pi ~= 7^7/2^18

HI Margo,

Thanks for the suggestion about using the pi = 22/7
approx.

I tried pi with 2 7 and 11 as the factors to try and got

Successive approx. to 3.14159265359/1 in form:
2^a * 7^b * 11^c

Max quotient to look for: 1e+050

2/1 2^2/1 11/2^2 2^5/11 2^12/11^3 11^8/2^26 2^57/11^16 2*11/7 11^38/(2^1
27*7) 7^7/2^18
(39627 values tested)

Values in cents
0.0 1200 2400 1751.3179 1848.6821 1946.0462 2010.5435 1978.9129 1982.492 1981.25
59 1981.7813

Cents diffs from target 1981.7954
-781.79536 418.20464 -230.47741 -133.1133 -35.749182 28.748184 -2.8824332 0.6966
8053 -0.53945198 -0.014010083

3.14159265359/1 = 1981.79535537 cents

I thought the program was going to find them in the order of increasing
values for the product of denumerator and denominator but clearly
it is using some other ordering. Looking at the code it doesn't
really say anything about how they are ordered, and I think perhaps
at the time I was just trying to find various xenharmonic bridges
without really being concerned about ordering them
in a systematic way.

Anyway was intrigued to find that 7^7/2^18 is a very
close approximation to pi indeed.

It works out at 3.1415672...
pi is
3.141592653...
22/7 is
3.142857142...

Anyone else noticed this before?

As for the cents values - you see those in the output.

Obviously I will need to do more work on the program if I want
to do some experimental investigating of the prime limit
type flavour of irrationals.

Robert