporation,
PO Box 5234, Manchester, NH, USA 03108-5234.
[$14.95, which includes $3.00 handling and shipping in the USA;
inquire via e-mail for non-USA shipping addresses].