T5: Patterns and Symmetry Flashcards
a repeated arrangement of numbers, shapes, colors and so on
PATTERN
is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns
Geometric pattern
If the set of numbers are related to each other in a specific rule, then the rule or manner is called a __________
PATTERN
defined as one shape is exactly like the other shape when it is moved, rotated, or flipped
- Symmetry
any non-empty plane set
motif
repetitions of a motif in the plane
pattern
is the rotation of a motif in a fixed angle about a fixed point
isometry
is either rigid or non-rigid
geometry transformation
is not an isometry since it either shrinks or enlarges a figure
dilation
The initial object to be transformed is called
pre-image
the transformed object is called
image
TYPES OF TRANSFORMATIONS
- Translation
- Reflection
- Rotation
- Dilation
It is a transformation in which the figure or object is mirror image of the other
REFLECTION
A mathematical term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way
TRANSLATION
It is a transformation that turns a figure about a fixed point called the center of rotation
ROTATION
is a transformation that changes the size of a figure. It can become larger or smaller, but the shape remains the same
DILATION
Translation and reflection can be combined to yield an effect
GLIDED REFLECTION
an English mathematician who is active in finite theory, knot theory, number theory, combinatorial game theory and coding theory
John Conway
patterns that repeat in a straight vertical or horizontal line
FRIEZE PATTERNS
A pattern which only involves translation
HOP
DIFFERENT TYPES OF FRIEZE PATTERNS
- Hop
- Step
- Slide
- Spinning hop
- Spinning slide
- Jump
- Spinning jump
it is a combination of translation and reflection shown by the following figure. Conway also called it glide reflection symmetry
- STEP
The third consists of translation and vertical reflection symmetries
SLIDE
It contains translation and rotation (by half turn or rotation at 180o angle) symmetries
SPINNING HOP
It contains translation, glide, reflection and rotation (by a half-turn or rotation at 180o angle) symmetries
SPINNING SLIDE
It contains translation and horizontal reflection symmetries
JUMP
It contains all symmetries ( translation, horizontal and vertical reflection, and rotation)
SPINNING JUMP
If translation symmetry is added in a second, independent direction
WALLPAPER GROUPS
meaning ‘to measure together’
symmetria
TWO KINDS OF SYMMETRY
- Bilateral symmetry
- Radial symmetry
if an object is not symmetrical
asymmetric
in which an object has two sides that are mirror images of each other
Bilateral symmetry
this is where a center point and numerous lines of symmetry could be drawn
Radial symmetry
A pattern covering a plane by fitting together replicas of the same basic shape
TESSELLATION
a square tablet or die used in gambling
tessera
DIFFERENT TYPES OF TESSELLATIONS
- Regular Tessellation
- Semi-Regular Tessellation
- Demi-Regular Tessellation
A tessellation made up of congruent regular polygons which have the following properties:
o The tessellation must tile a floor (that goes on forever) with no overlaps or gaps.
o The tiles must be the same regular polygons.
REGULAR TESSELLATION
Also known as Archimedean Tessellations are regular tessellations of two or more different polygons around a vertex which has the same arrangement of polygons
SEMI-REGULAR TESSELLATION
Is an edge-to-edge tessellation, but the order or arrangement of polygons at each vertex is not the same.
DEMI-REGULAR TESSELLATION
The function which iterates a figure to make it smaller and smaller or bigger and bigger using a scaling factor
FRACTALS
means repeating a process over and over
ITERATION
is a method for generating fractals involving a large number of calculations of a simple formula
- The Iterative Function System (IFS)
is a special kind of iteration
- Recursion
