Have you ever paused to admire the incredible shapes and patterns around us? Math is the basis of the natural world and is seen in many different ways.

**A Brief History of Math**

Even in prehistoric ages, people had a basic understanding of math concepts, as evidenced by the presence of records on various artifacts such as bones and wall carvings. Arithmetic, algebra, complex numbers, and probability are all aspects of math, a broad science that impacts our daily lives.

**How Important is Math in Our Everyday Lives?**

Numbers and figures are used in various ways, from cooking and medical fields to the media’s usage of percentages and graphs. For example, consider shopping, cooking, buying a new house, doing DIY, traveling, playing video games, or driving. None of these activities would be possible without math.

**Seen an Image Reflected in a Lake? Do You Know the Math Behind it?**

Many examples of the connection between reflection and symmetry can be seen in nature; for example, the image of mountains and trees is mirrored in surrounding water bodies, dewdrops accumulated on leaves glisten in the presence of sunshine, and so on.

Reflection is a mathematical transformation of a figure that produces a mirror image, also known as a flip. In a reflection, each point in a form is turned over across a line called the line of reflection, creating a new shape with a set of points equidistant from the line of reflection. The dimensions of the reflected image, including lengths and angle measures, are similar to those of the original.

Another example of reflection and symmetry is a kaleidoscope, a device made up of three or more mirrors that are commonly cylindrical or triangular in shape.

**What is Symmetry?**

We are surrounded by symmetry. Everything on the earth is symmetrical, including people, animals, and plants. Symmetry provides harmony and balance. Symmetrical compositions include leaves, fruits, animals, insects, spiderwebs, flowers, and many other objects.

But first, a quick idea of what symmetry is.

In math, an object or shape is said to be symmetrical if it remains intact when rotated, flipped, or scaled, and if it can be divided into equal-sized and shaped portions. It’s also called symmetrical if the object appears the same on both sides after drawing a line along with them (the Line of Symmetry).

Take, for instance, the heart. It has only one symmetry line. If you place a mirror on one side of the heart, you will be able to see the opposite side of it. This is because the two sides are identical.

Nature is inclined to symmetry. For centuries, the idea has attracted scientists, astronomers, mathematicians, painters, sculptors, philosophers, architects, and interior designers. Once you start searching for it, you’ll discover that you can’t stop, and it’s all around you.

Real-life examples of symmetry include:

- The reflection of trees in water and mountains in a lake.
- The left and right sides of most butterflies’ wings are similar.
- Some human faces are the same on the right and left sides.
- People can also have a symmetrical mustache.

**Animal Characterization Based on Body Symmetry**

Radial and bilateral symmetry are the two main types of symmetry.

**Radial Symmetry**

If a shape possesses rotational symmetry, it appears the same when rotated a certain number of degrees around a central axis.

The rays of the sun or the slices in a pie are obvious examples. This form of symmetry can be seen in the body patterns of corals, sea anemones, and other jellies.

**Bilateral Symmetry**

The division of an animal along a single plane, resulting in two mirror images, left and right halves, such as those of a butterfly, crab, or human body, is known as bilateral symmetry.

Humans are considered to have “bilateral symmetry,” which means a single line of symmetry running from our head to feet.

Other instances of bilateral symmetry include butterflies and moths. As they have a single symmetry line running down the middle of their bodies, their wing patterns are similar on both sides.

**The Beauty of Butterflies**

Butterflies have a special place in math. Did you know that there are around 20,000 species of butterfly? Since their evolution from an ancestral moth-like insect some million years ago, butterflies have been an object of wonder and inspiration due to the sheer beauty of their metaphorical transformation from pupa.

The concept of symmetry, especially reflection, is easily understood by looking at a butterfly’s wings. Since you may mirror a butterfly along the line of symmetry running down its center without changing its appearance, it is called symmetric.

There are also exceptions, and various butterfly wing designs are not always symmetrical.

**Symmetry Around Us**

Philosophers, astronomers, mathematicians, painters, architects, and physicists have all been intrigued by symmetry. We still embrace symmetry in all we do, from choosing our furniture layout to styling our hair. Here are a few instances of symmetry in our environment:

- Romanesco Broccoli: The entire vegetable is one giant spiral made up of tiny, cone-like buds that are mini-spirals.
- Honeycomb: Bees are not only excellent honey makers, but they also have a keen sense of geometry. The honeycomb is an example of wall symmetry, in which a repetitive pattern is used to cover a plane. According to scholars, it is the ideal form for bees to store the most quantity of honey while using less amount of wax.
- Sunflowers: Helianthus Whorl Sunflowers have radial symmetry as well as the Fibonacci sequence, which is a fascinating type of numerical symmetry.
- Spider Webs: There are around 4,000 known species of orb-web spiders, all of which spin almost flawless circular webs with nearly equidistant radial supports emerging from the center and a spiral constructed to catch prey. According to experts, radial symmetry evenly distributes the power of impact when prey strikes the web, resulting in fewer thread tears.

Mathematically speaking, we say an object is symmetric if it doesn’t change. This means that however you want to transform the object, it will always be similar to its original version.

Other examples of animals with bilateral symmetry are flatworms, common worms, clams, snails, octopuses, crustaceans, insects, brachiopods, sea stars, sea urchins, and vertebrates.

A mirror is a useful tool to check if a shape exhibits reflection or bilateral symmetry. Place the mirror where you believe the symmetry line should be and check whether the shape remains the same. It’s also fun to see how a symmetrical image would look. Now that you’ve learned quite a bit about symmetry, go for a walk around your neighborhood or garden and collect or photograph symmetrical objects.

Comment below about your favorite symmetrical object in nature, and to read more such articles on how math is related to nature, visit the BYJU’S FutureSchool blogs.

Sources:

http://www.biokids.umich.edu/critters/Araneidae/

https://www.naba.org/qanda.html#:~:text=There%20are%20approximately%2020%2C000%20species,species%20occurring%20regularly%20in%20Canada.