Patterns And Symmetries Flashcards
Any object drawn on a plane
Motif
Repetitions of a motif
Pattern
Turn, flip, or slide of any figure
Transformation
Creates an image that is congruent to the original figure
Isometry
Four operations of transformation
Translation
Rotation
Reflection
Dilation
Slides a figure along a straight line path
Translation
Turns a figure about a fixed point
Rotation
Flips a figure across a line
Reflection
Combination of a translation and reflection
Glide reflection
Result of stretching or shrinking of the motif.
The figure is no longer congruent to the original
Dilation
Composition of isometries in the plane
Symmetry
Type of symmetry that only has reflection and rotations
No translations or glide reflections
Rosette patterns
Type of symmetry that has a point at the center of the pattern that is left in place by every symmetry
Rosette patterns
A motif not restricted by a center point and can be moved in any direction or flip
Frieze patterns
7 Frieze patterns
F1 Hop
F2 Step
F3 Sidle
F4 Spinning hop
F5 Spinning sidle
F6 Jump
F7 Spinning jump
> > > >
Hop
> < > < > <
Sidle
> > > > < < < <
Spinning hop
<. .> <. .>
<. .>
Spinning sidle
.> <. .> <. .> <.
.> <. .> <. .> <.
Spinning jump
This type of symmetry can only have reflection and and glide reflection symmetry
Wallpaper groups
We add translation symmetry in a second independent direction
Wallpaper groups
Frieze pattern that has the same motif TRANSLATED horizontally
Hop
Frieze pattern that contains TRANSLATION and GLIDE REFLECTION
Step
Frieze pattern that contains TRANSLATION and VERTICAL SYMMETRY
Sidle
Frieze pattern that contains TRANSLATION and ROTATION
Spinning Hop
Frieze pattern that contains TRANSLATION, GLIDE REFLECTION, and ROTATION
Spinning Sidle
Frieze pattern that contains TRANSLATION and HORIZONTAL REFLECTION
Jump
Frieze pattern that contains all symmetries
Spinning jump
.> .> .> .>
.> .> .> .>
Jump
.> .> .> .>
.> .> .> .>
Step