Nature Educates Us on Mathematics

By  Vic Odarve

 Not everybody loves mathematics! "I don’t like numbers. That’s why I did not take up engineering courses," said one student. This summed up everything about his schooling! Since kindergarten up to high school, he has performed miserably in mathematics. But one thing is certain: whether he likes it or not, mathematics is a part of his everyday life. Unknown to many, math already existed in nature the moment we took our first breath of life. What we do is simply marvel at mathematics!

Petals on math sequence

Also, nature teaches mathematics! Nature and math work in never-ending harmony. From the particle world to billions of stars spreading in our cosmic ocean, mathematical laws seem to work, keeping the universe in order. From Newton’s law to Kepler’s laws of planetary motion and Einstein’s law of relativity, math offers our deep understanding of things around us.

 Nature has its own way of expressing mathematics! Patterns such as hexagonal beehives, spiraling Fibonacci flowering trees, fractal flowers and plants, fruits, and leaves, and many more are mathematics!

 FRACTALS, BEEHIVES, AND FIBONACCI’S NUMBERS

 Fractals are repeating geometric patterns. They are rough, fragmented geometric shapes that can be repeatedly subdivided into parts and where each small portion can be viewed as a replica of the whole. These are geometric designs we teach in classrooms. In mathematics, this is referred to as iterations or algorithms. Newton’s method, simplex programming, Gauss-Seidel, Jacobi, and many more algorithms are among a few examples.

 

Mapua University, October 2022

Some plants exhibit simple recursive operations such that, after a few repetitions or iterations, their shape can be recognized as a repeated geometric pattern. It's mathematical! Fractals in nature are always pleasing to our eyes – clouds, plant leaves and fruits, galaxies, shells, and many more. Plants such as sunflowers, ferns, cabbages, and papaya leaves are among a few of them.

The honeycomb structure is also a natural mathematical exhibition. Look at its hexagonal shape. Its cross-section is made of the comb, a latticework of hexagonal cells made of beeswax. It is an expression of geometry in action. The design might be the most economical in terms of labor and wax, hence expressing the least cost in economics and linear programming in mathematics!

Leaves on Fibonacci's sequence

 The Fibonacci number is a simple example illustrating the existence of sequences in mathematics just like arithmetic and geometric sequences and progressions. But in the Fibonacci sequence of numbers, each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21, etc. And these numbers are exhibited in various "family trees" and patterns of spirals of leaves and seeds. The image of a nautilus shell approximates the sequence of the Fibonacci numbers in nature. Once again, nature teaches math! Fractals, Fibonacci ‘s shells, and beehives are iconic images that capture the beauty of nature displayed in mathematical expressions. These displays are like ornaments to the eyes of mathematicians. This is a living math in motion for us to love and appreciate nature!

 

Indeed, nature educates us on mathematics!