Symmetry of Size, Shape and Orientation

Long before science, man was fascinated by symmetry. Plato wrote of the proportions of an ideal face, and today, these ‘golden proportions’ have been defined by similarity between the left and right sides.

Thus, from the Greeks who were partly correct in formulating this understanding comes the word ‘symmetry’ – to ‘measure together’.

Symmetry is observed everywhere in nature and is prevalent throughout human history across art, architecture, and design, in cultures around the world. What then is the role of symmetry? – It is usually considered attractive, but the inherent balance in the principle of symmetric form is useful in achieving stability as well. From the charm of a snowflake to the history of the Taj Mahal, it has an essential role in nature and art. The fact that it is found within, and used to describe everything from animate and inanimate objects of nature to manmade creations, makes it one of the most powerful concepts in science.

Identical and equal!

Picture Source: Pixabay

Bilateral Symmetry

When we think of symmetry, we generally think of mirror images. This is ‘bilateral symmetry’, where we see like pairs on both sides – two hands, two feet, two eyes. In many life-forms like jellyfish, for instance, we see sections replicate around a central axis. The size and shape of each segment are the same while the orientation changes through the rotation. Since each similar part is ‘radiating’ from a central point, it makes sense to call this ‘radial symmetry’.

Identical, elaborate six-fold radial symmetry. Picture source: https://pixabay.com/en/ice-crystal-ice-form-frost-fabric-64157/

As with the image above, snowflakes exhibit six-fold radial symmetry with elaborate, identical patterns on each of its arms. Understanding why plants and animals opt for symmetry seems complex but with inanimate objects it might seem baffling – it’s chemistry!

Biradial Symmetry

Biradial symmetry is a combination of radial and bilateral symmetry, as observed in Ctenophores (comb jellies). Here, the body components are arranged with similar parts on either side of a central axis, and each of the four sides of the body is identical to the opposite side.  This is thought to indicate a stage in the evolution of bilateral symmetry from a radially symmetrical ancestor.

A structurally symmetrical vision indeed. Picture Source: https://commons.wikimedia.org/wiki/File:Maja_crispata_(Maia_verrucosa)_-_Museo_Civico_di_Storia_Naturale_Giacomo_Doria_-_Genoa,_Italy_-_DSC03222_Cropped.JPG

When we closely examine the mathematical order in plants, we encounter an impressive geometrical plan at every level, right from the arrangement of branches and leaves to the veins in the structure of every leaf. Most often, a leaf split along the center of its length will result in two identical halves, and mirrored on either side of the midrib will be an equal distribution of veins.

The subject of symmetry is deep and wide, and regardless of where you step in, it will take you on a journey that penetrates the boundaries between natural, cognitive and social sciences, design, mathematics, humanities, and philosophy.

 

Edited by Pooja Gupta

Additional editing by Dominic D’Cruz