Preface to the Golden Ratio
The Golden Ratio Series
Introduction
Our visual lives are impacted by a handful of mathematical concepts and the golden ratio is probably the most widely visualized but subtle one. In this series of articles, I will walk the readers through the wonders of golden ratio, often denoted by the Greek letter ф.
Definition
The golden ratio is defined as the ratio that we obtain when a line is divided into two segments and the ratio between the longer segment and the shorter segment (golden ratio) is equal do the ratio between the total length and the longer segment. If the longest segment is denoted by L and the short segment is denoted by S, the condition becomes
When this above-mentioned condition is satisfied, the ratio becomes the golden ratio.
Diving into the underlying mathematics
Let us first take L/S as x. Once this is substituted in the equation, we get,
or,
We can solve this equation using quadratic equation solver as shown below.
Once this is solved the value of x is determined as,
Since √ 5 is greater than 1, the numerator becomes negative 4 one of the values of x. Therefore, the numerator becomes negative and it doesn’t…
