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symmetry

translation, reflection, rotation

line of symmetry

reflectional symmetry

definition: There is a rigid motion that allows the figure to…

What are 3 rigid motions?

What are the red lines?

definition: The figure can be mapped onto itself through a li…

symmetry

definition: There is a rigid motion that allows the figure to…

translation, reflection, rotation

What are 3 rigid motions?

symmetry

translation, reflection, rotation

line of symmetry

reflectional symmetry

definition: There is a rigid motion that allows the figure to…

What are 3 rigid motions?

What are the red lines?

definition: The figure can be mapped onto itself through a li…

symmetry

definition: There is a rigid motion that allows the figure to…

translation, reflection, rotation

What are 3 rigid motions?

center of rotation

line symmetry

point symmetry

rotational symmetry

Fixed point about which a rotation occurs.

Type of symmetry where the figure is the image of itself unde…

Every point on the figure is the image of itself under a rota…

Type of symmetry where the figure is the image of itself unde…

center of rotation

Fixed point about which a rotation occurs.

line symmetry

Type of symmetry where the figure is the image of itself unde…

Symmetry

Asymmetry

Radical Symmetry

Bilateral Symmetry

arrangement of body parts around an axis

body part can't be divided into similar sections

body parts are arranged around a central point

body can be divided into equal halves

Symmetry

arrangement of body parts around an axis

Asymmetry

body part can't be divided into similar sections

Enantiomorphic pair

Reflection

Why study symmetry and crystallography?

Center of symmetry (inversion)

A mirror image

Symmetry w/ respect to a mirror plane

To understand:... Hardness, velocity of light, cleavage, rate of…

Draw imaginary lines from every point in the object through a…

Enantiomorphic pair

A mirror image

Reflection

Symmetry w/ respect to a mirror plane

line symmetry

rotational symmetry

line of symmetry

dimensions

What a figure has if it can be folded about a line so that it…

can be turned about a central point and still look the same i…

divides a figure into halves; are the mirror images of each o…

measurement in length, width, and thickness

line symmetry

What a figure has if it can be folded about a line so that it…

rotational symmetry

can be turned about a central point and still look the same i…

TESSELLATION

TRANSLATION SYMMETRY

ROTATION

TRANSFORMATION

A DESIGN THAT COVERS A SURFACE WITHOUT GAPS OR OVERLAPS AND C…

WHEN YOU CAN SLIDE A DESIGN TO A POSITION IN WHICH IT LOOKS T…

A TRANSFORMATION THAT TURNS A FIGURE COUNTERCLOCKWISE ABOUT A…

A GEOMETRIC OPERATION THAT RELATES EACH POINT OF A FIGURE TO…

TESSELLATION

A DESIGN THAT COVERS A SURFACE WITHOUT GAPS OR OVERLAPS AND C…

TRANSLATION SYMMETRY

WHEN YOU CAN SLIDE A DESIGN TO A POSITION IN WHICH IT LOOKS T…

Symmetry

transformation

itself

point

_________ exists when a transformation maps a figure into its…

Symmetry exists when a ____________ maps a figure into itself.

Symmetry exists when a transformation maps a figure into ____…

a 180 degree rotation about ______ maps a figure into itself…

Symmetry

_________ exists when a transformation maps a figure into its…

transformation

Symmetry exists when a ____________ maps a figure into itself.

Zygote

Blastula

Gastrula

Endoderm

The sperm and the egg create a fertilized egg

Cells that form a fluid filled ball of cells

single-layered blastula is reorganized into a trilaminar

the innermost layer of cells or tissue of an embryo in early…

Zygote

The sperm and the egg create a fertilized egg

Blastula

Cells that form a fluid filled ball of cells

Congruent

Reflection

Line Symmetry

Rotational Symmetry

Having the same size and shape

A movement of a figure to a new position by flipping the figu…

What a figure has if it can be folded about a line so that it…

What a figure has it it can be turned about a central point a…

Congruent

Having the same size and shape

Reflection

A movement of a figure to a new position by flipping the figu…

symmetry

line symmetry

rotational symmetry

translation symmetry

a figure has this if there is a transformation of the figure…

figure that can be reflected across a line so that the image…

a figure has this if it can be rotated about a point by a ang…

a figure has this if it can be translated along a vector so t…

symmetry

a figure has this if there is a transformation of the figure…

line symmetry

figure that can be reflected across a line so that the image…

Bilateral symmetry

Radial symmetry

Asymmetry

Ectotherm (cold blooded)

