Session 1: What is Symmetry? – Reflection, Rotational and Translation Symmetry

The word “symmetry” is a 16th-century Latin derivative from the Greek words for “together” (syn-) and “measure” (metron).  Mathematically, a shape has symmetry if it becomes exactly like another when you turn, flip or slide it.

If an object can be divided into two halves that are exactly similar to each other, it is said to be symmetrical, and this property is known as symmetry. Not all objects have symmetry; if an object is not symmetrical, it is called asymmetric. 

Symmetrical figures, objects and architecture look aesthetically pleasing as all of us are drawn to balanced images. Mughal architecture is a remarkable example of symmetry. Humayun’s Tomb in Delhi is characterized by its symmetry, geometrical shapes and detailed ornamentation. Inspired by the Taj Mahal, this tomb ranks extremely high on the scale of using geometrical patterns and symmetry in its architecture. Even the garden of the mausoleum is symmetrical.

What is Tessellation?

Symmetry can be viewed when you flip, turn or slide an object. The figures below show some patterns that are formed by symmetrical figures. The translated shapes remain exactly the same as the original, so the shapes are symmetrical to each other. These geometrical patterns with no gaps and no overlaps are known as tessellations. They can be found in many real-life objects.

Types of Symmetry

There are three basic types of symmetry: reflection symmetry, rotational symmetry and translation symmetry.

Reflection Symmetry

The type of symmetry in which a line divides an object into two coincidental parts is called reflection symmetry. It is also called line symmetry or mirror symmetry. The line of symmetry can be horizontal, vertical or diagonal. Also, certain objects, like a hexagon or a circle, can have many lines of symmetry.

Rotational Symmetry

The type of symmetry in which an object fits onto itself more than once while being rotated through 360∘ is called rotational symmetry. It is also called radial symmetry. The order of symmetry is the number of times the object fits onto itself while being rotated through 360∘ and the angle of rotational symmetry is the smallest angle the object can be rotated to coincide with itself. Many geometrical shapes depict rotational symmetry like a circle or a square.

Translation Symmetry

The type of symmetry in which an object moves from one position to another, with the same orientation in the forward and backward motion, is called translation symmetry. 

Remember this!  

Symmetrical figure: A plane figure that can be divided into two halves that are exactly similar to each other. 

Reflection symmetry is the symmetry in which a line divides an object into two coincidental parts. 

Rotational symmetry is the symmetry in which an object fits onto itself more than once while being rotated through 360∘.

Translation symmetry is the symmetry in which an object moves from one position to another, with the same orientation in the forward and backward motion.