Studied by 0 people
Looks like no one added any tags here yet for you.
Transformation
process which shifts points of the plane to possibly new locations in the plane
Isometries
transformations which leave the dimensions of the object and its image unchanged
Translation
moves a shape in a given direction
Reflection
getting a mirror image
Rotation
has a point and an angle that tells where and how far the movement is made
Dilation
changes the size of an object
Glide Reflection
combination of reflection and translation
design
a figure with at least one non-trivial symmetry
pattern
a design that has a translation symmetry
Rosette
finite groups of isometries which can contain just rotations and reflections
Cyclic
has n-fold rotational symmetry and no reflectional symmetry
Dihedral
has n-fold rotational symmetry and reflectional symmetry
Frieze
an infinitely long strip imprinted with a design given by a repeating motif
Frieze
has translational symmetry in one direction
Frieze
has at least the basic unit and a copy of it by translation
Wallpaper
covers the plane and can be mapped onto itself by translations in more than one direction
Wallpaper
must have at least the basic unit, one copy by translation, and a copy of these two by translation in a second direction
Wallpaper
must be at least two rows, each one at least two units long
Basic unit
smallest region of the plane such that the set of its images under translations of the pattern generates the whole pattern
Fundamental region
smallest region in the basic unit whose images under the full symmetry group of the pattern cover the plane
Motif
subset of a fundamental region which has no symmetry but which generates the whole pattern under the symmetry group of the pattern
Leonardo of Pisa
invented the Fibonacci sequence
Fibonacci sequence
outcome of a mathematical problem about rabbit breeding
Fibonacci sequence
the first two numbers are 1 and 1, and each subsequent number is the sum of the previous two
Golden ratio
Shapes proportioned according to this have long been considered aesthetically pleasing
Fractals
a never-ending pattern
Fractals
infinitely complex patterns that are self-similar across different scales
Fractals
created by repeating a simple process over and over in an ongoing feedback loop
Fractals
involves symmetry of magnification
Benoit Mandelbrot
coined the word fractal
Note 
Flashcard (80)