Fibonacci Sequence: Crown jewels of mathematics

Feb 7, 2023 | West Caldwell

Fibonacci sequences and golden ratios have a close relationship. The Fibonacci sequence is recursive, generated by adding the two previous numbers in the sequence.: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987… If you were to draw a line starting in the right bottom corner of a golden rectangle within the first square and then touch each succeeding multiple square outside corners, you would create a Fibonacci spiral. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space. Humans have known about the GOLDEN RATIO for at least 4,000 years, some say even longer! The latest research shows that it was used in the design of hieroglyphics found on tomb walls, and also in the construction of the Egyptian pyramids and other ancient structures throughout the world.

The Mystifying Golden Spiral

Our perception of balance and proportion is shaped by the Golden Ratio, a mathematical concept. The golden ratio of 1.618 may be found in nature, geometry, the human body, and the solar system, among other places. The Golden Ratio was used by Leonardo Da Vinci in his works, including the “Mona Lisa.” It was also used by Michelangelo in his painting “The Creation of Adam” in the Sistine Chapel. “The Great Mosque of Kairouan,” “The Pyramids of Giza,” and “The Parthenon,” all incorporated it into their designs.

The Fibonacci Sequence in Nature

Fibonacci sequence illustrations depict what most would consider beautiful in real life. The most famous examples are found in nature. Several species of plants, in which the exact number of flower petals are always found to one that is found in the Fibonacci sequence. One of the most well-known examples is the sunflower. Sunflower seed spirals are often counted in one direction (e.g. clockwise) to produce a Fibonacci sequence number. On the other hand, counting the number of seed spirals in the opposite direction (e.g. counter-clockwise) will result in tallying up to a successive or preceding number to the initial Fibonacci number counted in the clockwise direction. The Fibonacci sequence may be found in unexpected places like honey bees, storms, spiral galaxies, DNA molecules, whirlpools, chameleon's tail, spiral galaxies, DNA molecules, whirlpools, the tail of a chameleon, ocean waves, and many more.

Fun Fact: November 23rd is Fibonacci Day since the digits "1, 1, 2, 3" come from the Fibonacci sequence. So, go ahead and let everyone know!

In almost every environment, Fibonacci sequences can be found. A grain of wheat, a hive of bees, or even the entire human race can benefit from it. If you found this blog interesting, why not read more such blogs by Mathnasium?