Symmetry Artist

Symmetrical pictures in maths or any symmetry art of an object imply symmetry if it can be divided into two similar pieces. When any given object has a symmetry, we call it a simple symmetrical design or just symmetrical. On the other hand, if an object does not have symmetry, then that object is termed asymmetrical. The concept of symmetry is most commonly found in geometry. The following image looks exactly the same from both the sides and can be divided into identical halves and this is a symmetric drawing.

Line of Symmetry in Geometry

The line of symmetry is a line that splits an object into two equal halves or identical pieces. This line of symmetry is also known as the axis of symmetry.

Here, we have a heart and we can easily fold it into two equal halves.

If we fold this given figure in half along its line of symmetry, we will observe that both the halves match each other exactly.

The following image illustrates symmetrical drawing.

Observations From Application of Symmetry

Depending upon the above examples, we get the following observations:

• The sides of the image divided by the line of symmetry, should look the same.

• If we fold the paper (on which image has been drawn) along the line of symmetry, each section of the image will totally overlap the other part.

• The above observations will also enable us to determine the line of symmetry in any shape.

Types of Symmetry in Math

Now it's time to explore the symmetrical images when they are cut differently:

• The line of symmetry will be vertical if it cuts the shape from top to bottom and vice-versa.

• The line of symmetry will be horizontal if it cuts the shape from left to right and vice-versa.

• Sometimes, we can divide a shape across the corners in order to form two identical halves. In such a case, the line of symmetry will be diagonal.

Geometric Shapes With More Than One Line of Symmetry

Some symmetrical shapes contain a single line of symmetry while others have more than one. Take the example of this triangle below, it has only one line of symmetry. Now, if you try to split it into any other way, the parts will be asymmetrical.

However, in comparison to the above image of a triangle, the one shown below contains 3 lines of symmetry. 

Real-life Examples of Symmetry Art

• Reflection of mountains in a lake.

• Reflection of trees in clear water.

• Wings of most butterflies are similar on the right and left sides.

• Some human faces are identical on the right and left side.

• Some men also have a symmetrical moustache.

Geometric Shapes With More Than One Line of Symmetry

Some symmetrical shapes contain a single line of symmetry while others have more than one. Take the example of this triangle below, it has only one line of symmetry. Now, if you try to split it into any other way, the parts will be asymmetrical.

Number of Lines of Symmetry and Figure

Solved Examples 

Example: 

Which of the following images have a line of symmetry and those that are not a line of symmetry?

Solution:

Figure (a) (c) and (d) have a line of symmetry but (b) and (e) does not have a line of symmetry.

Example: Determine if the given butterfly is a symmetrical art?

Solution:

If you see the butterfly does not look the same from the right and left sides. Thus, when we divide the figure, it will not split the shape into identical halves and thus asymmetrical. 

Fun Facts

• Symmetry is everywhere, in almost all plants, animals, and even humans 

• A kaleidoscope has mirrors inside it which generate images having multiple lines of symmetry.

• The angle between the mirrors of a kaleidoscope discerns the number of lines of symmetry.

• Decorative art like rangolis or kolams are several symmetrical objects we encounter in our daily life

• The striking facet of symmetric drawing can be observed in rangoli designs that are famous all around India for their unique and symmetrical art n patterns.

• These designs exhibit the colourful science of symmetry.

• All regular polygons are symmetrical in shape. The number of lines of symmetry of these polygons is the same as the number of its sides.

• An object and its image are symmetrical with respect to its mirror line.

• If a figure consists of rotational symmetry of 180 degrees, then it has a point symmetry.