Reflection and Symmetry

Isn’t it strange how nature loves symmetry? Everything in nature seems to have a symmetric shape. Let's take a perfect example of our planet earth having a shape of a circle.


When we hear the word symmetry we get a sudden click of a word proportion and balance. Reflection symmetry is often known as line symmetry or mirror symmetry, in the event of taking an image and drawing a line through it and getting a pair of mirror images, and that’s what is called reflection symmetry. So the line of symmetry divides the shape and object into two equal halves and both look exactly the copy of each other.


It can also be possible that the object or shape could have more than one line of symmetry and that can be any direction.


We can see the application of symmetry in almost everything. The most beautiful example of reflection symmetry is when you see the reflection of mountains and all the scenery in water as a reverted image.


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Application of Symmetry

Symmetry is considered to be one of the important mathematical concepts which play an extremely important role in problem-solving technique. From art to architecture symmetry is used almost everywhere. 

Uses of Symmetry

Symmetry is just not a concept it’s a part of our day to day life. If we focus on everything we see and use in a symmetrical form. Even our body is symmetrical. If we lose one leg it’s really hard to walk. So symmetry balances everything. Symmetry creates a sense of order and control to make things easier. We cannot always customize everything. Through symmetry, we do not need to measure both sides left and right. We know they both are mirror images. The same goes for designing a building. Everything in a symmetrical shape makes things easier to calculate and understand from art, architecture, textile technology, design creations, geometrical reasoning, Kolams, Rangoli, etc.


Reflection and Symmetry

Architecture is the best example of symmetry, it helps bind various elements of a structure together into a single, unified structure. It helps to create a sense of order and logic. We can look at symmetry as a relationship between single details to the layout of the complete structure and even to the entire city built on a symmetrical grid pattern.

So let’s take a real-world example of symmetry in architecture. An image of the Christiansborg Palace in Copenhagen is a highly symmetrical building, imagine a vertical line straight down the middle of that central tower, from top to base. The structure on the left of that line perfectly mirrors the structure on the right of it with the same color and the same number of windows on both sides.


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Application of Reflection

The Reflection of a shape or pattern is reflected in a line of symmetry. The reflected shape and the original will be the same, the same distance from the mirror line and the same size.

When we cut out of a paper of symmetric shape and fold it, both the ends will meet because both left and right sides were symmetrical and the point where the paper 

is folded will be the line of symmetry dividing them into two equal parts.


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Symmetry for Shapes

When we see geometric shapes some shapes may even have more than one line of symmetry like:


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In the above image, a parallelogram has no line of symmetry. This might look strange but to understand it more accurately you can cut the paper the same as a parallelogram and try to fold that piece of paper, but you will notice that sides do not coincide.

However, rectangle, rhombus, and square are also types of parallelograms, but they are symmetrical, meaning that they have a line of symmetry as you can see in the above picture.


Next is a Circle, it can be divided into two equal parts with their diameter, as a circle has an infinite diameter which makes a circle the shape with an infinite line of symmetry.


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If we see triangles,

Equilateral triangle will have three lines of symmetry,


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But in cases of other types of the triangle, it may differ from having 1,2 or maybe no line of symmetry.

FAQ (Frequently Asked Questions)

1. Does a rectangle have a diagonal as a line of symmetry?

A rectangle will not have a diagonal line of symmetry like square does because the sides are not of the same length. To understand this, let us take a rectangle with sides ABCD and draw a diagonal line of symmetry which cut through A and C, and when we fold the rectangle so that D touches the corner of B, we won’t be able to do it.

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But if we do this with a square, sides will meet and form a triangle because the square has four equal sides.

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2. What is rotational symmetry?

When a shape or an object turned around from a central point and remains the same from all sides then that object is said to have rotational symmetry.

For example, Square and circle when rotated look the same meaning they have rotational symmetry.


Center of rotation

If an object has a fixed point around which rotation occurs and the object appears same from all sides then that point is known as the center of rotation.


Order of rotational symmetry

To understand it better let’s know what is the order of symmetry, the number of position a shape or an object can be rotated and still look the same is known as the order of symmetry of the object.


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Say if we rotate a rectangle-shaped object from 0 to 360 degrees there will be 2 positions when the rectangle will be in its original shape one is 180 degrees and the other will be 360 degrees so, the order of the rotational symmetry for a rectangle is 2.