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Exploring Axial Symmetry: Take A Look In The Mirror

Exploring Axial Symmetry: Take A Look In The Mirror

Have you ever wondered how a snowflake manages to look so perfectly balanced? Or have you ever seen a butterfly flutter by and asked yourself how each of its wings can be identical to the other? In math class – and other classes, such as art – we learn about symmetry. And to answer our questions about the butterfly and the snowflake, the answer lies in a concept known as axial symmetry.

Axial symmetry is a fascinating mathematical idea that tries to explain, or at least label, some of the beautiful harmony and balance that we witness in the natural world all around us. Several other interesting mathematical concepts help us understand the natural world and its beauty, such as the golden ratio, but axial symmetry may just be the most interesting.

Let’s dive into axial symmetry, talk about where we can encounter it and what significant role it plays, and uncover some of the wonder laying beneath this simple yet captivating mathematical concept. 

Understanding Axial Symmetry

Like many of the more interesting math topics that middle school math students will learn, axial symmetry is best understood using an example from real life. Imagine you fold a piece of paper in half so that one side perfectly mirrors the other. Now, if you cut a shape into that folded piece of paper, each side of the shape will match up perfectly with the other.

This notion of matching shapes or patterns on either side of a fold is axial symmetry. We can think of it as a mirror line that divides shapes into halves that match up perfectly to one another as if one was the mirrored image of the other. This mirror line is called the axis of symmetry

In mathematics, we can define the axis of symmetry as a line through a shape so that each side is a mirror image. In math class, students will generally deal with axes of symmetry that are vertical or horizontal.

Where Can We Find Axial Symmetry?

The truth is that axial symmetry is all around us, both in the natural world and in objects made by human beings. You may not be aware of it, but axial symmetry can be found in a whole host of places. Here are some examples of how axial symmetry can be found in our societies:

Living Creatures

Humans, animals, and even insects exhibit axial symmetry. We’ve already explored the idea of the butterfly and its colorful wings, one of which usually mirrors the other one. Let’s go one step further, however, and think about our own faces. If we split it down the middle, there is a striking resemblance between each side. While the sides of a human face are rarely exactly the same, the symmetrical nature of many human faces can’t be ignored.


Many flowers’ petals are presented symmetrically around the center point of the flower. That means that if we draw a line through the center of the flower, the petals on each side of that line will mirror each other.


Perhaps the most famous example of axial symmetry can be found in the intricate patterns of beautiful snowflakes. On closer inspection, you will notice that all of the delicate ice crystals are arranged symmetrically around its central axis.

Art and Design

Axial symmetry is a tool used by artists and various designers to create balanced compositions that appeal to the human eye. Examples can be found in virtually every culture around the globe.

Buildings and Architecture

Architects throughout history have created structures that exhibit axial symmetry. Many grand buildings will have a centered main entrance with windows symmetrically arranged on either side of the central axis that cuts through the middle of the entrance.

The Importance of Axial Symmetry

Axial symmetry isn’t just about making things look nice for the human eye, the concept has several practical uses too. Being able to recognize axial symmetry helps math students understand patterns more easily. When children identify a pattern, they can better predict the next steps in that pattern, allowing them to solve the problems facing them in class.

We mentioned how artists and designers use axial symmetry to create balanced and visually-pleasing works of art. Axial symmetry is vital in creating some of the most-used structures in our society and played a key role in allowing some of the world’s greatest artists to create their masterpieces.

Finally, axial symmetry is extremely important for biologists and other scientists. By studying axial symmetry to understand how living organisms grow and develop, scientists gain valuable insights into genetics, evolution, and other groundbreaking areas of scientific exploration.


Axial symmetry often captures the imagination of middle-school math students, helping them perform well and comfortably handle several topics in math as they progress through school. Unfortunately, some students struggle with axial symmetry and other topics, resulting in gaps in their knowledge.

At OMC, an experienced team of math professionals is ready and waiting to give your child the time and attention they need in our one-to-one tutoring classes. We also offer prep classes for the Math SAT and math competitions.

Contact OMC today and find out more.

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