What is the golden ratio?

Mario (2002) states that the Golden Ratio was become known as a formalised deductive system around 300 BC by Euclid of Alexandria, the founder of geometry.  Euclid defines a proportion derived from a simple division of a line (see Figure 2.1) into what he called as “extreme and mean ratio”.

            From the straight line in Figure 2.1, the ratio of the whole segment (AB) is the same to the larger segment as the larger segment is to the shorter segment (Rune, 2005).

In other words, line AB is absolutely longer than the segment AC but at the same time, the segment AC is longer than CB. Thus , then the line has been cut into an extreme and mean ratio which is the Golden Ratio.  The relationship between the ratios of AC to CB in Figure 1 produce the never-ending number 1.6180339887…, and such never-ending numbers have create an interest among the researchers (Mario, 2002).