patterns and symmetries Flashcards
it is ideal to stat with the concept of motif
transformation and isometries
a motif is “any non-empty plane set”
according to Grunbaum and Shephard, 1987
a pattern can be described as “____”
repetitions of a motif in the plane
each rotation of a figure is a ____
isometry
“the image of the basic motif under the additional no. of rotation is a pattern”
renee scott 2008
this is not a symmetry as it either shrinks or enlarges a figure
dilation
what is the difference between transformation and isometries
transformation:
changes the size, shape, position of a figure = create a new figure
geometry transoformation. two types are rigid (isometry) and nonrigid
isometry
change the rotation, translation and reflection = does not change the size or shape of figure
what are the types of transformations
translation
rotation
reflection
dilation
initial image =
transformed object =
initial image = pre-image
transformed object = image
briefly explain the different type of transformations
translation: moves object a certain distance (object is not altered)
reflection: mirror image
rotation: turns figure abt a fixed point called the center of rotation (clockwise and counterclockwise)
dilation: changes the SIZE of figure (smaller/ larger) but the SHAPE remains the same
naming of frieze patterns is attributed to ___
john conway, an english mathematician
John Conway is active in ____, ____, ____, ____ and____
finite theory
knot theory
number theory
combinational game theory
coding theory
these are patterns that repeat in a straight vertical or horizontal line
frieze pattern
where can frieze patterns be found
architecture
fabrics
wallpaper boarder
what are the 7 frieze patterns
hop
step
sidle
spinning hop
spinning sidle
jump
spinning jump
hop
translation only
step
translation and reflection (gidle reflection)
sidle
translation and vertical reflection
spinning hop
translation and rotation
spinning sidle
translation, gidle, reflection and rotation
jump
translation
horizontal reflection symmetry
spinning jump
all symmetries (translation, horizontal and vertical reflection and rotation )
how many different plane symmetry groups in wallpaper groups
17
symmetria means
to measure tgt