patterns and symmetries

Question 1

it is ideal to stat with the concept of motif

Answer 1

transformation and isometries

Question 2

a motif is “any non-empty plane set”

Answer 2

according to Grunbaum and Shephard, 1987

Question 3

a pattern can be described as “____”

Answer 3

repetitions of a motif in the plane

Question 4

each rotation of a figure is a ____

Answer 4

isometry

Question 5

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

Answer 5

renee scott 2008

Question 6

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

Answer 6

dilation

Question 7

what is the difference between transformation and isometries

Answer 7

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

Question 8

what are the types of transformations

Answer 8

translation
rotation
reflection
dilation

Question 9

initial image =
transformed object =

Answer 9

initial image = pre-image
transformed object = image

Question 10

briefly explain the different type of transformations

Answer 10

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

Question 11

naming of frieze patterns is attributed to ___

Answer 11

john conway, an english mathematician

Question 12

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

Answer 12

finite theory
knot theory
number theory
combinational game theory
coding theory

Question 13

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

Answer 13

frieze pattern

Question 14

where can frieze patterns be found

Answer 14

architecture
fabrics
wallpaper boarder

Question 15

what are the 7 frieze patterns

Answer 15

hop
step
sidle
spinning hop
spinning sidle
jump
spinning jump

Question 16

hop

Answer 16

translation only

Question 17

step

Answer 17

translation and reflection (gidle reflection)

Question 18

sidle

Answer 18

translation and vertical reflection

Question 19

spinning hop

Answer 19

translation and rotation

Question 20

spinning sidle

Answer 20

translation, gidle, reflection and rotation

Question 21

jump

Answer 21

translation
horizontal reflection symmetry

Question 22

spinning jump

Answer 22

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

Question 23

how many different plane symmetry groups in wallpaper groups

Answer 23

17

Question 24

symmetria means

Answer 24

to measure tgt

Question 25

it is widely used in the study of geometry

Answer 25

symmetry

Question 26

how does 2 object become symmetrical

Answer 26

have same size and shape
with one object having a diff orientation from the first

Question 27

an object is not symmetrical

Answer 27

asymmetric

Question 28

symmetry and patterns appear in ____ and ____

Answer 28

chemistry
biology

Question 29

briefly explain the 2 types of symmetry

Answer 29

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)

Question 30

Patterns in living things are explained by the …. (example)

Answer 30

Biological process of natural and sexual selection (bacterial population growth)

Question 31

A pattern covering a plane by fitting tgt replicas of the same basic shape

Answer 31

Tessellation

Question 32

The Latin word tessera means

Answer 32

A square table or die used in gambling

Question 33

Semi-regular tessellations is aka

Answer 33

Archimedean tessellations

Question 34

Briefly explain the different types of tessellations

Answer 34

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

Question 35

The function which iterates a figure to make it smaller and smaller or
bigger and bigger using a scaling factor

Answer 35

Fractals

Question 36

means repeating a process over and over

Answer 36

Iteration

Question 37

What is the special kind of iteration

Answer 37

Recursion

Question 38

Explain Iterative function system

Answer 38

It is a method for generating fractals involving a large no.of calculations of a simple formula.