2 alike sides

organized around a center point like a BIcycle

no alike sides

animals that have a body temperature that changes with the te…

Bilateral symmetry

2 alike sides

Radial symmetry

organized around a center point like a BIcycle

transformation

translation

rotation

center of rotation

the movement of geometric figures

slides a figure horizontally or vertically and matches point…

a transformation the turns a figure about a fixed point and m…

the point around a figure is rotated

transformation

the movement of geometric figures

translation

slides a figure horizontally or vertically and matches point…

Reflection Symmetry

Rotation Symmetry

Translation Symmetry

Line of Symmetry

A shape with reflection symmetry has two halves that are mirr…

A shape has rotation symmetry if it can be rotated less than…

A figure has translation symmetry if it can be moved along a…

A line that divides a figure into two halves that are mirror…

Reflection Symmetry

A shape with reflection symmetry has two halves that are mirr…

Rotation Symmetry

A shape has rotation symmetry if it can be rotated less than…

symmetry

translation, reflection, rotation, and…

line of symmetry

reflectional symmetry

definition: There is a rigid motion that allows the figure to…

What are 4 rigid motions?

What are the red lines?

definition: The figure can be mapped onto itself through a li…

symmetry

definition: There is a rigid motion that allows the figure to…

translation, reflection, rotation, and…

What are 4 rigid motions?

Symmetry

Translation

Transformation

Rotation

The correspondence of the form and arrangement of elements or…

Where every point is the same distance from the central line…

Means moving. Without rotating, resizing or anything else jus…

Means turning around a center. The distance from the center t…

Symmetry

The correspondence of the form and arrangement of elements or…

Translation

Where every point is the same distance from the central line…

Which type(s) of symmetry does the upp…

Which type of symmetry is shown by the…

What type(s) of symmetry is/are shown…

Which of the following three-dimension…

reflectional and point symmetry

reflectional symmetry

reflectional and rotational symmetry

a rolling pin

Which type(s) of symmetry does the upp…

reflectional and point symmetry

Which type of symmetry is shown by the…

reflectional symmetry

Combinations of symmetry operations are

An operation can be undone by its

Point Group Cs Symmetry Elements

Ci symmetry elements

associative

inverse operation

E, one σ plane

E, one (principal) n-fold axis

Combinations of symmetry operations are

associative

An operation can be undone by its

inverse operation

symmetry

Proper

improper

Bounded

a rigid motion of the plane that leaves the object apparently…

preserves orientation- after the motion is applied an image o…

reserves orientation meaning it turns a right hand into a lef…

fully contained in some square in a plane, otherwise called u…

symmetry

a rigid motion of the plane that leaves the object apparently…

Proper

preserves orientation- after the motion is applied an image o…

Use of color

Symmetrical balancr

Assymmetrical balancr

Asymmetrical balance

False with regard to a work of art

Most formal type of balance

Features unlike objects on either side of an imaginary line

Type of balance illustrated here?(woman in yellow and blue)

Use of color

False with regard to a work of art

Symmetrical balancr

Most formal type of balance

Motif

Operation

Element

2D Rotation

the fundamental part of symmetric design that can create the…

the act that reproduces the motif to create the pattern

a point of reference about which symmetry operation can take…

2-fold/3-fold/4-fold/6-fold

Motif

the fundamental part of symmetric design that can create the…

Operation

the act that reproduces the motif to create the pattern

asymmetrical

bi -lateral symmetry

radial symmetry

classification

animals with no body plan or symmetry

animals whose bodies are symmetrical or mirror imaged.

animals that have more than one way to cut them mirror imaged…

Assignment of objects or people to categories on the basis of…

asymmetrical

animals with no body plan or symmetry

bi -lateral symmetry

animals whose bodies are symmetrical or mirror imaged.

