Tip/Thought of the Day

The Delicate Balance

Math seems silly to most of us. We regularly ask the question, “When will I ever use it?”. Of course, we understand its application whenever we buy something. But even scheduling how much time it takes to get from point A to point B, how long we can go before requiring more gas, making dinner with just the right proportions, playing music, decorating, sewing, gardening. . .depend on math.

It’s inherent to every aspect of our lives. 

But what we don’t truly appreciate is that it’s so much more than just numbers, math is in the essence of all life.

Pi is a mathematical constant, the ratio of a circle’s circumference to its diameter. It’s called irrational, because it cannot be expressed as a fraction, and it never ends or repeats itself. It goes on for infinity. If you converted the numbers to letters it would contain every word ever uttered in any language.

According to Cornell mathematics professor Steven Stogatz, 

“The beauty of pi is that it puts infinity within our reach. They seem to go on at random, yet they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi. What distinguishes pi from all other numbers is its connection to cycles. Whenever we think about rhythms- processes that repeat periodically, with a fixed tempo, like a beating heart or an orbiting planet- we inevitably encounter pi.”

Wherever there’s a circle, there’s pi. In the sun, the spiral of the DNA helix, our pupils. It defines sound and light waves as well as the ripples that travel outward when a stone hits water. The “meandering ratio” of rivers or how much it twists and turns approaches pi. Even the patterns of stripes and spots seen on many animals is encoded by one simple constant- pi.

The real life applications are enormous. It’s used to track the dynamics of populations, solve electrical problems, study the structure of the eye, understand DNA, design pendulums, allow GPS navigation, and analyze probabilities.

It’s breathtaking in its breadth and applications. 

As is the Fibonacci sequence, also known as the golden ratio. It has fascinated human beings for centuries. It starts like this,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. . .and on forever. Each number is the sum of the preceding two. It seems simple enough. But this incredible sequence, phi, or the golden ratio-1,61803…- appears to be a built-in numbering system to the cosmos. It’s everywhere we look in nature.

In order to survive, flower petals can’t overlap too much or they won’t get equal exposure to the much-needed rays of the sun and nutrients. They do this by following the Fibonacci sequence. Whether it’s the lily’s 3, buttercups 5, or the daisy’s 34, phi demands the ideal packing arrangement. Each and every petal on earth is placed at a ratio of .618034 as it turns around a 360 degree circle.

The most famous, and recognizable, Fibonacci pattern in nature is the spiral. Even the cosmos must follow its order. As seen in the spiraling arms of the Milky Way. Other great examples are snails, seashells, spider webs, the eye of a storm and the cochlea of the inner ear.

It also impacts how we see ourselves. What we perceive as beautiful can be attributed to phi. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. The same proportions exist from the side and even the eye and ear itself as they follow a perfect spiral. The more closely our proportions tend to phi the more aesthetically pleasing we seem.

But don’t forget our bodies. They too follow the Fibonacci sequence. From our belly button to the floor and the top of our head to the belly button all form the golden ratio. Animals, starfish, sand dollars, ants, bees. . .All follow the same ratio.

Down to our DNA, we can’t escape the golden ratio. The measurement of one DNA molecule is 34 angstroms by 21 angstroms. Their ratio closely approximates phi, 1.61904 vs 1.61803.

Math is the basic building block in nature. Its a precious balancing act that connects everything. Changing even one small aspect can have consequences we never anticipated. Making sure we honor those balances is imperative to all our futures.

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