Nature Teaches 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 on his schooling! Since kinder 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 mathematics!


The “petals” flower form spirals curve describing Fibonacci’s numbers.

Also nature teaches mathematics! Nature and math works in never-ending harmoniously. From the particle world of 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 on things around us.

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


Fractals are repeating geometric pattern. They are rough fragmented geometric shapes that can be repeatedly subdivided into parts and that each small portion can be viewed as a replica of the whole. These are geometric designs we teach in classrooms. Since repeated, in mathematics is called iterations or algorithms. Newton’s method, simplex programming, Gauss Seidel, Jacobi, and many more algorithms are among few examples. Some plants exhibit simple recursive operations that after a few number repetitions or iterations their shape can be recognized as a repeated geometric pattern. It is mathematics! Fractals in nature are always pleasing to our eyes – clouds, plants leaves and fruits, galaxies, shells and many more. Plants such as sunflowers, ferns, cabbages, and papaya leaves are among a few of them.

Leaves arrangement suggests repetition

Leaf arrangement suggests repetition

Honeycomb structure is also a nature 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 least cost in economics and linear programming in mathematics!
Fibonacci number is a simple example illustrating the existence of sequence 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’s number in nature. Once again, nature teaches math!

Fractals, Fibonacci‘s shells, and beehives are iconic images that capture the beauty of nature displays in mathematical expressions. These displays are like ornaments to the eyes of the mathematicians. A living math in motion in order for us to love and appreciate nature! Indeed, nature teaches mathematics!

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