Isomorphism

Rigid Equivalence Theorem

Rigid Equivalence

Da Vinci's Theorem

One-to-one matching between two groups' members that translat…

If true for 2 objects, then their symmetry groups are isomorp…

True for 2 objects in the plane if there exists a rigid motio…

The symmetry group of any bounded object in the plane is eith…

Isomorphism

One-to-one matching between two groups' members that translat…

Rigid Equivalence Theorem

If true for 2 objects, then their symmetry groups are isomorp…

symmetry

reflectional symmetry

line of symmetry

criteria for lines of symmetry

having the same shape, size, and position on both sides of a…

A plane figure has reflectional symmetry if its reflection im…

a line that divides a figure into two halves that are mirror…

1. When crossing from angle to angle, it must be an angle bis…

symmetry

having the same shape, size, and position on both sides of a…

reflectional symmetry

A plane figure has reflectional symmetry if its reflection im…

Symmetry

Translational symmetry (2D)

Translational symmetry (3D)

3 basic symmetry operations

Repetition of a pattern component to produce the whole pattern.

The repetition of nodes from one vector to another to create…

In 3D the repetition of the vectors creates a space lattice i…

Rotations... Mirrors... Inversions

Symmetry

Repetition of a pattern component to produce the whole pattern.

Translational symmetry (2D)

The repetition of nodes from one vector to another to create…

Symmetry

Tawdry

Ambulatory

Idolatry

Exact corrospondence of form on opposite sides of dividing li…

Gaudy and cheap in appearance or nature

Of or for walking capable of walking

Blind or excessive.

Symmetry

Exact corrospondence of form on opposite sides of dividing li…

Tawdry

Gaudy and cheap in appearance or nature

radial symmetry

bilateral symmetry

"median sagittal" plane

sagittal plane, what is it also known…

circular, no matter where you cut it is symmetrical

two sides that match

cut straight down the middle, between eyes kind of middle

cut straight down the middle, longitudinal

radial symmetry

circular, no matter where you cut it is symmetrical

bilateral symmetry

two sides that match

TESSELLATION

TRANSLATION SYMMETRY

ROTATION

BASIC DESIGN ELEMENT

A DESIGN THAT COVERS A SURFACE WITHOUT GAPS OR OVERLAPS AND C…

WHEN YOU CAN SLIDE A DESIGN TO A POSITION IN WHICH IT LOOKS T…

A TRANSFORMATION THAT TURNS A FIGURE COUNTERCLOCKWISE ABOUT A…

PART OF A DESIGN THAT, WHEN TRANSFORMED USING AT LEAST ONE TY…

TESSELLATION

A DESIGN THAT COVERS A SURFACE WITHOUT GAPS OR OVERLAPS AND C…

TRANSLATION SYMMETRY

WHEN YOU CAN SLIDE A DESIGN TO A POSITION IN WHICH IT LOOKS T…

What is a symmetry operation?

Types of symmetry element

The identity, E

Axis of symmetry, Cₙ

an action which, when performed on an object results in the o…

the identity, axis of symmetry, mirror plane, centre of symme…

operation of "doing nothing", all molecules posses it

rotation by 360/n about this axis

What is a symmetry operation?

an action which, when performed on an object results in the o…

Types of symmetry element

the identity, axis of symmetry, mirror plane, centre of symme…

Reflection Symmetry

Rotation Symmetry

Translation Symmetry

Line of Symmetry

A shape with reflection symmetry has two halves that are mirr…

A shape has rotation symmetry if it can be rotated less than…

A figure has translation symmetry if it can be moved along a…

A line that divides a figure into two halves that are mirror…

Reflection Symmetry

A shape with reflection symmetry has two halves that are mirr…

Rotation Symmetry

A shape has rotation symmetry if it can be rotated less than…

Symmetry

Three types of symmetry

Reflection symmetry

Examples of reflection symmetry

A rigid motion that gives an image that is the same shape as…

Rotational, point, reflection

-A type of rigid motion for a 2-D shape (known as line symmet…

-flat shapes in nature... -nature often also uses symmetry

Symmetry

A rigid motion that gives an image that is the same shape as…

Three types of symmetry

Rotational, point, reflection

Symmetry in chemistry

Symmetry element

Group theory

Closed set

And object is unchanged after a transformation or operation

Point, line, or plane with respect to which a symmetry operat…

A branch of algebra that requires the set of symmetry element…

The result of two or more successive symmetry operations must…

Symmetry in chemistry

And object is unchanged after a transformation or operation

Symmetry element

Point, line, or plane with respect to which a symmetry operat…

max number of lines of symmetry

regular polygon always has the number…

rotational symmetry

regular polygon angle of rotation

number of sides

sides

when a figure looks the same under a rotation

360/number of sides

max number of lines of symmetry

number of sides

regular polygon always has the number…

sides