Exploring the Golden Ratio

By Trang Ninh

Image source: Exitus capital

Known as “orderly chaotic”, the golden ratio presents the perfect balance between 

complexity and simplicity. Underlaid by simplistic equations, the art of nature - Golden Ratio - tends to be the most visually appealing to our brains. Thus, it consolidates the art field's development; since the ancient age, when pyramids were built, until nowadays, as we study compositions design. Let’s find out about this concept. 

What is the Golden Ratio? 

The Golden Ratio (or golden section), is presented by the Greek letter phi (Φ), has the approximate value of 1.618… 

The irrational value Φ could be calculated by dividing a line into 2 parts, where the value of length a divided by length b is equal to the length of the whole line divided by length a as shown in figure 1. 

Why is the Golden Ratio special? 

According to neuroscientists’ research, our brain naturally perceives a proportion which is close to the Golden Ratio as harmonious and pleasing. As our visions are built to interpret the world as efficiently as possible, patterns which follow the Golden Ratio creates cognitive comforts where it takes less effort to follow through. Thus, this structure appears as intuitively balanced, makes us feel “right”, and visually appealing. 

Fibonacci Sequence and Golden Ratio: 

Many students may have known the Fibonacci Sequence as the series where each number is the sum of the two preceding numbers (usually start with 0 and 1): 0,1,1,2,3,5,8,13...  But is it just a normal sequence? 

As the sequence continues, the quotient of a number and its predecessor converges and approaches closer to the value Φ (the golden ratio). For example 8/5 =1.6 and 13/8=1.625. 

This sequence appears frequently in nature (seashells, sunflower’s seed arrangement,...) by drawing arcs connecting squares’ corners where the squares’ sides are values in the fibonacci sequence. This causes the curvature of the structures to be relatively aligned with the Golden Ratio making it becoming the Golden Spiral Structure. 

In nature, the golden spiral structure is idealised as it fosters and protects organisms. Plants, such as succulents and trees, often utilise this structure in leaves arrangement (at a golden angle) to ensure limiting shading and maximise the rate of photosynthesis. Similarly, sunflowers and pinecones also articulate their seed arrangement to the Fibonacci numbers in order to optimise seed density (for seed to not be overcrowded nor having too much space between seeds). Furthermore, the Golden spiral structure in shells, such as nautilus, allows this organism to grow in a structurally stable shape as the sequence matches the shells’ logarithmic spiral expansion.  

References

EBSCO. (2019, 12 4). Nature’s MATHterpiece: The Fibonacci Sequence. Nature’s MATHterpiece: The Fibonacci Sequence. Retrieved 2 28, 2026, from https://about.ebsco.com/blogs/ebscopost/natures-mathterpiece-fibonacci-sequence#:~:text=Named%20after%20Italian%20mathematician%20Leonardo,even%20the%20spirals%20of%20DNA

Liu, K. (2024, September 3). Are These 10 Natural Occurrences Examples of the Fibonacci Sequence? Discover Magazine. Retrieved February 28, 2026, from https://www.discovermagazine.com/are-these-10-natural-occurrences-examples-of-the-fibonacci-sequence-46574

Montalvo, F. (2020, 10 22). Patterns in Nature and Finance. The Fibonacci Sequence and the Golden Ratio. Exitus Capital. Retrieved 2 28, 2026, from https://exituscapital.com/patterns-in-nature-and-finance-the-fibonacci-sequence-and-the-golden-ratio/

9 Examples of the Golden Ratio in Nature + Definitions. (2024, July 25). Mathnasium. Retrieved February 28, 2026, from https://www.mathnasium.com/blog/golden-ratio-in-nature

Scott, G. (2024, December 9). Fibonacci and the Golden Ratio: Technical Analysis to Unlock Markets. Investopedia. Retrieved February 28, 2026, from https://www.investopedia.com/articles/technical/04/033104.asp

Sharma, R. (n.d.). Golden Ratio & Fibonacci: Patterns in Nature Explained. Vedantu. Retrieved February 28, 2026, from https://www.vedantu.com/maths/numbers-nature-golden-ratio-fibonacci