• Pranav Nandurkar

Do you know : Nature of mathematics and mathematics in nature?

"The laws of nature are but the mathematical thoughts of God" - Euclid

Nature of Mathematics

- ­Mathematics reveals hidden patterns that help us understand the world around us. Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modeled mathematically.

- Mathematics has its own language, it means mathematical terms concepts symbols, principles and formulas.

- Mathematics is an exact science. Its knowledge is always clear, logical and systematic and that may be understood easily. It provides clears and exact response like yes or no, right or wrong.

- It is the science of logical reasoning. It involves inductive and deductive reasoning and can generalize any proposition universally

- It is related to each aspect of human life and knowledge. Mathematics helps in self evaluation. In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols.

- The special role of mathematics in education is a consequence of its universal applicability. The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty.

- From medical technology (CAT scanners) to economic planning (input/output models of economic behavior), from genetics (decoding of DNA) to geology (locating oil reserves), mathematics has made an indelible imprint on every part of modern science, even as science itself has stimulated the growth of many branches of mathematics.

So form above context it is clearly understood how nature of Math’s is widely spread throughout. Now let’s see Mathematics in nature.

Mathematics in nature

Introduction Mathematics is all around us. As we discover more and more about our environment and our surroundings we see that nature can be described mathematically. The beauty of a flower, the majesty of a tree, even the rocks upon which we walk can exhibit nature sense of symmetry. Although there are other examples to be found in crystallography or even at a microscopic level of nature .Mathematics in nature can be seen through Geometrical shapes, Symmetry, Fibonacci spiral, the golden ratio, Fractals.

Some of the best examples for mathematics in nature are

1 Solar Eclipse

- The sun has a diameter of 1.4 million kilometers, while Moon, has a meager diameter of 3,474 kilometers. With these figures, it seems near impossible that the moon can block the sun’s light and give us around five solar eclipses every two years.

- So what causes these solar eclipses? By sheer coincidence, the sun’s width is roughly four hundred times larger than that of the moon, while the sun is about four hundred times further away. The symmetry in this ratio causes the moon and sun to appear almost the same size when seen from Earth, and, therefore, it becomes possible for the moon to block the sun when the two align.

2 Body Structure Star Fish

- Starfish or sea stars belong to a phylum of marine creatures called echinoderm. Other notable echinoderm include sea urchins, brittle stars, sea cucumbers and sand dollars.

- The larvae of echinoderms have bilateral symmetry, meaning the organism’s left and ride side form a mirror image. However, during metamorphosis, this is replaced with a superficial radial symmetry, where the organism can be divided into similar halves by passing a plane at any angle along a central axis.

- Sea stars or starfish are invertebrates that typically have five or more ‘arms’. These radiate from an indistinct disk and form something known as penta-radial.

3 Honey Comb

- Bees are renowned as first-rate honey producers, but they’re also adept at geometry. For centuries, mankind has marveled at the incredible hexagonal figures in honeycombs. This is a shape bees can instinctively create; to reproduce it, humans need the assistance of a compass and ruler!

- Honeycombs are an example of wallpaper symmetry. This is where a pattern is repeated until it covers a plane. Other examples include mosaics and tiled floors.

- Mathematicians believe bees build these hexagonal constructions because it is the shape most efficient for storing the largest possible amount of honey while using the least amount of wax. Shapes like circles would leave gaps between the cells because they don’t fit perfectly together.

So from above examples we get to know about how mathematics can be seen in nature.