patterns and symmetries Flashcards

1
Q

it is ideal to stat with the concept of motif

A

transformation and isometries

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2
Q

a motif is “any non-empty plane set”

A

according to Grunbaum and Shephard, 1987

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3
Q

a pattern can be described as “____”

A

repetitions of a motif in the plane

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4
Q

each rotation of a figure is a ____

A

isometry

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5
Q

“the image of the basic motif under the additional no. of rotation is a pattern”

A

renee scott 2008

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6
Q

this is not a symmetry as it either shrinks or enlarges a figure

A

dilation

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7
Q

what is the difference between transformation and isometries

A

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

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8
Q

what are the types of transformations

A

translation
rotation
reflection
dilation

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9
Q

initial image =
transformed object =

A

initial image = pre-image
transformed object = image

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10
Q

briefly explain the different type of transformations

A

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

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11
Q

naming of frieze patterns is attributed to ___

A

john conway, an english mathematician

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12
Q

John Conway is active in ____, ____, ____, ____ and____

A

finite theory
knot theory
number theory
combinational game theory
coding theory

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13
Q

these are patterns that repeat in a straight vertical or horizontal line

A

frieze pattern

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14
Q

where can frieze patterns be found

A

architecture
fabrics
wallpaper boarder

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15
Q

what are the 7 frieze patterns

A

hop
step
sidle
spinning hop
spinning sidle
jump
spinning jump

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16
Q

hop

A

translation only

17
Q

step

A

translation and reflection (gidle reflection)

18
Q

sidle

A

translation and vertical reflection

19
Q

spinning hop

A

translation and rotation

20
Q

spinning sidle

A

translation, gidle, reflection and rotation

21
Q

jump

A

translation
horizontal reflection symmetry

22
Q

spinning jump

A

all symmetries (translation, horizontal and vertical reflection and rotation )

23
Q

how many different plane symmetry groups in wallpaper groups

24
Q

symmetria means

A

to measure tgt

25
it is widely used in the study of geometry
symmetry
26
how does 2 object become symmetrical
have same size and shape with one object having a diff orientation from the first
27
an object is not symmetrical
asymmetric
28
symmetry and patterns appear in ____ and ____
chemistry biology
29
briefly explain the 2 types of symmetry
bilateral symmetry: object that has 2 sides that are mirror images of e/o radial symmetry: center point and numerous lines of symmetry could be drawn (example: spiderweb)
30
Patterns in living things are explained by the …. (example)
Biological process of natural and sexual selection (bacterial population growth)
31
A pattern covering a plane by fitting tgt replicas of the same basic shape
Tessellation
32
The Latin word tessera means
A square table or die used in gambling
33
Semi-regular tessellations is aka
Archimedean tessellations
34
Briefly explain the different types of tessellations
1. Regular tessellations Made up of congruent regular polygons (tessellations must tile the floor w/o overlapping & and must be the same regular polygons) 2. Semi-regular tessellations 2 or more diff polygons arnd a vertex which has the same arrangement of polygons 3.Demi-regular tessellations Edge to edge tessellations. order of arrangement polygons at each vertex is not the same
35
The function which iterates a figure to make it smaller and smaller or bigger and bigger using a scaling factor
Fractals
36
means repeating a process over and over
Iteration
37
What is the special kind of iteration
Recursion
38
Explain Iterative function system
It is a method for generating fractals involving a large no.of calculations of a simple formula.