Mathematics of Life and Nature

Mathematics of Life and Natureby Chris Banescu –

“Mathematics is the alphabet with which God has written the universe.” ~ Galileo Galilei

Mathematics is typically considered an abstract subject, a complex theoretical framework that the human mind has devised to make sense of the physical world and the observable universe. Mathematics is often described as the “language of physics.” Furthermore, mathematics shape the foundation and science behind quantum mechanics and astrophysics.

What many might not realize is that mathematics is also embedded in the complex framework of all life and the entire superstructure of the natural world around us.

As the video below shows, mathematics plays a key role in the language of biological life, including plants, insects, and animals. Nature not only reflects mathematical principles, it is deeply immersed in them. Mathematical formulas describe the design and structure of all life from the simplest cell to the enormously complex human body.

Fibonacci Sequence – Fibonacci Spiral
The first part of the video highlights the Fibonacci sequence and how it describes the spiral pattern seen in the structure of a nautilus. The Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … . It is a sequence of numbers where the next number is calculated by adding the preceding two numbers. The same Fibonacci logarithmic spiral pattern can be found in many other animals, plants, flowers, and even in the design of the cochlea inside the human ear.
Fibonacci Numbers Spiral

The Golden Ratio
The video transitions into a visual representation of the golden ratio. In mathematics two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities: (a/b = (a + b)/a) if expressed algebraically. The golden ratio is approximately 1.618 = (1+sqrt(5))/2.
Golden Ratio

The Golden Angle
The clip continues to show how the golden ratio is related to the golden angle. The golden angle is the angle subtended by the smaller (b, red) arc when two arcs that make up a circle are in the golden ratio (see figure below). The approximate value of the golden angle is 137.51 degrees.
Golden Ratio Angle Rectangle

The Sunflower and The Golden Angle
The video then highlights how the golden angle determines the distribution of seeds on a sunflower head. Each new seed appears in the center of the sunflower at precisely 137.5 degrees in relation to the preceding seed. Interestingly enough, this precise placement process creates the same spacing between all seeds and produces the most optimal method of filling the sunflower head full of seeds. Even minor variations (as small as 1/10 of a degree) will destroy this optimization process.
Golden Angle Golden Mean Sunflower Fibonacci

 

Resources:
http://en.wikipedia.org/wiki/Golden_ratio
http://en.wikipedia.org/wiki/Golden_angle
http://www.mathsisfun.com/numbers/golden-ratio.html
http://www.creationresearches.com/cr5_e.shtml
http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html