Some time ago, someone wrote and suggested I write something on the golden ratio. I hope to finally post something on the topic today (this post has been in progress now for QUITE some time).
The “golden ratio” is a special name given to describe a ratio that seems to relate indirectly or directly to many aspects of God’s creation. The ratio is approximately 1.618 (see Wikipedia for a more exact definition).
To understand how we observe the ratio 1.618 in God’s creation, we need to take a look at a special sequence called the Fibonacci numbers. This special sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…and continues, with each new number formed by adding the previous two numbers together (1 + 2 = 3, 3 + 5 = 8, etc.). The ratio between most numbers in this sequence is very close to the golden ratio. This means that if you were to divide two neighboring numbers in the Fibonacci sequence, you’d get a number close to 1.618!
Since we find neighboring Fibonacci numbers all over creation, it follows that we also find the golden ratio all over too. For example, the seeds in any given sunflower are arranged in two patterns of spirals. If one of the patterns has 55 spirals; the other will have either 34 or 89—the number of spirals in each pattern are always neighboring numbers in the Fibonacci sequence! This also means that the ratio between the two patterns is always very close to the “golden” ratio. No matter how large or small the sunflower, one spiral pattern always contains approximately 1.618 times the number of seeds as the other pattern. Guess what? This ratio allows for the most number of seeds to fit in any given sunflower! God sure thinks of all the details, doesn’t He?
If we were to look at plants, pinecones, or pineapples, we would again find Fibonacci numbers and the golden ratio and be awed again at the Creator (please see the websites listed at the end of this article for a more detailed explanation). Scientists have even found ways where things like the nautilus’ shell relates indirectly to the golden ratio. And artists and architects have discovered that rectangles based on the golden ratio are artistically pleasing (surprise!).
Many marvel over how the golden ratio (and numbers in the Fibonacci sequence) keeps popping up all over creation. As Christians, we know the ratio appears everywhere because God designed the golden ratio to have the properties it has, and then designed each part of His creation with infinite care and wisdom, using this ratio to give sunflowers, pinecones, and more just what they needed. He also created our minds to appreciate this same ratio as something “beautiful”—as testified to by the many buildings and paintings that incorporate this ratio.
Below are four sites that offer more details about the golden ratio. The first two approach the ratio from a biblical perspective; the last two do not have a biblical perspective, but contain some fascinating information and easy-to-understand explanations of the Fibonacci sequence and the Golden Ratio you might find helpful.
Note that one of the sites uses the name “golden mean” instead of “golden ratio” to refer to this ratio. The sites also refer to the “golden rectangle” or “golden section”—this is a rectangle whose sides follow the proportion of the golden ratio (one side is approximately 1.618 times the other side). Most of the sites also discus the Fibonacci sequence—remember that neighboring numbers in this sequence have a ratio that approaches the golden ratio.
I hope you enjoy!
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After having her own view of math transformed, Katherine has been researching, writing, and speaking on a biblical worldview of math for more than a decade. Her books on math and a biblical worldview have been used by individuals, homeschool groups, and Christian schools and colleges, and she recently finished a junior high math curriculum. Receive her free Math from a Biblical Worldview e-mail course at www.mathisnotneutral.com