Golden Mean Series
Background: Historically, four of the most famous irrational mathematical constants are , , , and . Most of these have well documented and explicit representations in the form of infinite series and continued fractions (see table below for a summary of these representations). While investigating the Golden Mean, no equivalent infinite series was found that explicitely defined .
Although the infinite series presented here for Phi, as well as the other series in the table above, are not necessarily the fastest way to calculate many decimal places for irrational numbers, the equations here are a straight forward way to calculate out the value of these constants using Excel or other symbolic calculation programs like Mathematica.