Sint-Lucas Department for Architecture, Paleizenstraat 65, 1030 Brussels, Belgium
E-mail address: firstname.lastname@example.org
(Received June 12, 2004; Accepted September 6, 2004)
Keywords: Golden Number, Color Theory, Gray Tone
Abstract. Literature describes the golden number f = 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 f - 1 = 1/f = 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 rth-part of a gray tone and (1 - r)th-part of a double layer of that gray tone, the result can be surprising. Indeed, when a disk divided into halves (r = 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.