Figures with Symmetry

Geometry and Symmetry

Geometry and Symmetry do not sound like photographic techniques more than the sort of things you would study from a math book.

Mathematically, symmetrical shapes are beautiful, powerful compositional tools that make images stand out from the crowd. Geometry and symmetry are two techniques that work better when combined. Both are powerful compositional tools in their own terms. Both Geometry and symmetry are found in nature as well as in man-made worlds when combined in one single shot can lead to some fantastic images. In this article we will discuss symmetry geometry, what are geometry and symmetry, Meaning of symmetry in Mathematics, etc.

Meaning of Symmetry in Geometry

In symmetry Geometry, an object has symmetry if there is an operation or transformation (such as rotational, reflection or translation) that represents a figure or objects to its original shape. Hence, symmetry geometry can be defined as the immunity to change. For example, a circle  when rotated about its center will have a similar shape and size as the original circle as all the points of the circle after and before transformation would be indistinguishable. Hence, a circle in geometry is said to be symmetric under rotation or rotational symmetry.

What are Geometry and Symmetry?

Let's study about geometry and symmetry in photography.

Symmetry is drawn when either the bottom, top, left or right diagonals are mirror images of each other. Symmetry by its definition enables you to think outside of the rule of thirds'.

Symmetry even feels unnatural to seasoned photographers to use a center point to define your composition. Although symmetry occurs in nature, it is quite more visible in the man-made world.

Geometry is the Science of Different Shapes.

Square,line of triangles and circle all are geometrical elements that can be used in geometry. We can make use of hard-edge geometrical shapes to design bold imagery or more subtle "soft-edged" geometry to define a composition.

Both geometry and symmetry do not have to be restricted to physics. Lights and shapes can also have geometrical shapes and manifest symmetry.

Symmetry in Mathematics.

In Mathematics,symmetry is defined that one shape will exactly look like another shape when it is flipped, turned or rotated. For example, if you draw the heart shape in a paper and cut out from a piece of paper, design one - half of the heart at the fold and cut it to find the other half exactly similar to the first half. The heart extracted is an example of symmetry

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The definition of symmetry in Maths states that 'symmetry pictures in Maths is a mirror image'.When an image exactly looks like the original image after it has been turned or flipped then it is known as symmetry.

Symmetry Picture in Maths

Here, we will discuss symmetry pictures in Maths.

We know that symmetrical pictures in Maths may have one or more than one line of symmetry.

Some symmetrical pictures in maths have one line of symmetry, two lines of symmetry or infinite lines of symmetry.

The symmetrical shapes given below having one line of symmetry

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The symmetrical shapes given below have two lines of symmetry.

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The symmetrical shape given below having three lines of symmetry.

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The symmetrical shape given below having four lines of symmetry.

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The Symmetrical shape given below has an infinite line of symmetry.

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Solved Examples

1. The Picture Given Below is the Half Part and its Line of Symmetry. Complete the Picture Below.

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Solution:

The complete picture of the figure given in the questions is given below:

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The other part of the picture should be the same as the given half. We can use the grids to find the other part of the picture.

2. Which of the Figures Given Below Does not have a Line of Symmetry?

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Solution:

If we wrap both the papers from top to down as shown in figure A1 and B1, we find a line of symmetry in figure A but not in figure B. If we wrap both the papers from left to right as shown in figure below A2 and B2, we will not find any line of symmetries in both A and B.

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Quiz Time

1. Which of the Following Letters Below has no Line of Symmetry

  1. U

  2. H

  3. S

  4. A

2. How Many Lines of Symmetry are there in a Scalene Triangle?

  1. 3

  2. 0

  3. 2

  4. 1

3. What Letter Given Below Looks the Same after Reflection when the Mirror is Placed Vertically?

  1. H

  2. Q

  3. P

  4. S

Fun Facts

  • The line of symmetry is also known as the mirror line or axis of symmetry.

  • Infinite lines of symmetry are there in a circle.

FAQ (Frequently Asked Questions)

1. Explain the Line of Symmetry

Line of symmetry is an imaginary line or axis on which you fold a figure to get a symmetrical half. The line of symmetry divides an object into two mirror-image halves.The line of symmetry can either be vertical, horizontal or diagonal. In a single figure, there can be one or more than one line of symmetry.

The word ATOYOTA has only one line of symmetry along the axis that passes through Y.

The circle drawn below has infinite lines passing through the center of the circle and still, it is symmetrical.

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The below letter H and X has two lines of symmetry i.e. horizontal symmetry and vertical symmetry.

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2. Explain Reflection and Rotational Symmetry

Reflective symmetry- Reflective symmetry is symmetry when any geometrical shape or pattern is reflected in a line of symmetry/ mirror line. The reflected shape will exactly be the same as the original, the equal distance from the mirror line and the equal size.

In rotational symmetry, any geometrical shape or pattern can be rotated or turn around a central point and remains the same. It can be defined that a shape has an order of symmetry N which means that the shape can be turned around a central point and remains the same N times.