Are you by any chance getting this stuff from the Karl Sabbagh book
"the Reimann Hypothesis'? It is covering such numbers as the (sqrt 5+1)/2
which they identify as the 'golden mean' as the solution to a=1+1/a which is the solution to the infinite series 1/1+(1/1+1).....which starts out as 2/3 then 3/5 and converging on the sqrt 5 thing posted above.
This is my present read and a dang fine book, it also includes the solution by De Branges, which he submitted 3 years ago but is basically being dissed by the maths community even though he made some major contributions to maths.