Golden Gray

摘要

Literature describes the golden number PHI=1.618 ...and related golden angle of 36° extensively,including statements of doubtful verification.Still,the authors propose to introduce a new "golden" concept,since PHI-1=PHI=0.618 ...occurs in color theory.This unusual field of mathematical application uses the "gray value" of a transparent layer,that is,its part w of white(transparent)pixels(the remaining 1-w pixels being black).If a rotating disk is divided in a pth-part of a gray tone and(1-p)th-part of a double layer of that gray tone,the result can be surprising.Indeed,when a disk divided into halves(p=1/2)and when the resulting gray is half white(w=1/2),the golden number provides the gray tone to be used.The concept provides an experimental determination for the golden number.