What Are the Different Types of Symmetry in Math?
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.
FAQs on Symmetry Artist: Explore Types, Examples, and Applications
1. What is symmetry in the context of art and Maths?
In both art and Maths, symmetry refers to a sense of balanced and proportionate similarity. An object is considered symmetrical if it remains unchanged after a transformation, such as being flipped, turned, or slid. It creates a sense of harmony and order. For example, a butterfly has symmetrical wings, and the letter 'H' is symmetrical along a central vertical line.
2. What are the main types of symmetry a student should know?
The primary types of symmetry studied as per the CBSE syllabus are:
Reflection Symmetry: Also known as line or mirror symmetry, it occurs when one half of an object is the mirror image of the other half. The imaginary line that divides the object into two identical halves is called the line of symmetry.
Rotational Symmetry: An object has this symmetry if it looks the same after being rotated by less than a full 360-degree turn around a central point. The fixed point is the centre of rotation.
Point Symmetry: This is a special case of rotational symmetry. A figure has point symmetry if it looks identical after being rotated by 180 degrees around a central point.
3. How is rotational symmetry different from reflection symmetry?
The key difference lies in the transformation applied. Reflection symmetry involves 'flipping' a shape across a line to get an identical half, like looking in a mirror. In contrast, rotational symmetry involves 'turning' a shape around a central point. A rectangle has reflection symmetry across two lines, but it also has rotational symmetry of order 2 around its centre.
4. What does the 'order of rotational symmetry' mean? Give an example.
The order of rotational symmetry is the number of times a figure or object fits onto itself during a full 360-degree rotation. For example, a ceiling fan with three blades has an order of rotational symmetry of 3 because it looks identical at three different positions as it completes one full turn (at 0°, 120°, and 240°).
5. How do famous artists and architects use symmetry in their work?
Artists and architects use symmetry to create balance, harmony, and visual appeal. A classic example in Indian architecture is the Taj Mahal, which exhibits perfect reflection symmetry. Many artists, from Leonardo da Vinci in 'The Last Supper' to modern graphic designers, use symmetrical layouts to guide the viewer's eye and convey a sense of stability and order.
6. Can a shape have multiple lines of symmetry? Provide an example.
Yes, a shape can have multiple lines of symmetry. The number of lines of symmetry depends on the shape's properties. For example:
A square has four lines of symmetry (two diagonal, two connecting the midpoints of opposite sides).
An equilateral triangle has three lines of symmetry.
A circle has infinite lines of symmetry, as any line passing through its centre will divide it into two identical halves.
7. Where can we find examples of symmetry in nature?
Nature is filled with beautiful examples of symmetry. Most animals exhibit bilateral (reflection) symmetry, such as butterflies, human faces, and tigers. Starfish and snowflakes are stunning examples of rotational symmetry. This natural balance is often a result of efficient growth and functional advantages.
8. How can I practice creating symmetrical drawings?
A simple and effective way to practice creating symmetrical art is the paper-folding method. Fold a piece of paper in half, draw half of a design (like half a heart or a butterfly wing) along the fold, and then cut it out. When you unfold the paper, you will have a perfectly symmetrical shape. You can also use online symmetry drawing tools or apps that mirror your strokes to create intricate patterns.
