Engagio recently celebrated our 233rd customer. We took an entire day to commemorate customer #233 by drinking wine at Wente Vineyards, playing bocci ball at Campo de Bacci, eating pizza, and enjoying each other’s company.
You can see some pictures from our outing in the main image for this post above.
Most companies celebrate “normal” milestones like their 50th, 100th, and 500th customer. So why would we celebrate this weird, odd, prime number? To answer that, we have to take a journey into number theory, art, nature and more, so let me explain.
It all started in Italy.
The Story of Leonardo
It was 1170 in Pisa, Italy. Guglielmo Bonaccio, a merchant and customs officer, and his wife Alessandra, gave birth to a little boy named Leonardo. They were a happy family until tragedy struck – when he was 9, Leonardo lost his mother, which forced him to live a life on the sea traveling with his father.
He quickly learned the trade and lent a helping hand in his father’s business dealings. He took a liking to numbers, and at every stop on their trade route, Leonardo learned about the local systems of arithmetic. It was in Bugia that he discovered what today we call the Hindu–Arabic decimal number system, which he deemed superior to their standard Roman numeral systems.
As he grew older, he began spreading the Hindu–Arabic system through his trade routes. However, it wasn’t until age 32 when he used all of the knowledge that he gained during his travels to write the Liber Abaci (which translates to The Book of Abacus or The Book of Calculation). Subsequently, the decimal number system began to gain popularity throughout Europe mainly because it made trading, bookkeeping, measuring, and arithmetic easier.
In Liber Abaci, Leondardo solves a theoretical problem of the multiplication of a population of rabbits. It seeks to answer the question, “how fast rabbits could breed in ideal circumstances?” His solution was a sequence of numbers; each number is the sum of the previous two numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.
Centuries later, scholars studying Liber Abaci incorrectly translated text in its title, “filius Bonacci” (which means “son of Bonaccio”) to Fibonacci.
Today, we know Leonardo as Fibonacci, and his sequence of numbers as The Fibonacci Sequence.
The Fibonacci Sequence
Liber Abaci was the beginning of the spread of the decimal number system and could be considered Leonardo’s greatest achievement, but not his most well known. That accomplishment belongs to the Fibonacci Sequence.
The most famous representation of the Fibonacci Sequence is in geometry. Start with two squares of 1×1 next to each other. Next to those squares, draw a square that spans the distance of the two previous squares, which will result in a 2×2 square. Now, repeat. Each new square will have a side which is as long as the sum of the latest two square’s sides. When you connect the corners of the square with an arc, you get the famous Fibonacci spiral:
The Fibonacci sequence is so much more than a simple sequence of numbers, a recursive function or a math equation (𝐹 𝑛+1 = 𝐹𝑛 + 𝐹 𝑛−1). It turns out that the Fibonacci sequence is a natural phenomenon that reflects patterns of growth spirals found in nature.
Math can be beautiful. This pattern shows up in nature because it’s the most efficient way to achieve its goal. For example, when you look at flowers, the angle between one petal and the next, then the one after that is fairly consistent so that each petal gets the optimal amount of sun. That irrational number just happens to be a beautifully rational choice.
The Golden Ratio
To further explain the magic of the sequence, let’s examine the relationship of the numbers in the pattern more closely. Take any numbers in the sequence, then divide by its immediate predecessor. Their ratio is very close to the Golden Ratio. The bigger the pair of numbers, the closer we get to the golden ratio (1.61803398875…).
The golden ratio (represented by the Greek letter Phi or Φ) is a special number. It’s the only number whose square is greater than itself by one (expressed mathematically as Φ² = Φ + 1 = 2.618). It’s also the only number whose reciprocal is less than itself by one, expressed as 1/Φ = Φ – 1 = 0.618.
The first written definition of the golden ratio was in 300 B.C. by Euclid in his work titled Elements, one of the most important mathematical treatises of its time. The golden ratio was recently brought to pop culture by Dan Brown in 2003 in his best-selling novel, “The Da Vinci Code” and the subsequent movie release of the same name. It’s a cornerstone concept in geometry because the length of a regular pentagon diagonal is Φ times its side.
The Golden Ratio in Real Life
Here are some more examples of the golden ratio in nature.
Plants: Look at the pattern of seeds in the center of a flower, and you’ll find the familiar spiral curving in both directions. When you count the spirals in each direction, your total will be a Fibonacci number. Divide the number of clockwise spirals by the number of counter-clockwise spirals, and you’ll get the golden ratio. You’ll see this spiral pattern wherever you look, from pinecones to pineapples and from lilies to sunflowers.
Animals: When you look at the human form, you can’t help but find gold in the ratios. The mouth and nose are each positioned at perfect golden ratios of the distance between the eyes and the bottom of the chin. The measurement from the navel to the floor and the top of the head to the navel is the golden ratio. Even DNA molecules follow this sequence, measuring 34 angstroms long and 21 angstroms wide for each full cycle of the double helix.
Music: Fibonacci numbers are plentiful in the sound of music. There are 13 notes in the span of any note through its octave. A scale is composed of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords, and are based on a tone which are a combination of 2 steps and 1 step from the root tone, that is the 1st note of the scale.
The universe: I don’t want to get too metaphysical on you, but you’ll find that even spiral galaxies also follow this pattern. Look no further than the spiral arms of the Milky Way.
Engagio by the Numbers
Now, perhaps our Customer #233 celebration makes more sense. At Engagio, we choose to celebrate customer milestones that fall along the Fibonacci series, partly because there’s just something so brilliant and rich about the number, but also because the ratio from one number to the next is the golden ratio. This means that on average, the time between celebrations will be about the same — which makes a lot more sense than celebrating 100, 500, 1000, etc.
If you couldn’t tell, some of us at Engagio are math nerds. In fact, Engagio was founded on Pi day (3/14/15). It’s baked (no pun intended) into our DNA. So, to us, Pi day is more than just a day when we make math-themed baked goods – it’s our culture day.
But it doesn’t end there. The “E” on our logo has both Pi and the golden ratio hidden in its design, which explains why it’s so beautiful (but then again, I may be a little biased). The length of the top and bottom bar of the E versus the middle bar is 1.618, the golden ratio. The length of the I vs circumference of the O is Pi.
If you too are a math nerd and want to join our team, visit the Engagio careers page to learn more.
I’ll end this post with a cool video I found about how to draw a Fibonacci spiral to the length of Pi using the golden ratio.