Sakshi MehtaX E15

The universe is built on a plan of the profound symmetry of which is Somehow present in the inner structure of the intellect.

-Paul Valery

WHAT DOES SYMMETRY WHAT DOES SYMMETRY EVEN MEANEVEN MEAN

SymmetricalSymmetrical - characterized by or exhibiting - characterized by or exhibiting symmetrysymmetry; well-proportioned, as a body or whole; ; well-proportioned, as a body or whole; regular in form or arrangement of corresponding regular in form or arrangement of corresponding parts.parts.

Symmetrical = Same on both sidesSymmetrical = Same on both sides Symmetries preserve distances, angles, sizes, and Symmetries preserve distances, angles, sizes, and

shapesshapes

BASIC TYPES OF SYMMETRY

Vertical Line

Horizontal Line

Line Symmetry: when one half of an image is the mirror image of the other half.

WHERE CAN WE FIND SYMMETRY?WHERE CAN WE FIND SYMMETRY?• Symmetry can be found in art, nature, sports, math, and even in

the mirror.

THE EUCLIDEAN PLANETHE EUCLIDEAN PLANE

Types of symmetry that transform the plane the object is on

Four main types of Euclidean Planes Translation Rotation Reflection Glide Reflection

Similar concepts can be found in 3-D or spatial symmetries also.

TRANSLATIONTRANSLATION:: To translate an object means to move it To translate an object means to move it

without rotating or reflecting it. without rotating or reflecting it. Every translation has a direction and a Every translation has a direction and a

distance.distance.

Example of Translation:

If a family of ducks all lined up in a row is moved forward or back by one, two, or more ducks they have translated on the plane. This translation does not change the appearance of the procession, it just moves it on the plane.

ROTATIONROTATION:

To rotate an object means to turn it around. Every rotation has a center and an angle.

Before Rotation

After Rotation

Center

[Angle 90˚]

Rotational Symmetry:Rotational Symmetry: The kaleidoscope image of a flower below as well as

the wheel are both examples of rotational symmetry. They can rotate around the center point up to 360 degrees and still look exactly the same.

What other items can you think of that have rotational symmetry? You might be surprised how many there are.

The object does not have to rotate 360 degrees to be rotational symmetry, as long as it has a center that it rotates around and an angle or amount of rotation, it is considered rotational.

REFLECTIONREFLECTION:

To reflect an object means to produce its mirror image. Every reflection has a mirror line.

A reflection of a “B" is a backwards “B".

Mirror Line

Reflection:Reflection:Most common form of symmetryReflection symmetry is formed when any

image is reflected or a mirror of itself on either side of the mirror line.

The Taj Mahal has both horizontal and vertical reflection symmetry.

The Vitruvian Man by Leonardo DaVinci has vertical reflection symmetry.

GLIDE REFLECTION:GLIDE REFLECTION: A glide reflection combines a reflection with a

translation along the direction of the mirror line. Glide reflections are the only type of symmetry

that involve more than one step.

[Before Glide Reflection]

[After Glide Reflection]

Mirror Line

SYMMETRY IN 2D SHAPES:SYMMETRY IN 2D SHAPES:

In shapes such as the triangle, square, pentagon, etc. there are approximately the same number lines of symmetry as there are sides of the shape. To test this cut out shapes and fold them to find how many lines of symmetry there really are.

Clip art and Animated Graphics. Clip art and Animated Graphics. http://www.adrianbruce.com/Symmetry/

Clip Art. Microsoft Office Clip Art GalleryClip Art. Microsoft Office Clip Art Gallery

"Euclidean plane isometry." "Euclidean plane isometry." Wikipedia, The Free Wikipedia, The Free EncyclopediaEncyclopedia. 17 Mar 2008, 16:40 UTC. Wikimedia . 17 Mar 2008, 16:40 UTC. Wikimedia Foundation, Inc. 12 May 2008 <Foundation, Inc. 12 May 2008 <http://en.wikipedia.org/w/index.php?title=Euclidean_plane_isometry&oldid=198885950>.>.