GEOMETRIC DESIGNS Flashcards
It changes the size, shape, or position of a figure and creates a new figure
TRANSFORMATION
An isometry formed by combining two isometries such as reflection and translation.
GLIDE REFLECTION
It is a transformation which is determined by a vector.
TRANSLATION
This pattern consists of taking a motif or an element and rotating or reflecting the element.
ROSETTE PATTERN
A 5-fold rotational symmetry is mapped by a rotation angle of ____ onto itself.
72 degrees
A 9-fold rotational symmetry is mapped by a rotation angle of ____ onto itself.
40 degrees
It is an infinitely long strip imprinted with a design given by a repeating motif.
FRIEZE PATTERN
It is also known as flip transformation.
REFLECTION
What are the rigid transformations?
REFLECTION
ROTATION
TRANSLATION
It is a transformation which changes the orientation of a geometric shape through a center and an angle.
ROTATION
It requires a line of symmetry.
REFLECTION
It consists of 60 degrees, 120 degrees, 90 degrees and 180 degrees
WALLPAPER PATTERN
Operation of Frieze pattern
180 degrees
An isometry is a
TRANSFORMATION
a function which changes the position, orientation, and possible the size of a geometric shape.
TRANSFORMATION
Transformations which leave the dimensions of the object and its image unchanged are called
RIGID TRANSFORMATIONS / ISOMETRIC TRANSFORMATIONS / ISOMETRIES
It means “same measurement”
ISOMETRY
A/ an _______________________is a mapping that preserves distance (and therefore shape).
isometry of the plane
a product of a reflection and a translation whose direction is parallel with the line of reflection.
GLIDE TRANSFORMATION
A glide reflection is determined by a
REFLECTION LINE AND PARALLEL LINE
Every motion of the plane is one of these transformations: a translation, a rotation, a reflection or a glide transformation
CHASLE’S THEOREM
is the set of all isometries that map the figure onto itself.
SYMMETRY GROUP
a figure with at least one non-trivial symmetry.
DESIGN
a design that has a translation symmetry.
PATTERN
has symmetry if there is an isometry of the plane that preserves it.
PLAIN PATTERN
The symmetry group of a frieze pattern necessarily contains
TRANSLATIONS IN ONE DIRECTION
a horizontal reflection
a vertical reflection
a rotation of 180˚ about some point in the design
a glide reflection
FRIEZE PATTERN
