Lesson 4 Flashcards
a repeated arrangement
of numbers, shapes, colors and so
on. The Pattern can be related to
any type of event or object
Pattern
a regularity in the world, in
human-made design, or in abstract
ideas
Pattern
Sometimes, patterns are also known
as a _________. Patterns are ________or
_________in numbers.
Sequence
Finite
Infinite
a kind of pattern formed of geometric shapes
and typically repeated like a wallpaper
design
A geometric pattern
Defined as one shape is
exactly like the other shape when it is
moved, rotated, or flipped
Symmetries
Symmetry in everyday language refers
to a sense of harmonious and beautiful
__________and _________.
proportion
balance
used to refer to an object that is invariant
under some transformations; including
translation, reflection, rotation or
scaling
Symmetries
any non-empty plane set
Any object drawn in a plane
A motif
The rotation of a motif in a fixed angle about a fixed point
Isometry
changes the size, shape, or position of a figure and creates a new figure
A transformation
either rigid or non-rigid; another word for a rigid
transformation is “isometry”
geometry transformation
is not an isometry since it either shrinks or enlarges a figure
Dilation
The initial object to be transformed is
called _______and the transformed object is
called _______
Pre-image
Image
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 in which the figure or object is mirror image of the other.
REFLECTION
a transformation that changes the size of a figure. It can
become larger or smaller, but the shape remains the same.
Dilation
It is a transformation that turns a figure about a fixed point called the center of rotation. Rotations can be done clockwise or counterclockwise
ROTATION
Translation and reflection can be combined to yield an effect shown below.
GLIDED REFLECTION
attributed to John Conway, an English mathematician who is active in finite theory, knot theory, number theory, combinatorial game theory and coding theory
FRIEZE PATTERNS
patterns that repeat in a straight vertical or
horizontal line. Found in architecture, fabrics, and
wallpaper borders, just to name a few.
FRIEZE PATTERNS
A pattern which only involves translation
HOP
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 horizontal reflection symmetries.
JUMP
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 SIDLE
It contains all symmetries ( translation, horizontal and vertical reflection, and rotation)
SPINNING JUMP
If translation symmetry is added in a second, independent direction, one gets _____________.
wallpaper groups
Filipino Indigenous fabrics showcasing patterns and symmetries
FILIPINO ARTS
Symmetry comes from a Greek word __________meaning ‘to measure together’
symmetria
if an object is not symmetrical, it is
called ____________.
Asymmetric.
in which an object has two sides that
are mirror images of each other.
Bilateral symmetry
Subjects that use symmetry and patterns
Math, Chemistry, Biology and Human anatomy
The word tessellation comes from Latin
word _________
Tessera
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
Is an edge-to-edge tessellation,
but the order or arrangement of
polygons at each vertex is not the
same
Demi-Regular Tessellation
The tessellation must ____a
floor (that goes on forever)
with no ________or ________
TILE
Overlaps or Gaps
Tessellations are regular
tessellations of two or more
different polygons around a
vertex which has the same
arrangement of polygons.
Archimedean (Semi-Regular Tessellation)
The tiles must be the same
regular _______.
Polygons.
he function which iterates a figure to make it smaller and
smaller or bigger and bigger using a scaling factor is called
FRACTALS
means repeating a process over and over. In
mathematics, iteration means repeating a function over and
over.
Iteration
a method for generating fractals involving a large number of calculations of a simple formula
The Iterative Function System (IFS) i
