Math is everywhere! It is in the objects we admire, in the art we create, the music we listen to, sports we play, dance, etc.

Mathematics has always been crucial to the growth of science and technology. It is used in everything from building construction to the finding of new planets, from trades to technological advancements, in biology, philosophy, engineering, and the arts.

But are you aware of the crucial role math plays in nature? Math plays an important role in nature, as it contains, reveals, and charms in various forms, intrigues scientists and researchers, and inspires poets. Although we may not notice it right away, math is present largely within nature, and mathematical shapes and concepts can be found in the landscape, species of plants and animals, and so on. The concept of symmetry is one such idea that best embodies mathematics in all of its elegance.

We can find symmetry within nature in the beauty of a flower, the grandeur of a tree, and even the stones and pebbles we look at.

 So What Does the Term “Symmetry” Mean?

There are various definitions of symmetry, “such as ‘proportion,’ ‘perfect, or harmonious proportions,’ and ‘a structure that allows an object to be divided into parts of an equal shape and size’.”1 

In simpler terms, if an object has symmetry, it can be transformed by being cut, moved, rotated, divided, or flipped, but the shape will remain identical.

There are mainly two types of symmetry⏤reflective and rotational symmetry. Reflective or line symmetry means that one half of an image is the mirror of another, and rotational symmetry means that an object can be turned around a central point but will match itself several times. An example of line symmetry can be a butterfly, and the example of rotational symmetry can be a five-pointed star.1 

What is Radial Symmetry?

Radial symmetry is a kind of rotational symmetry; it means that a cone or a disk shape is symmetrical around a central axis. For example, jellyfish, starfish, hydras, corals, and sea anemones.1 

By definition, radial symmetry describes “living and non-living forms; these forms can be equally divided into three or more sections that, when rotated through a center of rotation by more than 0° and less than 360°, exactly match each other in orientation and shape.”2

Radial symmetry concerns a complete or partial form that results from a series of anatomical sections that repeat on multiple planes. 

Radial Symmetry in Nature2

There is an abundance of symmetry present within nature, and these symmetrical or radial shapes in nature are the best examples of the presence of mathematical concepts in nature. Although one of the most common types of symmetry present may be bilateral symmetry, radial symmetry is also abundant in nature. 

The most simple and visible examples of radial symmetry in nature are actinomorphic flowers such as lilies. While there may be many flowers that are random, the shape of actinomorphic flowers is not at all random.

The significance of the presence of radial symmetry in these flowers is that it helps more insect types land on the flowers, drink the nectar, and unwittingly transport pollen to other flowers of the same species. The shape of the flower is a survival mechanism that increases its chances of reproduction because the shape of a multifold form is recognized as a food source.

When you slice through the center of most fruits, like oranges, you can find some beautiful examples of radial symmetry. Radial symmetry can be found in the segment of an orange, the seed distribution of a Kiwi fruit, and the five-pointed star of an apple core.

Similar to leaves, plants, flowers, and fruits, we can also find radial symmetry in snowflakes. Are you aware of the research from China that concluded that no two snowflakes are alike?1 What makes them so different is, in fact, the radial symmetry in them. Each of these small ice crystals has various branches, and the branches of the snowflakes have a distinct identical design that results in a six-fold radial symmetry. Every snowflake is unique as it goes through a distinct set of atmospheric factors that help crystallize it, resulting in its symmetry. Because of the way water molecules arrange themselves when ice develops, all snowflakes have this kind of symmetry. It serves as a reminder that symmetry is inherent in the world around us.1 

Let’s now look at the presence of radial symmetry in animals. Radially symmetrical animals characteristically do not have a front or back, distinctive left or right sides, but only a top and bottom. The radial nature of these animals allows them to move in all directions, unlike bilaterally symmetrical organisms like humans, whales, or seals, which have distinct front, back, right, and left sides.3

Radially symmetrical creatures, such as starfish and jellyfish, have sensory organs spread throughout their bodies rather than a centralized nerve system. Sea stars, for instance, have eye spots at the tips of their arms rather than in their heads.

Animals with radial symmetry, such as jellyfish and starfish, lack a central nervous system and instead have sensory structures that are scattered throughout their bodies. The eye spots in sea stars, for example, are located at the tips of their arms rather than on their heads.3

This is beneficial because the organisms are able to regenerate any lost body parts. As long as a portion of the central disk of the sea star is present, it can regenerate any lost body parts or even grow a new one entirely.3

Many insects, such as orb spiders, also use radial symmetry to weave their webs. Even some molecules, like methane, exhibit radial symmetry.2

This is only a small sample of the radial symmetry that is inherent in nature.As human beings are naturally drawn to symmetry and proportion, these mathematical concepts create harmony, beauty, and proportion in the world.

The presence of these beautiful radial shapes in nature shows the hidden beauty of mathematics that can be found in everything from flowers, plants, fruits, insects, animals, sea life, and inanimate objects. So just look closely and you’ll notice the beauty of mathematics in almost everything you see!

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  1. Symmetry in Nature – TeacherVision. (n.d.). Retrieved May 5, 2022, from
  2. Radial Symmetry – The Definitive Guide | Biology Dictionary. (n.d.). Retrieved May 5, 2022, from
  3. Radial Symmetry in Marine Life. (n.d.). Retrieved May 5, 2022, from