Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b] This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music. The opposite of symmetry is asymmetry. In geometry[edit] Main article: Symmetry (geometry) The triskelion has 3-fold rotational symmetry. A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6] An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7] An object has translational symmetry if it can be translated without changing its overall shape.[8] An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9] An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]

1. Ronnith Nandy
Symmetry

2. In mathematics, certain basic concepts, such as
symmetry and infinity, are so pervasive and adaptable that
they can become elusive
Introduction to Symmetry

3. Types of Symmetry
[1.] Linear Symmetry
(a) Latitudinal (b) Longitudinal

4. Types of Symmetry
The dotted line shows the line of symmetry.
[2.]Rotational
Symmetry
This is also called radially symmetric and it has got infinite lines of
symmetry passing through a fixed point

5. Importance of
SymmetryFor symmetrical balance, a vertical axis is needed. The
symmetry axis for human beings is vertical, which is why
balanced weight is needed on both feet.
Symmetry is applicable in classical laws of motion and
quantum mechanics.
The law of nature is based on symmetry, but with many
symmetry-breaking mechanisms in place.
Humans have to find a symmetrical balance in order to learn
how to walk or ride a bike.

6. Importance of
SymmetrySymmetry is found everywhere in nature and is also one of the
most prevalent themes in art, architecture, and design-in
cultures all over the world and throughout human history.
The tool that he developed to understand symmetry, namely
group theory, has been used by mathematics ever since to
define, study, and even create symmetry.
Symmetry is certainly one of the most powerful and pervasive
concepts in mathematics.
In the Elements, euclid
exploited symmetry from the
very first proposition to make
his proofs clear and
straightforward. Recognizing
the symmetry that exists
among the roots of an
equation, Galois was able to
solve a centuries old
problem.

7. What is Line of
Symmetry?
The "Line of Symmetry" (shown here as a black line) is the
imaginary line where we could fold the image and have both
halves match exactly.

8. The Line of Symmetry
The dotted line shows the line of
symmetry
To find the lines of symmetry for an object, fold the figure in half. If the
two sides match, then the fold is a line of symmetry.
A line of symmetry can be a vertical
line, a horizontal line, or a diagonal
line.

9. Symmetry in
NatureMathematics is all around us. As we discover
more and more about our environment and
our surroundings we see that nature can be
described mathematically.
The beauty of a flower, the majesty of a tree,
even the rocks upon which we walk can
exhibit nature's sense of symmetry.
Although there are other examples to be
found in crystallography or even at a
microscopic level of nature, we have chosen
representations within objects in our field of
view that exhibit many different types of
symmetry.
It seems that everywhere we look now our
eyes are drawn first to the patterns of
symmetry that exist, and that the object itself
is a secondary consideration.

10. Symmetry in
Nature

11. Natural Symmetric
ObjectThe dotted line shows the line of symmetry.
Symmetry exists all around us. If we look around, we will find
plenty of examples of symmetrical things: our body, the
buildings, pet like cats and dogs, shapes appearing on the
screen, etc.
1.Symmetry In Flower : Sunflower exhibits radial symmetry and
also numerical symmetry which is called as Fibonacci sequence.
2. Symmetry In Birds: The peacock is one example of a beautiful
bird attractive symmetrical tail .
Following are few examples of symmetry in
daily life:-

12. Natural Symmetric object
The dotted line shows the line of symmetry.
3.Symmetry In Fruits and Vegetables: Broccoli and oranges
are the vegetable and fruit which displays symmetry. It can be
divided
into equal fraction and each part is similar.
4.Symmetry in Natural Scenes: Snowflakes are symmetrical
beautiful in nature. It has six fold radial symmetry.
Honeycombs are another symmetrical object which a good
example for hexagon figure.

13. Thank You