Gardening In Depth

Math, plants & beauty: experiencing the Golden Ratio and Fibonacci Sequence

Romanesco broccoli - a beautiful equation at Tyrant Farms

The Mathematics of Beauty… 

Outside of Tyrant Farms, we run a boutique digital branding & creative agency, bitTyrant, where we do lots of design work. As a result, our eyes are particularly attuned to the aesthetic side of things—whether that be the line spacing or font in a magazine or the color and texture on a head of broccoli.

Have you ever noticed how certain designs intuitively evoke a calming, harmonious feeling, whereas other designs just intuitively feel “off”? Designers aren’t alone in experiencing this sensation, it’s something many other people notice too, even if they can’t say precisely what’s causing that sense of visual discordance.

As it turns out, there is an actual mathematical reason why we view many elements of nature as aesthetically beautiful: it’s called the “Golden Ratio.”

The Golden Ratio

Euclid of Alexandria, the famed Greek mathematician and founder of modern Geometry, offered the first recorded description of the Golden Ratio in 300BCE. Two quantities are said to be in the Golden Ratio if the ratio of the sum of the numerical values to the larger quantity is equal to the ratio of the larger quantity to the smaller one. This ratio (1.618) is a mathematical constant that commonly occurs in nature, appearing in seemingly diverse elements ranging from spiral galaxies to pine cones to nautilus shells to your index finger.

Spiral Galaxy NGC 1187 (we didn't take this photo, NASA did).

Meet Spiral Galaxy NGC 1187, which lives about 60 million light years away in the Constellation of Eridanus and makes for a beautiful example of the Golden Ratio (we didn’t snap this photo, the ESO did).

It’s fun to walk around your garden and try to spot the various plants that express the Golden Ratio—then eat them. Go give it a taste!

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A Tyrant Farms cabbage going to seed and displaying some beautiful math.

A Tyrant Farms cabbage going to seed and displaying some beautiful math.

The Fibonacci Sequence 

Without going into too many technical details, the mathematical basis of the Golden Ratio is closely related to the Fibonacci sequence. Starting with 0, each subsequent number in the Fibonacci sequence is the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. When you divide a number in this sequence by the number before it, the output is a number very close to 1.618 (the Golden Ratio). In fact, this number is fixed at exactly 1.618 after the 13th division in the Fibonacci Sequence series.

Fibonacci Sequence - Tyrant Farms

What Does This Mean? 

Trying to put our own interpretations on various mathematical ratios and patterns of the universe is not necessarily our forte, although we find it all infinitely fascinating. Rocks on the cold, lifeless surface of Mars are likely not nearly as impressed by these ratios as we are from our sentient perspectives here on the life-nurturing surface of Earth in 2013.

Regardless of how we choose to interpret these mathematical patterns, everyone can agree that life and our shared experiences of this time and place are an awesome thing to ponder and appreciate. On a more practical level, we can each consider incorporating these mathematical ratios into the designs of our own gardens (or other designs) in order to make them more aesthetically pleasing to people that happen to gaze and graze upon them. It’s Awe Natural!

Thanks for reading!

KIGI,


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  • http://www.goldennumber.net Gary Meisner

    Most if not all spirals in nature are equiangular spirals, but not all equiangular spirals are golden spirals. See more at http://www.goldennumber.net/spirals/. You can find the spirals that really contain the golden ratio with the app at http://www.phimatrix.com.

  • http://www.goldennumber.net Gary Meisner

    Hi Aaron and Susan,

    Nice article on the edible side of the golden ratio. Given your interest in this topic, I thought you might also enjoy my sites at http://www.goldennumber.net and http://www.phimatrix.com.

    I tried to send you an email via your contact us page but it gave an error message. Please check that out or email me at the address given below re an idea for your blog.

    All the best to you,

    Gary Meisner

    • http://www.tyrantfarms.com Aaron

      Hello and thanks for the tip about our contact page, Gary. We’ll fix it asap. I’ll also check out your sites later today after work. Thanks!